PATENT DOCUMENT

Abstract:
A liquid crystal display device includes a display panel including row electrodes and column electrodes which cross the row electrodes. Display dots are formed at points where the column electrodes cross the row electrodes. A column electrode driver drives each of the column electrodes in accordance with display data to be displayed on the display dots. A waveform generator generates at least four different sets of waveforms. A row electrode driver drives the row electrodes by applying to the row electrodes respective voltages having respective ones of the waveforms in a selected one of the at least four different sets of waveforms, the selected one changing after each frame period. The display data is displayed on the display panel in accordance with the driving of the row electrodes by the row electrode driver and the driving of the column electrodes by the column electrode driver.

Full Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation of application Ser. No. 08/869,779 filed on Jun. 5, 1997, now U.S. Pat. No. 5,977,943, which is a division of application Ser. No. 08/340,485 filed on Nov. 14, 1994, now U.S. Pat. No. 5,638,088, which is a continuation of application Ser. No. 08/077,774 filed on Jun. 18, 1993, now abandoned. The contents of application Ser. Nos. 08/869,779, 08/340,485, and 08/077,774 are hereby incorporated herein by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method of driving liquid crystals and a display apparatus therefor, and in particular to a driving method of displaying STN (Super Twisted Nematic) liquid crystals with high contrast and a display apparatus therefor. 
     2. Description of the Related Art 
     As a conventional driving method of a liquid crystal display apparatus having a matrix structure, there is known a technique described in “Ultimate Limits for Matrix Addressing of RMS-Responding Liquid-Crystal Displays,” IEEE Transactions on Electron Devices, Vol. ED-26, No. 5, May 1979 (pp. 795-802) and “Active Addressing Method for High-Contrast Video-Rate STN Displays,” SID 92 DIGEST, pp. 228-231. According to this technique, each row electrode is provided with a voltage depending upon an orthogonal function, whereas each column electrode is provided with a voltage depending upon a function obtained as a sum of products of every display information of that column and a function of the scanning side. The driving method will hereafter be described in detail by referring to FIGS. 1 to  4 . 
     FIG. 1 shows the structure of a liquid crystal display panel having a matrix structure consisting of N rows by M columns. An intersection of a row electrode and a column electrode forms a dot D(i,j). A voltage represented by a function f(i) (i=1, 2, . . . N) is supplied to each of the N row electrodes. A voltage represented by a function g(j) (j=1, 2, . . . M) is supplied to each of the M column electrodes. U(i,j) denotes a voltage supplied to the dot D(i,j). The voltage U(i,j) is a difference between values of the voltage functions f(i) and g(j). In the ensuing description, voltage is normalized. FIG. 2 is a diagram showing an example of orthogonal function voltages supplied to row electrodes to drive STN liquid crystal displays. This example is generally used at the present time. Assuming now that the function f(i) is represented by FIG. 2, the functions f(i) and g(j) can be represented by equations (1) and (2), respectively. 
     
       
           f ( i )= FP·δ ( i,t )  (1)  
       
     
     
       
         
           
             
               
                 
                   
                     g 
                      
                     
                       ( 
                       j 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         N 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                        
                       
                           
                       
                        
                       
                         
                           P 
                            
                           
                             ( 
                             
                               i 
                               , 
                               j 
                             
                             ) 
                           
                         
                          
                         
                           f 
                            
                           
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     In the equations (1) and (2), δ(i,t) is 1 for i=t and 0 for i≠t. FP is a constant given by the following equation (3).              FP   =         N        N         2        (       N     -   1     )                   (   3   )                                
     P(i,j) denotes display information of the dot D(i,j). P(i,j) is −1 for a display-on state and 1 for a display-off state. By using equations (1), (2) and (3), the effective voltage U rms (i,j) applied to the dot D(i,j) at this time can be represented by the following equation (4).                        U   rms          (     i   ,   j     )       =              A2               =                  [         1   T            ∫   0   T              f        (   i   )       2                        t           +       1   T            ∫   0   T              g        (   j   )       2          2   T            ∫   0   T            f        (   i   )            g        (   j   )                          t                 ]       1   /   2                     (   4   )                                
     Letting T=N and rewriting (4) gives                  1   T            ∫   0   T              f        (   i   )       2                        t           =         1   N            ∑     t   =   1     N                       (       FP   ·   δ                     (     i   ,   t     )       )     2         =       N       2        (       N     -   1     )                   (   5   )                   1   T            ∫   0   T            g        (   j   )       2         =         1   N            ∑     t   =   1     N                       (       1     N                         ∑     i   =   1     N                       P        (     i   ,   j     )            f        (   i   )             )     2         =         1   N            ∑     t   =   1     N            [       1     N              ∑     i   =   1     N                       P        (     i   ,   j     )                  N        N         2        (       N     -   1     )           ·   δ                     (     i   ,   t     )           ]     2         =           1   N     ·     1   N     ·       N        N         2        (       N     -   1     )                  ∑     t   =   1     N                       [       ∑     t   =   1     N                       P        (     i   ,   j     )                     δ                   (     i   ,   t     )         ]     2         =         1   N                         N       2        (       N     -   1     )         ·   N       =       N       2        (       N     -   1     )                         (   6   )                   2   T            ∫   0   T            f        (   i   )            g        (   j   )                          t           =         2   N            ∑     t   =   1     N                       f        (   i   )              ∑     i   =   1     N                       1     N            P        (     i   ,   j     )            f        (   i   )                 =       2   N            ∑     t   =   1     N                           N        N         2        (       N     -   1     )           ·            δ                   (     i   ,   t     )                       ∑     i   =   1     N                       1     N                       P        (     i   ,   j     )                  N        N         2        (       N     -   1     )           ·   δ                     (     i   ,   t     )           =         2     N        N         ·       N        N         2        (       N     -   1     )         ·       ∑     t   =   1     N                     δ                   (     i   ,   t     )            ∑     i   =   1     N                       P        (     i   ,   j     )                     δ                   (     i   ,   t     )               =       2     2        (       N     -   1     )         ·     P        (     i   ,   j     )                               (   7   )                                
     From equations (5), (6) and (7), therefore, the effective voltage U rms (i,j) can be written as                        U   rms          (     i   ,   j     )       =                  [         N       2        (       N     -   1     )         +       N       2        (       N     -   1     )         -       2     2        (       N     -   1     )                         P        (     i   ,   j     )           ]       1   /   2                   =                  [         2        N         2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   /   2                     (   8   )                                
     Assuming that the dot D(i,j) is in the display-on state, P(i,j)=−1 and the effective voltage U rms (i,j) is represented by equation (9). Assuming that the dot D(i,j) is in the display-off state, P(i,j)=1 and the effective voltage U rms (i,j) is represented by equation (10).                  U   rms          (     i   ,   j     )       =         [         2        N         2        (       N     -   1     )         -       -   2       2        (       N     -   1     )           ]       1   2       =       [         N     +   1         N     -   1       ]       1   2                 (   9   )                   U   rms          (     i   ,   j     )       =         [         2        N         2        (       N     -   1     )         -     2     2        (       N     -   1     )           ]       1   2       =   1             (   10   )                                
     The voltage applied to the dot D(i,j) is (f(i)−g(j)) and has a waveform as shown in FIG. 3 on the basis of equations (1) and (2). In FIG. 3, S 1 , S 2  and S 3  are represented by the following equations.        S1   =                 N        N         2        (       N     -   1     )           +         N       2        (       N     -   1     )                   (   11   )               (       When                   D        (     i   ,   j     )         =     display                 on       )                                   N        N         2        (       N     -   1     )           -         N       2        (       N     -   1     )                                (   12   )                 (       When                   D        (     i   ,   j     )         =     display                 off       )                                                    S2   =         N       2        (       N     -   1     )                                (   13   )               S3   =     -         N       2        (       N     -   1     )                     (   14   )                                
     Assuming now that N=240, we get S 1 =12.1 (when D(i,j)=display on), S 1 =10.6 (when D(i,j)=display off), S 2 =0.73, and S 3 =−0.73. As a result, a large voltage is applied once (i=t) during one frame (i.e., a period of t=1 to N) and a low voltage is applied during the remaining intervals. In fast responding STN liquid crystal displays, the display luminance lowers while this low voltage is being applied. 
     As a driving method for avoiding this, a method described below has been proposed. FIG. 4 shows orthogonal functions called Walsh functions. In the example shown in FIG. 4, the number of divisions (time intervals) of the Walsh functions is 8. Assuming now that Walsh functions with the number of divisions being equivalent to T are used as the function f(i) of the voltage applied to row electrodes of the liquid crystal display panel of FIG. 1 and N Walsh functions are selected out of T Walsh functions (T≧N) and used as the function f(i), the effective voltage value U rms (i,j) of the dot D(i,j) will be is derived. 
     It is assumed that the functions f(i) and g(j) are represented by the following equations (15) and (16). 
     
       
           f ( i )= FP·W ( i,t )  (15)  
       
     
     
       
         
           
             
               
                 
                   
                     g 
                      
                     
                       ( 
                       j 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         N 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                        
                       
                           
                       
                        
                       
                         
                           P 
                            
                           
                             ( 
                             
                               i 
                               , 
                               j 
                             
                             ) 
                           
                         
                          
                         
                           f 
                            
                           
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     In these equations, W(i,t) is a Walsh function and has a value of 1 or 31 1. FP is a constant indicated by equation (17).              FP   =         N       2        (       N     -   1     )                   (   17   )                                
     In equation (4),                        1   T            ∫   0   T              f        (   i   )       2                        t           =                  1   T                       ∑     t   =   1     T                       (     FP   ·     W        (     i   ,   t     )         )     2                     =                  1   T          {         FP   2            W        (     i   ,   1     )       2       +       FP   2            W        (     i   ,   2     )       2       +   …   +       FP   2            W        (     i   ,   T     )       2         }                   =                    1   T     ·     FP   2     ·       T        (     ±   1     )       2       =       FP   2     =       N       2        (       N     -   1     )                           (   18   )                         1   T            ∫   0   T              g        (   j   )       2                        t           =                  1   T            ∑     t   =   1     T            (       1     N              ∑     i   =   1     N                         P        (     i   ,   j     )       ·         N       2        (       N     -   1     )                  W        (     i   ,   t     )             )     2                     =                    1   T     ·     1   N     ·       N       2        (       N     -   1     )                          ∑       t   =   1     T            ∑     i   =   1     N            (       P        (     i   ,   j     )       ·     W        (     i   ,   t     )         )     2                     =                    1   T     ·     1   N     ·       N       2        (       N     -   1     )                             ∑     t   =   1     T          {           P        (     1   ,   j     )       2            W        (     1   ,   t     )       2       +   …   +                                          P        (     N   ,   j     )       2            W        (     N   ,   t     )       2       }                 =                      1   T     ·     1   N                           N       2        (       N     -   1     )         ·   T   ·   N       =       N       2        (       N     -   1     )                         (   19   )                         2   T            ∫   0   T            f        (   i   )            g        (   j   )                          t           =                  2   T            ∑     t   =   1     T                       FP   ·     W        (     i   ,   t     )                ∑     i   =   1     N            1     N                       P        (     i   ,   j     )            FP   ·     W        (     i   ,   t     )                               =                    2   T     ·     1     N       ·       N       2        (       N     -   1     )                          ∑       t   =   1     T          W        (     i   ,   t     )              ∑     i   =   1     N            P        (     i   ,   j     )            W        (     i   ,   t     )                         =                    2   T     ·     1     2        (       N     -   1     )                          ∑       t   =   1     T          P        (     i   ,   j     )              W        (     i   ,   t     )       2                   =                  2        P        (     i   ,   j     )           2        (       N     -   1     )                       (   20   )                                
     The effective voltage U rms (i,j) of the dot D(i,j) becomes                        U   rms          (     i   ,   j     )       =                  [         N       2        (       N     -   1     )         +       N       2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   2                   =                  [         2        N         2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   2                     (   21   )                                
     As evident from the results heretofore described, the effective voltage U rms (i,j) obtained when the Walsh function is used becomes identical with equation (8). U rms (i,j) has a value of equation (9) for the display-on state, whereas U rms (i,j) has a value of equation (10) for the display-off state. 
     In this case, g(j) of equation (16) is rewritten as                      g        (   j   )       =                  1     N              ∑     i   =   j     N                       P        (     i   ,   j     )            f        (   i   )                         =                  FP     N                       (       2      D     -   N     )                     (   22   )                                
     where D is the number of coincident values of P(i,j) with respect to W(i,t) with i=1 to N in the j-th column (P(i,j) assumes a value of ±1, and W(i,t) assumes a value of ±1). At this time, the value of D has a normal distribution represented by the following equation.                P        (   D   )       ≃         2     π                 N                         exp              [       -       (       2      D     -   N     )     2         2      N       ]               (   23   )                                
     As indicated by equation (23), D has a normal distribution around N/2. Therefore, equation (22) also has a normal distribution in the same way. As compared with FIG. 3, therefore, the average voltage over the period of t=1 to N is applied to the dot D(i,j) as the voltage waveform (f(i)−g(j)). 
     D can assume a value ranging from 0 (complete noncoincidence) to N (entire coincidence). From equation (22), the peak value of g(j) becomes                        g        (   j   )         P   -   P       =       FP     N            (     ±   N     )                   =       ±     N          FP                   (     23   ′     )                                
     Furthermore, g(j) can have any one of N+1 levels. Regarding this liquid crystal display device as a display device for a personal computer, N=240 rows are needed. As the column voltage g(j), therefore, a liquid crystal driver generating 241 levels and generating a peak voltage of approximately 22.65 volts (in case the nonselection voltage of the liquid crystal display is 1 volt) on the basis of equation (23) is needed. Since it is difficult to realize such a liquid crystal driver, it is said that the liquid crystal driver having 64 levels (where the peak voltage is 5.95 volts) is sufficient on the basis of the property of D having a normal distribution. In this case, however, overflow, i.e., a voltage exceeding 64 levels, might be needed with a probability of once every 115 frames. However, it is said that overflow occurs very rarely in an actual display and hence there is no problem in the above described conventional technique. 
     If a Walsh function is used as the voltage function supplied to the row electrodes in the above described driving method, however, the voltage function g(j) supplied to the column electrodes becomes as represented by the following equation (24) on the basis of equations (15) and (16). For determining the voltage applied to one dot at a certain time t, it is necessary to calculate the sum of products of the display information P(i,j) for i=1 to N and the Walsh function W(i,t). The implementation of this is difficult, and a specific driving circuit for doing so has not been clearly described                      g        (   j   )       =       1     N              ∑     i   =   1     N                       P        (     i   ,   j     )            FP   ·     W        (     i   ,   t     )                           =       FP     N              ∑     i   =   1     N                       P        (     i   ,   j     )            W        (     i   ,   t     )                           (   24   )                                
     Assuming that the voltage function supplied to the row electrodes is the function shown in FIG. 2, the voltage function g(j) applied to the column electrodes is represented by the following equation (25).                      g        (   j   )       =       1     N              ∑     i   =   1     N                       P        (     i   ,   j     )            FP   ·   δ                     (     i   ,   t     )                       =       FP     N              ∑     i   =   1     N                       P        (     i   ,   j     )                     δ                   (     i   ,   t     )                       =       FP     N            P        (     i   ,   j     )                       (   25   )                                
     The product summation thus becomes unnecessary and the circuit configuration becomes simple. In this case, however, the voltage waveform applied to the dot D(i,j) assumes a high voltage during only one interval in N intervals, and assumes a low voltage during the remaining N−1 intervals. In the case of fast responding STN liquid crystal displays, therefore, the contrast drops. 
     Furthermore, in the conventional technique, a liquid crystal driver generating the column voltage is required to provide N+1 levels and the peak voltage expressed by equation (23). However, it is said that a liquid crystal driver having 64 levels and approximately 5.95 volts suffices for a personal computer display having N=240, considering the property of the value assumed by D. Therefore, overflow occurs with a probability of once every 115 frames. In this case, it is considered that overflow occurs with a probability defined by the normal distribution following the above described theory when the contents of display change momentarily as in a moving picture display. In displays used for information processing devices such as personal computers or work stations, however, contents of displays are not always moving pictures but are still pictures in many cases. If overflow occurs once in a still picture, therefore, overflow occurs in every frame and D loses its property of having a normal distribution. Therefore, the effective value of the pertinent column electrode voltage decreases and the quality of the display is degraded. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a circuit which has a simple circuit configuration and which does not degrade contrast for fast responding STN liquid crystal displays. 
     Another object of the present invention is to provide a new liquid crystal driving method which can also be applied to displays of still pictures in personal computers or the like using fast responding STN liquid crystal displays. 
     In order to achieve the above described objects, a display apparatus includes a row function generation circuit, a function generation circuit, a line memory for storing display data of X rows, a computation circuit for performing computation based on the output of the function generation circuit, and a voltage conversion circuit for converting the output of the computation circuit to a voltage. 
     The row function generation circuit generates a function for N rows so that only X rows out of the N rows are Walsh functions at a certain time t and the remaining rows are 0. The row function generation circuit supplies the function thus generated to a row electrode driver of the liquid crystal display. The function generation circuit generates values identical with values of the above described Walsh functions of X rows. The outputs are subjected to computation together with the output of the line memory. The result of the computation is converted into voltage, which is supplied to the column electrode drive. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram showing a liquid crystal display panel having an N-column M-row matrix structure; 
     FIG. 2 is a diagram showing an example of orthogonal function voltages applied to row electrodes, which are generally used as driving waveforms of STN liquid crystal displays at the present time; 
     FIG. 3 is a diagram showing a liquid crystal display driving voltage waveform applied to a dot D(i,j); 
     FIG. 4 is a diagram showing an example of orthogonal functions called Walsh functions having 8 divisions; 
     FIG. 5 is a block diagram of a first embodiment of a liquid crystal display apparatus according to the present invention; 
     FIG. 6 is a block diagram of a column signal generation circuit; 
     FIG. 7 is a diagram showing an example of a partial orthogonal function driving method in which Walsh functions having 16 divisions are applied to only 8 of N row electrodes at a time, with one frame period T being 2N; 
     FIG. 8 is a diagram representing dot information of a liquid crystal display panel  28  when the liquid crystal display panel is formed by 4 rows by 4 columns in the present embodiment; 
     FIG. 9 is a diagram showing values of X-row function data  13  of a function generation circuit  12  in respective t values; 
     FIGS. 10A and 10B are diagrams showing the timing relation between X-row display data  10  and X-row function data  13 ; 
     FIG. 11 is a block diagram of an embodiment of a computation circuit  11 ; 
     FIG. 12 is a diagram showing the operation of a decoder circuit  33 ; 
     FIG. 13 is a diagram showing values of function data  23  outputted by a row function generation circuit  22  in respective t values; 
     FIGS. 14A to  14 D are timing diagrams for illustrating the operation of a column electrode driver  18  and a row electrode driver; 
     FIG. 15 is a diagram showing a voltage function of row electrodes, which are used in a version when the Walsh function is applied to only 8 rows among N row electrodes, one frame period T is 2N (where N is the number of display rows), and the Walsh function of 8 rows is driven with the number of divisions equivalent to 16; 
     FIG. 16 is a diagram showing distribution of the voltage function of row electrodes in which W 0  is changed to W 0  and 0 in the version of FIG. 15; 
     FIG. 17 is a block diagram of a second embodiment of a liquid crystal display apparatus; 
     FIGS. 18A to  18 F are timing diagrams of display data  35  inputted to the liquid crystal display apparatus; 
     FIGS. 19A to  19 F are diagrams showing timing of frame memory read data  45  read out from a frame memory  44  and a data control bus  43 ; 
     FIG. 20 is a block diagram showing the frame memory  44 ; 
     FIGS. 21A to  21 E are timing diagrams illustrating the operation of the frame memory  44 ; 
     FIG. 22 is a block diagram of a column signal generation circuit  46 ; 
     FIGS. 23A to  23 D are diagrams illustrating the writing operation of a line memory-A  92 ; 
     FIG. 24 is a block diagram of the line memory-A  92  depicted from a viewpoint of the writing operation; 
     FIGS. 25A to  25 E are diagrams illustrating the writing operation of the line memory-A  92 ; 
     FIG. 26 is a block diagram of the line memory-A  92  dericted from a viewpoint of the reading operation; 
     FIGS. 27A to  27 I are diagrams illustrating the reading operation of the line memory-A  92 ; 
     FIG. 28 is a block diagram of a computation circuit  103 ; 
     FIG. 29 is a block diagram of a function generation circuit  101 ; 
     FIG. 30 is a diagram illustrating the operation of an orthogonal function memory  122 ; 
     FIGS. 31A to  31 C are timing diagrams illustrating the operation of a line block counter  123 ; 
     FIGS. 32A to  32 F are timing diagrams illustrating the operation of a column electrode driver  53 ; 
     FIG. 33 is a block diagram of a row function generation circuit  50 ; 
     FIGS. 34A to  34 F are timing diagrams illustrating the reading operation from the frame memory  44 ; 
     FIG. 35 is a block diagram of a variant of the column signal generation circuit  46 ; 
     FIGS. 36A to  36 F are timing diagrams illustrating the operation of a data converter  140 ; 
     FIG. 37 is a block diagram illustrating the interface between a display controller of a system apparatus and a display apparatus; 
     FIGS. 38A to  38 F are timing diagrams of an example of an interface signal  142 ; 
     FIGS. 39A to  39 F are timing diagrams showing the interface signal  142  in case a frame memory controller and a frame memory are provided in a display controller  141  of the system apparatus; 
     FIGS. 40A to  40 F are timing diagrams showing another example of the interface signal  142  in case a frame memory controller and a frame memory are provided in a display controller  141  of the system apparatus; 
     FIG. 41 is a block diagram showing a display controller  141  of a system apparatus; 
     FIG. 42 is a block diagram of a display controller of a system apparatus using the interface signal shown in FIGS. 39A to  39 F; 
     FIG. 43 is a block diagram of a buffer  154 ; 
     FIGS. 44A to  44 I are timing diagrams illustrating palette data  150 ; 
     FIGS. 45A to  45 I are timing diagrams illustrating readout from a display memory  149  of a display controller  141  using the interface signal shown in FIGS. 40A to  40 F; 
     FIG. 46 is a diagram showing details of a column signal generation circuit  17 ; 
     FIG. 47 is a diagram showing details of an overflow detector  20 ; 
     FIG. 48 is a diagram showing details of a row function generation circuit  22 ; 
     FIGS. 49 to  52  are diagrams showing orthogonal function data  34 ; 
     FIG. 53 is a diagram showing another example of a row function generation circuit  22  which generates different row function data by using a switch matrix; and 
     FIG. 54 is a diagram showing details of another example of the column signal generation circuit  17 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     By referring to the attached drawings, a display apparatus of the present invention will hereafter be described in detail. 
     FIG. 5 shows a liquid crystal display apparatus. A circuit  17  generates column analog display data  16  from display data  1 . A column electrode driver  18  takes in analog display data  16  for one row, and thereafter outputs data for one row at a time. Taking in data for one row is performed in one division interval. Numerals  19  to  21  denote column electrodes. Numerals  19 ,  20  and  21  denote a first column electrode, a second column electrode, and an Mth column electrode, respectively. A circuit  22  generates a row function. The circuit  22  writes row function data  23  of rows associated with one division interval into a row electrode driver  24 . After writing has been completed, the row electrode driver  24  outputs voltages depending upon row function data  23  to row electrodes. Writing this row function data  23  is also conducted in one division interval, and it is in synchronism with the period equivalent to one division interval of the operation of writing analog display data  16  into the column electrode driver  18 . Numerals  25  to  27  denote row electrodes. Numeral  25 ,  26  and  27  denote a first row electrode, a second row electrode, and an Nth electrode, respectively. Numeral  28  denotes an STN liquid crystal panel for providing a display of N rows by M columns. The active matrix driving technique is disclosed in U.S. patent application Ser. No. 08/003,448 filed on Jan. 12, 1993, now U.S. Pat. No. 5,854,879, the contents of which are hereby incorporated by reference. 
     FIG. 6 is a block diagram of an embodiment of a column signal generation circuit  17  implementing a partial orthogonal function driving method of the present invention. Display data  1  represents the display-on state as “1” and represents the display-off state as “0”. Each of numerals  5  and  6  denotes a line memory for storing data corresponding to X rows. A write circuit  2  writes data A and data B into a line memory-A  5  and a line memory-B  6  via lines  3  and  4 , respectively. At this time, the write circuit  2  writes data alternately into the memory-A  5  and memory-B  6  every X rows. A read circuit  9  reads out data A and B via lines  7  and  8  from either of the line memories A 5  and B 6  which is not being subjected to the writing operation. In this reading operation, data for X rows are read out simultaneously. Display data for X rows read out from one line memory by the read circuit  9  are supplied to a computation circuit  11  via a line  10 . The computation circuit  11  computes the sum of products of the X-row display data  10  and X-row function data  13  supplied from a function generation circuit  12 . The computation circuit  11  supplies computation data  14  obtained as a result of computation to a voltage converter circuit  15 , which in turn converts the computation data  14  into analog voltage  16 . A technique for using line memories for the purpose of multi-level tone display is described in U.S. patent application Ser. No. 08/015,896, now U.S. Pat. No. 5,583,530 the contents of which are hereby incorporated by reference. Furthermore, a technique of driving a bisected display panel by using line memories is disclosed in U.S. Pat. No. 4,985,698, the contents of which are hereby incorporated by reference. 
     Prior to description of the operation of the liquid crystal display apparatus shown in FIG. 5, voltage functions applied to the panel  28  will now be described. FIG. 7 is a diagram showing a partial orthogonal function driving method in which the voltage function applied to N row electrodes includes Walsh functions having 16 divisions applied to only 8 row electrodes at a time, with one frame period being 2N. In the same way as in the above described example of the conventional technique, the liquid crystal display panel provides a display of N rows by M columns. In this case, a voltage function applied to the row electrodes and a voltage function applied to the column electrodes are represented by the following equations (26) and (27), respectively. In the following description, however, the voltage function is normalized by the applied voltage. 
     
       
           f ( i )= FP·W ( i,t )  (26)  
       
     
     
       
         
           
             
               
                 
                   
                     g 
                      
                     
                       ( 
                       j 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         N 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                        
                       
                           
                       
                        
                       
                         
                           P 
                            
                           
                             ( 
                             
                               i 
                               , 
                               j 
                             
                             ) 
                           
                         
                          
                         f 
                          
                         
                             
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     In these equations, FP is a constant indicated by the following equation (28) and W(i,t) is a function shown in FIG.  4 .              FP   =         N   8     ·       N       2        (       N     -   1     )                     (   28   )                                
     In the same way as the above described example of the conventional technique, P(i,j) becomes “−1” when dot D(i,j) of the ith row in the jth column is in the display-on state whereas P(i,j) becomes “1” when the dot D(i,j) is in the display-off state. By using equations (26) and (27), the effective voltage value U rms (i,j) of dot D(i,j) is calculated as indicated by the following equation.                  U   rms          (     i   ,   j     )       =         [       (       f        (   i   )       -     g        (   j   )         )     2     ]       1   2       =       [         1   T            ∫   0   T              f        (   i   )       2                        t           +       1   T            ∫   0   T              g        (   j   )       2                        t           -       2   T            ∫   0   T            f        (   i   )            g        (   j   )                          t             ]       1   2                 (   29   )                                
     Letting T=2N and rewriting (29) gives            1   T            ∫   0   T              (     f        (   i   )       )     2                        t           =         1     2      N              ∑     t   =   1       2      N                         N   8     ·       N       2        (       N     -   1     )         ·       (     W        (     i   ,   t     )       )     2           =           1   16     ·       N       2        (       N     -   1     )                  ∑     t   =   1       2      N                         (     W        (     i   ,   t     )       )     2         =         1   16     ·       N       2        (       N     -   1     )                (         (     W        (     i   ,   1     )       )     2     +       (     W        (     i   ,   2     )       )     2     +   …   +       (     W        (     i   ,     2      N       )       )     2       )                                  
     As for W(i,j) of the ith row shown in FIG. 7, only 16 W(i,j)s are a Walsh function each having a value of “±1”, and the remaining W(i,j)s are “0”. Therefore,          The                 first                 term     =         1   16     ·       N       2        (       N     -   1     )         ·   16     =       N       2        (       N     -   1     )                       1   T            ∫   0   T              g        (   j   )       2                        t           =         1     2      N              ∑     t   =   1       2      N                         1   N            (       ∑     i   =   1     N            P        (     i   ,   j     )       ·         N   8                       N       2        (       N     -   1     )             ·     W        (     i   ,   t     )           )     2           =           1     2      N       ·     1   8     ·       N       2        (       N     -   1     )                  ∑     t   =   1       2      N                         (       ∑     i   =   1     N                       P        (     i   ,   j     )            W        (     i   ,   t     )           )     2         =                    1     2      N       ·     1   8     ·       N       2        (       N     -   1     )                  ∑     t   =   1       2      N            (           P        (     1   ,   j     )       2            W        (     1   ,   t     )       2       +         P        (     2   ,   j     )       2            W        (     2   ,   t     )       2       +   …   +         P        (     N   ,   j     )       2            W        (     N   ,   t     )       2         )                                    
     As for W(i,j) shown in FIG. 7 at a certain time t, Walsh functions having a value of “±1” are applied to only 8 rows, and the remaining rows are provided with “0”. Therefore,                  The                 second                 term     =           1     2      N       ·     1   8              N       2        (       N     -   1     )              8     t   =   1       2      N                    =         1     2      N              1   8     ·       N       2        (       N     -   1     )         ·   8   ·   2        N     =       N       2        (       N     -   1     )                               
            2   T            ∫   0   T            f        (   i   )            g        (   j   )                          t           =         2     2      N              ∑     t   =   1       2      N                         FP   ·     W        (     i   ,   t     )            1          ∑     i   =   1     N                       P        (     i   ,   j     )            FP   ·     W        (     i   ,   t     )                   =           2     2      N       ·     1     N       ·     N   8     ·       N       2        (       N     -   1     )                  ∑     t   =   1       2      N                         W        (     i   ,   t     )              ∑     i   =   1     N                       P        (     i   ,   j     )            W        (     i   ,   t     )                 =           1   8     ·     1     2        (       N     -   1     )                  ∑     t   =   1       2      N                         W        (     i   ,   t     )            {         P        (     1   ,   j     )            W        (     1   ,   t     )         +       P        (     2   ,   j     )            W        (     2   ,   t     )         +     …                   P        (     N   ,   j     )            W        (     N   ,   t     )           }           =         1   8     ·     1     2        (       N     -   1     )                  ∑     t   =   1       2      N                         P        (     i   ,   j     )              W        (     i   ,   t     )       2                         (   31   )                                
     As for W(i,t) of the ith row shown in FIG. 7, only 16 W(i,t)s are a Walsh function having a value of “±1”, and the remaining W(i,t)s are “0”. Therefore,                The                 third                 term     =           1   8     ·     1     2        (       N     -   1     )         ·   16          P        (     i   ,   j     )         =       2        P        (     i   ,   j     )           2        (       N     -   1     )                   (   32   )                                
     From the above equations, we get                        U   rms          (     i   ,   j     )       =       [         N       2        (       N     -   1     )         +       N       2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   /   2                   =       [         2        N         2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   /   2                     (   33   )                                
     When D(i,j) is in the display-on state, therefore, P(i,j) becomes “−1” and hence the effective voltage value is represented by the following equation (34). When D(i,j) is in the display-off state, P(i,j) becomes “1” and hence the effective voltage value is represented by the following equation (35).                        U   rms          (     i   ,   j     )       =       [         2        N         2        (       N     -   1     )         -       -   2       2        (       N     -   1     )           ]       1   /   2                   =           N     +   1         N     -   1                       (   34   )                         U   rms          (     i   ,   j     )       =       [         2        N         2        (       N     -   1     )         -     2     2        (       N     -   1     )           ]       1   /   2                   =   1                 (   35   )                                
     By comparing equations (34) and (35) with equations (9) and (10), it can be seen that the effective voltage values U rms  in the display-on state and in the display-off state do not change from those of the above described example of the conventional technique even if the voltage function as shown in FIG. 7 is applied to row electrodes. In this way, the orthogonality does not change even if the Walsh function is used for only 8 lines and respective portions are moved on the basis of the number of divisions. 
     In the foregoing description, the Walsh function is used for 8 lines among N lines and the Walsh function of the 8 lines is driven with “16” divisions. However, the present invention is not limited to this. In general, it is also possible to use the Walsh function for R rows among N rows and drive the Walsh function with K divisions. It is assumed at this time that relations R&lt;N and K≧R are satisfied. 
     Equations (36) and (37) express f(i) and g(j) of the generalized case, respectively. FP in this case is indicated by equation (38). 
     
       
           f ( i )= FP·W ( i,t )  (36)  
       
     
     
       
         
           
             
               
                 
                   
                     g 
                      
                     
                       ( 
                       j 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         N 
                       
                        
                       
                           
                       
                        
                       
                         
                           P 
                            
                           
                             ( 
                             
                               i 
                               , 
                               j 
                             
                             ) 
                           
                         
                          
                         
                           f 
                            
                           
                             ( 
                             i 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
             
               
                 
                   FP 
                   = 
                   
                     
                       
                         N 
                         R 
                       
                       · 
                       
                         
                           N 
                         
                         
                           2 
                            
                           
                             ( 
                             
                               
                                 N 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
                 
         
             
         
      
     
     The effective voltage value U rms (i,j) of dot D(i,j) at this time is calculated by the following equation. 
     Letting here T=N/R·K, gives                    U   rms          (     i   ,   j     )       =         [       (       f        (   i   )       -     g        (   j   )         )     2     ]       1   /   2       =       [         1   T            ∫   0   T              f        (   i   )       2                        t           +       1   T            ∫   0   T              g        (   j   )       2             t           -       2   T            ∫   0   T            f        (   i   )            g        (   j   )               t             ]       1   /   2                
            The                 first                 term     =         1   T            ∫   0   T              f        (   i   )       2             t           =       1   T            ∑     t   =   1     T                       N   R     ·       N       2        (       N     -   1     )         ·       W        (     i   ,   t     )       2                       (   39   )                                
     As for W(i,t) of the ith row, the Walsh function is applied to only KW(i,t)s and remaining W(i,t)s are provided with “0”. Therefore,                  The                 first                 term     =         1   T     ·     N   R     ·       N       2        (       N     -   1     )         ·   K     =           1   T     ·   T            N       2        (       N     -   1     )           =       N       2        (       N     -   1     )                    
            1   T            ∫   0   T              g        (   j   )       2             t           =         1   T            ∑     t   =   1     T                       (       1     N              ∑     i   =   1     N                       P        (     i   ,   j     )       ·   FP   ·     W        (     i   ,   t     )             )     2         =           1   T     ·     1   R                N       2        (       N     -   1     )         ·       ∑     t   =   1     T                       (       ∑     i   =   1     N                       P        (     i   ,   j     )            W        (     i   ,   t     )           )     2           =         1   T     ·     1   R                N       2        (       N     -   1     )         ·       ∑     t   =   1     T          (           P        (     1   ,   j     )       2            W        (     1   ,   t     )       2       +         P        (     2   ,   j     )       2            W        (     2   ,   t     )       2                   …     +         P        (     N   ,   j     )       2            W        (     N   ,   t     )       2         )                       (   40   )                                
     As for W(i,j) at certain time t, the Walsh function having a value of “±1” is applied to only R W(i,j)s, and remaining W(i,j)s are provided with “0”. Therefore,                The                 second                 term     =           1   T     ·     1   R     ·       N       2        (       N     -   1     )                  ∑     t   =   1     T        Rt       =       N       2        (       N     -   1     )                   (   41   )                   2   T            ∫   0   T            f        (   i   )            g        (   j   )               t           =         2   T            ∑     t   =   1     T            FP   ·     W        (     i   ,   t     )       ·     1     N                ∑     i   =   1     N                       P        (     i   ,   j     )            FP   ·     W        (     i   ,   t     )                   =         2   T            1     N       ·     N   R     ·       N       2        (       N     -   1     )                  ∑     t   =   1     T            B        (     i   ,   t     )              ∑     i   =   1     N            P        (     i   ,   j     )            W        (     i   ,   t     )                 =         2   T     ·     1     N       ·     N   R     ·       N       2        (       N     -   1     )                  ∑     t   =   1     T            P        (     i   ,   j     )              W        (     i   ,   t     )       2                                                        
     As for W(i,t) of the ith row, the Walsh function is applied to only KW(i,t)s and remaining W(i,t)s are provided with “0”. Therefore,                    2   T     ·     1     N       ·     N   R     ·       N       2        (       N     -   1     )         ·     P        (     i   ,   j     )            K     =       2        P        (     i   ,   j     )           2        (       N     -   1     )                 (   42   )                                
     From these equations, we get                  U   rms          (     i   ,   j     )       =       [         2        N         2        (       N     -   1     )         -       2        P        (     i   ,   j     )           2        (       N     -   1     )           ]       1   /   2               (   43   )                                
     This coincides with equation (33). Even under supposition as described above, the effective voltage value U rms (i,j) at the dot D(i,j) becomes in general identical with the example of the conventional technique provided that the following equation (44) is satisfied. 
     
       
           T=N/R K   (44)  
       
     
     In the present embodiment, description has been given by using the Walsh function. However, the present embodiment is not limited to this, but an orthogonal function having values “1” and “−1” may be used as evident from the process of calculation of the effective value. This driving method is hereafter referred to as “partial orthogonal function driving method” and it will now be described. 
     Display data are serially transmitted in the order of dots D( 1 , 1 ), D( 1 , 2 ), . . . , D( 2 , 1 ), D( 2 , 2 ), . . . , D( 4 , 1 ), D( 4 , 2 ), . . . , D( 4 , 4 ) of the liquid crystal panel  28  shown in FIG.  8 . The display data are written alternately every two rows into the line memory-A  5  and line memory-B 6  by the write circuit  2 . That is to say, data to the first and second rows are written into the line memory-A  5 , and data of the third and fourth rows are written into the line memory-B  6 . When data of the third and fourth rows are being written into the line memory-B  6  after data of the first and second rows have been written, the read circuit  9  reads out display data from the line memory-A  5 . At this time, display data A in the row direction are simultaneously read out. For example, D(1,1) and D(2,1) are read out simultaneously, and D(1,2) and D(2,2) are read out simultaneously. Data thus read out are outputted to the computation circuit  11  as the X-row display data  10 . In accordance with time t, the function generation circuit  12  generates X-row function data h( 1 ) and h( 2 ) shown in FIG.  9 . As for time t, a cycle of t=1 to 4 is repeated because two rows are driven with four divisions. The function data h( 1 ) and h( 2 ) are 1-bit data and represent “−1” as “0” and “+1” as “1”. Timing of the operation of the generation circuit  12  and the operation of the read circuit  9  will now be described by referring to FIGS. 10A and 10B. When the X-row function data  13  are h( 1 ) and h( 2 ) at t=1 as shown in FIG. 10B, the read circuit  9  reads out two-row data of the first column to the fourth column serially as shown in FIG.  10 A. This is repeated up to t=4. Thereafter, the generation circuit  12  generates X-row function data  13  from t=1 again. On the other hand, the read circuit  9  reads out display data from the line memory-B  6  in the same way. Operation of the computation circuit  11  will now be described by referring to FIGS. 11 and 12. As for display data, the display-on state is represented by “1”, whereas the display-off state is represented by “0”. Assuming that the X-row display data are D(1,1) and D(2,1) and X-row function data are h( 1 ) and h( 2 ), therefore, D(1,1) and D(2,1) are inverted by inverter circuits  29  and  30  in order to conform to the expression of P(i,j) in equation (27). The inverted data are exclusive-ORed with h( 1 ) and h( 2 ) respectively by circuits  31  and  32 . Resultant outputs are decoded by a decoder  33  in accordance with FIG.  12 . This means that computation of the following equation is conducted and the sum of products expressed by equation (27) is calculated.                      g        (   j   )       =                  1     N              ∑     i   =   1     N            P        (     i   ,   j     )            f        (   i   )                         =                    1     N       ·   F                   P          ∑     i   =   1     N            P        (     i   ,   j     )            W        (     i   ,   t     )                         =                    1     N       ·   F                     P        (       2        Y        (   t   )         -   N     )                       (   45   )                                
     Y(t) is the sum of values over i=1 to N, each value being “1” when P(i,J)=W(i,t). 
     Therefore, the computation data  14  assumes one of values shown in FIG.  12 . As evident from equations (30), (31), (32) and (33), the computation data are converted to a voltage value of the following equation by the voltage converter circuit  15  and outputted as analog display data  16 .                (     Analog                 display                 data                 16     )     =       1     N                N   R     ·       N       2        (       N     -   1     )             ×     (     computation                 data                 14     )     ×     V   off               (   46   )                                
     In the present embodiment, N=4 and R=2. V off  is a coefficient for conducting conversion to actual driving voltage because the display-off voltage is determined to be “1” as expressed by equation (29). As heretofore described, the column signal generation circuit  17  of FIG. 6 has realized the partial orthogonal function driving described before by referring to equations (26) to (35). The analog display data  16  are successively taken in the column electrode driver  18 . When one row has been taken in, the data are outputted to column electrodes simultaneously. As shown in FIG. 13, the row function generation circuit  22  successively outputs data  23  of functions f( 1 ), f( 2 ), f( 3 ) and f( 4 ). The driver  24  receives the row function data  23 . After all data for one column have been received, the driver  24  outputs them as the row electrode signal. The operation timing of the drivers  18  and  24  heretofore described is shown in FIGS. 14A to  14 D. 
     In the above described example of the conventional technique, computation of the column signal expressed by equation (27) needs calculation of N rows. In the STN liquid crystal driving method according to the present invention heretofore described, however, calculation of R rows (where R&lt;N) suffices and the circuit can be formed more easily. One computation time unit of 240 rows by 640 columns (t a  of FIG. 10A) will now be derived. It is now assumed that the same frequency is 60 Hz, R=8, and K=16.          t   a     =       1     60                 Hz   ×   240   ×   630   ×     16   8         ≈     54                 ns                              
     That is to say, reading and executing computation on data of 8 rows (R=8) during approximately 54 ns suffices. On the other hand, t a  of the conventional driving method becomes          t   a     =       1     60                 Hz   ×   256   ×   640       ≈     101                 ns                              
     As compared with the partial orthogonal function driving, t a  itself becomes longer. In the logic circuit aspect, however, it is difficult to read and execute computation on data of 240 rows during approximately 100 ns. That is to say, data processing speed is 0.4 ns per row. Even if the speed is lowered to a value attainable by a logic circuit by using parallel driving, the number of parallel paths becomes large, resulting in an excessively large logic scale. As compared with this, the partial orthogonal function driving needs fewer rows for computation and can be realized with a smaller logic scale. 
     A modification of the present invention will now be described. If in general the voltage function applied to N row electrodes is the Walsh function for only  m  rows, the period of one frame is T, and the number of divisions of the Walsh function for the m rows is  s , then voltage function F h  applied to each row electrode, voltage function G j  applied to each column electrode, and effective value U rms  of voltage applied to a picture element of the ith row in the jth column are represented by the following equations. 
     
       
           N  lines are divided into    n    parts each having  m  lines:  mn=N    
       
     
     
       
             m    lines are driven with the number    s    of divisions:  sn=T    
       
     
     Furthermore, representing line  h  as h=pm+i (p=0 to n−1, i=1 to m) and time  k  as k=qs+t (q =0 to n−1, t=1 to s), orthogonal function S hk  is represented by the following equation.                S   hk     =       S       pm   +   i     ,     qs   +   t         =     {         Wi         (     p   =   q     )             Wo         (     p   ≠   q     )                       (   47   )                                
     Therefore, row electrode voltage function F h  (k) is represented as 
     
       
           F   h ( k )= {overscore (F)}S   hk    (48)  
       
     
     Assuming that display information of the ith row in the jth column is l ij , column electrode voltage function Gj(t) is represented by the following equation.                  G   j          (   t   )       =       c          ∑     i   =   1              l   ij            F   i          (   t   )                     where                   l   ij           =     {           -   1           display                 on               +   1           display                 off                       (   49   )                                
     By representing equation (49) by  h  and  k , we get                    G   j          (   k   )       =       ∑     p   =   0       n   -   1              {     c          ∑     i   =   1     m            l       pm   +   i     ,   j              F     pm   +   i            (   k   )             }          δ     p   ,   q                     where                         
                       δ     p   ,   q       =     {         1         (     p   =   q     )             0         (     p   ≠   q     )                       (   50   )                       U   rms     =                    1   T            ∫   0   T              {         F   r          (   t   )       -       G   j          (   t   )         }     2             t                         =                    1   T            ∑     k   =   1     T            {         F   r          (   t   )       -       G   j          (   t   )         }     2                       =                    1   T            ∑     k   =   1     T          {           F   r          (   k   )       2     +         G   j          (   k   )       2     -     2          F   r          (   k   )              G   j          (   k   )           }                         (   51   )                                
     The first term of equation (51) becomes                  1   T            ∑     k   =   1     T              F   r          (   k   )       2         =         1   T            ∑     k   =   1     T              F   _     2          S   rk   2           =       F   _     2               (   52   )                                
     The second term of equation (51) becomes                  1   T            ∑     k   =   1     T            G   j          (   k   )           =         1   T            ∑     k   =   1     T            [       ∑     p   =   0       n   -   1              {     c          ∑     i   =   1     m            l       pm   +   1     ,   j              F     pm   +   1            (   k   )             }          δ     p   ,   q           ]     2         =         1   T            ∑     q   =   0       n   -   1                         ∑     t   =   1     s            [       ∑     p   =   0       n   -   1              {     c          ∑     i   =   1     m            l       pm   +   1     ,   j              F     pm   +   i            (   k   )             }          δ     p   ,   q           ]     2           =       1   T     [                    ∑     t   =   1     s            {     c          ∑     i   =   1     m            l     i   ,   j              F   i          (   t   )             }     2       +       ∑     t   =   1     s            {     c          ∑     i   =   1     m            l       p   +   i     ,   j              F     m   +   i            (   t   )             }     2       +   …   +       ∑     t   =   1     s            {     c          ∑     i   =   1     m            l           (     n   -   1     )        m     +   i     ,   j              F         (     n   -   1     )        m     +   i            (   t   )             }     2         ]                 (   53   )                                
     where                  ∑     t   =   1     s            {     c          ∑     i   =   1     m            l     i   ,   j              F   i          (   t   )             }     2       =     c2          ∑     t   =   1     2                       ∑     i   =   1     m            l     i   ,   j     2              F   i          (   t   )       2                         =         c   2            F   _     2            ∑     t   =   1     s            ∑     i   =   1     m            l     i   ,   j     2          W   i   2             =       smc   2            F   _     2                                      
     Therefore, the second term of equation (51) can be expressed as                        1   T            ∑     k   =   1     T              G   j          (   k   )       2         =                  1   T          {         smc   2            F   _     2       +       smc   2            F   _     2       +   …   +       smc   2            F   _     2                         =                    1   T                     nsmc   2            F   _     2       =     m                   c   2            F   _     2                       (   54   )                                
     The third term of equation (51) becomes                  1   T            ∑     k   =   1     T          2          F   r          (   k   )                         G   j          (   k   )             =         2   T            ∑     q   =   0       n   =   1                         ∑     t   =   1     s            F   _            S   r          (   k   )              ∑     p   =   0       n   -   1              {     c          ∑     i   =   1     m            l       pm   +   i     ,   j          F                     W   i          (   t   )             }          δ     p   ,   q                   =         2      c          F   _     2       T          [       {       ∑     t   =   1     s              S   r          (   k   )              ∑     i   =   1     m            l     i   ,   j                         W   i          (   t   )               }     +     {       ∑     t   =   1     s              S   r          (   k   )              ∑     i   =   1     m            l       m   +   i     ,   j                         W   i          (   t   )               }     +   …   +     {       ∑     t   =   1     s              S   r          (   k   )              ∑     i   =   1     m            l         (     n   -   1     )        m     +   i              W   i          (   t   )               }       ]                 (   55   )                                
     where S r  is indicated by r=pm+i, and S r  becomes W 0  in portions with p=q and is orthogonal to W i (t). 
     Therefore, the third term of equation (51) becomes                  1   T            ∑     k   =   1     T                     2          F   r          (   k   )              G   j          (   k   )             =           2      c          F   _     2       T            ∑     t   =   1     s              W   i          (   t   )              ∑     i   =   1     m            l       pm   +   i     ,   j              W   i          (   t   )                 =           2      c          F   _     2       T          l   rj            ∑     t   =   1     s              W   i          (   t   )          2         =           2      sc          F   _     2       T          l   rj       =         2      c          F   _     2       n          l   rj                     (   56   )                                
     Therefore,                        U   rms     =           F   _     2     +     m                 c          F   _     2       -         2      c          F   _     2       n          l   rj                       =       F   _            1   +     m                   c   2       -         2      c     n          l   rj                          
            l   rj     =     {             +   1                   display                 on                 -   1                   display                 off                       (   57   )                                
     From the description given heretofore, the effective value U rms  of voltage applied to the picture element of the ith row in the jth column is expressed by equation (57). Furthermore, since I ij  becomes “−1” when display is on whereas I ij  becomes “+1” when display is off, respective effective voltage values are represented by equations (58) and (59).                  U   rms          (   on   )       =       F   _            1   +     m                   c   2       +       2      c     n                   (   58   )                   U   rms          (   off   )       =       F   _            1   +     m                   c   2       -       2      c     n                   (   59   )                                
     Operation margin R is defined by the following equation (60).                    R   =           U   rms          (   on   )           U   rms          (   off   )         =         F   _            1   +     m                   c   2       +       2      c     n               F   _            1   +     m                   c   2       -       2      c     n                           =       1   +       2      a                 c       1   +     m                   c   2       -     a                 c                           (   60   )                                
     
       
         where  a= 2/ n    
       
     
     Deriving  c  maximizing the operation margin R in equation (60), we get equation (61).                            c          R     =   0          
        Therefore        
          c   =     1     m                 (   61   )                                
     Substituting equation (61) in equations (58) and (59), U rms (on) and U rms (off) can be expressed by equations (62) and (63).                  U   rms          (   on   )       =       F   _            2        (     1   +     1     nN         )                   (   62   )                   U   rms          (   off   )       =       F   _            2        (     1   -     1     nN         )                   (   63   )                                
     Substituting equation (61) in equation (60), the operation margin R can be expressed by equation (64).              R   =           nN     +   1         nN     -   1                 (   64   )                                
     Letting U rms (off) be 1, F is given by equation (65) from equation (63).              F   =         nN       2        (       nN     -   1     )                   (   65   )                                
     Substituting equation (65) in equations (62) and (63), U rms (on) and U rms (off) can be expressed by equations (66) and (67).                  U   rms          (   on   )       =           nN     +   1         nN     -   1                 (   66   )                                
     
       
         Urms(off)=1   (67)  
       
     
     In case the voltage function applied to row electrodes has distribution shown in FIG. 15 as heretofore described, it would be understood by comparing equations (66) and (67) with equations (9) and (10) that the effective voltage value of the display-on state and display-off state are identical with those obtained by replacing N in the above described example of the conventional technique by nN. Furthermore, in the present embodiment, description has been given by using the Walsh function. However, the present embodiment is not limited to this, but an orthogonal function having values of “1” and “−1” suffices as evident from the progress of effective value calculation. In the same way as the embodiment described before, this driving method will hereafter be referred to as partial orthogonal driving method. 
     The above described modification will now be described in further detail. Blocks of a column signal generation circuit implementing the partial orthogonal function driving method have the same configurations as the blocks of embodiment described before have and will not be described. Since the operation is also similar to that of the embodiment described before, description of respective portions will be omitted. Parts differing in operation will now be described. The column electrode driver  18  takes an analog display data corresponding to one row during one division interval and thereafter outputs data of one row simultaneously. The row function generation circuit  22  generates the row function shown in FIG.  15 . After the row function data  23  have been completely written, the row electrode driver  24  outputs voltages depending upon the values to row electrodes. The operation of writing the row function data  23  is also conducted in one division interval and is in synchronism with the period of one division interval for writing analog display data  16  by using the driver  18 . For convenience of description, the present embodiment will now be described assuming that the liquid crystal panel  28  has 4 rows by 4 columns, X=2, and the two rows are driven with 4 divisions. That is to say, one frame is driven with 8 divisions (see equations (34) and (35)). As heretofore described, the column signal generation circuit of FIG. 7 implements partial orthogonal function driving. 
     In case a display apparatus having N rows is to be driven by using an orthogonal function, which is divided into K parts while taking R rows as the unit, as the voltage function in the embodiment and modification heretofore described, division into K parts has been conducted consecutively as shown in FIGS. 7 and 15. The embodiment and modification can also be implemented by using an orthogonal function shown in FIG.  16 . The orthogonal function of FIG. 16 provides “0” in the embodiment described before, and provides an alternate combination of “0” and “W 0 ” during intervals yielding W 0  in the modification. Detailed description of the embodiment of this case will not be given, but it would be evident from the description of the embodiment described before and the above described modification that this can be implemented in the same way. Furthermore, in FIG. 16, “0” and “W 0 ” are alternated. However, this is not restrictive, but the number of them and how to give them may also be changed. 
     A second embodiment of the present invention will now be described. Assuming now that a display apparatus having N rows is driven by 8 rows with 16 divisions, for example, the second embodiment shows a concrete circuit of a driving method whereby 16 divisions are distributed among W 1  to W 4  each having 4 divisions (i.e., k1 to k4 included in 16 divisions k1 to k16 are distributed to W 1 , and k5 and k8 are distributed to W 2 , whereas k9 to k12 are distributed to W 3 , and k13 to k16 are distributed to W 4 ). In this case, 16 divisions are simply distributed. Therefore, it is evident that the display apparatus can be driven by display-on voltage and display-off voltage identical with those of the first embodiment by conducting computation on the 8 rows and calculating voltages to be applied to column electrodes during the distributed time. As a known example, Japan Display &#39;92 Digest, pp. 503 to 505 can be mentioned. However, its operation and concrete circuit are not described therein. 
     The second embodiment will hereafter be described in detail by referring to drawings. FIG. 17 is a block diagram of a liquid crystal display apparatus of the second embodiment. Numeral  35  denotes display data,  36  an H signal which is a horizontal synchronizing signal, and  37  a V signal which is a vertical synchronizing signal. Numeral  38  denotes DCLK synchronized with the display data  35 . Numeral  39  denotes a display signal representing a duration for the display data  35  to be displayed on the display apparatus, by “high” levels. As for the display data  35 , it is assumed that 640 dots for one line are transmitted during one horizontal interval equivalent to one period of the H signal  36  and data for 240 lines are transmitted during one frame time equivalent to one period of the V signal  37 . Numeral  40  denotes a frame memory controller,  41  frame memory write data,  42  a frame memory control signal for controlling writing and reading data inputted to the frame memory, and are a data control signal. The controller  40  performs serial-parallel conversion on the display data  35  and generates the frame memory data  41  as 4-dot parallel data. Furthermore, the controller  40  generates signals for the control signal  42  and  43  on the basis of the H signal  36 , V signal  37 , DCLK  38 , and display signal  39 . Details of these generated signals will be described later. Numeral  44  denotes a frame memory, and numeral  45  denotes frame memory read data. Numeral  46  denotes a column signal generation circuit. In the same way as the first embodiment, the column signal generation circuit  46  conducts computation on the frame memory read data  45  for 8 lines and generates liquid crystal data  47 . Numeral  48  denotes a column signal control signal, and numeral  49  denotes a function signal. The column signal control  48  and the function signal  49  are generated by the generation circuit  46 . Numeral  50  denotes a row function generation circuit,  51  row data, and  52  a row data control signal. By using the function signal  49 , the generation circuit  50  generates the row data  51  and the row data control signal  52 . Numeral  53  denotes a column electrode driver. Numerals  54  to  56  denote column electrode signals of the first column, the second column, and the 640th column, respectively. The liquid crystal data  47  are written into the driver  53  by the column signal control signal  48 . On the basis of the liquid crystal data  47 , the driver  53  selects one out of 9 kinds of voltage and outputs ti to the corresponding column electrode. In FIG. 17, the 9 kinds of voltage are not illustrated. As one example, however, the 9 kinds of voltage can be realized by generating the 9 kinds of voltage in an external voltage divider circuit using resistors and giving them to the column electrode driver. Numeral  57  denotes a row electrode driver. Numerals  58  to  60  denote row electrode signals of the first row, the second row, and the 240th row. The row data  51  are written into the driver  57  by the signal on the row data control signal  52 . On the basis of the written row data  51 , the driver  57  selects one out of three kinds of voltage and outputs it to the corresponding column electrode. In FIG. 17, the three kinds of voltage are not illustrated. However, the circuit therefor can be formed in the same way as the case of the driver  53 . Furthermore, operation of the drivers  53  and  57  is identical with that of a TFT liquid crystal driver “HD66310” produced by Hitachi Ltd. with the exception of the number of selected voltages. It would be thus self-evident that the drivers  53  and  57  can be easily formed. Numeral  61  denotes a liquid crystal display panel having 640 dots in the lateral direction and 240 lines in the longitudinal direction. The intersection of a column electrode and a row electrode forms one dot. By the effective value of the potential difference at the intersection, display-on and display-off are represented. 
     FIGS. 18A to  18 F are timing diagrams of display data  35  inputted to the present liquid crystal display apparatus. FIGS. 19A to  19 F are timing diagrams showing timing of the frame memory read data  45  read from the frame memory  44  and the data control signal  43 . In FIGS. 19A to  19 F, a read V signal  81 , a read H signal  82  and a read display signal  83  are of the data control signal  43 . 
     FIG. 20 is a block diagram of the frame memory  44 . Numeral  62  denotes a frame memory-A for storing display information of 640 dots×240 lines for one frame. Numeral  63  denotes a frame memory-B for storing display information for one frame in the same way. Numeral  64  denotes AW reset for ordering the memory-A  62  to reset the write address,  65  AW clock for writing data into the memory-A  62 ,  66  AR reset for ordering the memory-A  62  to reset the read address, and  67  AR clock for reading data into the memory-A  62 . Numeral  68  denotes BW reset for ordering the frame memory-B  63  to reset the write address,  69  BW clock for writing data into the memory-B  63 ,  70  BR reset for ordering the memory-B  63  to reset the read address, and  71  BR clock for reading data into the memory-B  63 . Numeral  72  denotes a frame memory R/W signal. The R/W signal  72  indicates writing data into the memory-A  62  and reading data from the memory-B  63  when it is at a “high” level. The R/W signal  72  indicates reading data from the memory-A  62  and writing data into the memory-B  63  when it is at a “low” level. Numerals  73  and  74  denote selectors A and B, respectively. The selector-A  73  and the selector-B  74  conduct selection operation respectively in accordance with the R/W signal  72 . Numeral  75  denotes memory-A reset,  76  memory-A clock,  77  a memory-A R/W signal,  78  memory-B reset,  79  memory-B clock, and  80  a memory-B R/W signal. 
     The memory-A  62  and memory-B  63  conduct read/write operation in accordance with respective R/W signals  77  and  80 . (Write operation is conducted when the R/W signal is “high”, whereas read operation is conducted with the R/W signal is “low”.) Read and write addresses of the memory-A  62  and memory-B  63  are reset to “0” by respective reset signals  75  and  78 , and thereafter increased after write/read operation has been conducted by respective clocks  76  and  79 . 
     FIGS. 21A to  21 E are timing diagrams illustrating operation of the frame memory  44 . FIG. 22 is a block diagram of the column signal generation circuit  46  shown in FIG.  17 . In FIG  22 , numeral  85  denotes a write circuit,  86  A data,  87  A control signal,  88  a line address,  89  B control signal,  90  B data,  91  an AW signal,  92  a line memory A, and  93  a line memory B. The write circuit  85  outputs the frame memory read data  45  having 4 parallel bits as the A data  86  and B data  90 . In addition, the write circuit generates signals for the A control signal  87 , line address  88 , B control signal  89 , and AW signal  91  on the basis of the signal on the data control signal  43 . Write operation is conducted alternately to the line memory-A  92  and line memory-B  93  every 8 lines of the read data  45 . A “high” level of the AW signal  91  indicates writing data into the line memory-A  92 , whereas a “low” level of the AW signal  91  indicates writing data into the line memory-B  93 . Numeral  95  denotes an A read control signal,  96  a B read control signal,  94  a read circuit,  97  A read data, and  98  B read data. By using the data control signal  43 , the read circuit  94  generates the A read control signal  95  and B read control signal  96  and reads data from the line memory-A  92  and line memory-B  93  respectively as the A read data  97  and B read data  98 . As for this read operation, data are read from a line memory, which is not being subjected to write operation, by using the AW signal  91 . Numeral  99  denotes 8-line data which are read data. Numeral  100  denotes a read count. The 8-line data  99  and the read count  100  are generated by the read circuit  94 . Numeral  101  denotes a function generation circuit. Numeral  102  denotes orthogonal function data. The generation circuit  101  generates eight orthogonal functions with 16 divisions by using the data control signal  43  and outputs them as the orthogonal function data  102 . Numeral  103  denotes a computation circuit, which calculates the sum of products of the 8-line data  99  and the orthogonal function data  102  and outputs liquid crystal data  47 . Its concrete computation method and circuits will be described later. 
     FIG. 24 is a block diagram depicted from a viewpoint of write operation of the line memory-A  92  shown in FIG.  22 . Numeral  113  denotes AW reset and number  114  denotes AW clock. The AW reset  113  and AW clock  114  are signals on the A control bus  87 . Numerals  106  to  108  denote line memories each storing display information corresponding to one line. Numerals  106 ,  107  and  108  denotes a line-1 memory, a line-2 memory, and a line-8 memory, respectively. In FIG. 24, line-3 to line-7 memories are not illustrated for clarity. Numeral  109  is a write address decoder. The write address decoder  109  decodes the line address  88  and indicates which line memory data should be written into . Numeral  110  denotes a line memory- 1  write signal,  111  a line memory- 2  write signal, and  112  a line memory- 8  write signal. Write operation is conducted for a memory having a “high” write signal. In each line memory, the write address is reset to “0” by the AW reset  113 , and thereafter write operation and address increment are successively conducted by the AW clock  114 . FIGS. 23A to  23 D and FIGS. 25A to  25 E are diagram illustrating the write operation of data into the line memory-A  92 . 
     FIG. 26 is a block diagram depicted from a viewpoint of read operation of the line memory-A  92 . An AR reset  116  and an AR clock  117  are signals of the A read control bus  95 . Numerals  113  to  115  denote read data of the line- 1  memory  106 , line- 2  memory  107  and line- 8  memory  108 , respectively. Numerals  113 ,  114  and  115  denote line memory A 1  data, line memory A 2  data and line memory A 8  data, respectively. As for read operation, the read address is set to “0” by the AR reset  116 , and thereafter one dot is read simultaneously from every 8-line memories including the line- 1  memory  106  to line- 8  memory  108 . Thus 640 dots are successively read out. FIGS. 27A to  27 I are timing diagrams illustrating the operation of reading data from the line memory-A  92 . 
     FIG. 28 is a block diagram of the computation circuit  103  shown in FIG.  22 . Numeral  119  denotes an EX-OR circuit, which conducts exclusive OR operation on each data of the 8-line data  99  containing 1-bit data information corresponding to 8 lines and each data of orthogonal function data  102  containing 8 orthogonal functions. Numeral  120  denotes computation data outputted from the EX-OR  119 . Numeral  121  denotes a decoder for decoding the number of “high” levels contained in the computation data  120 . The result of decoding is outputted as the liquid crystal data  47 . 
     FIG. 29 is a block diagram of the function generation circuit  101 . Numeral  122  denotes an orthogonal function memory for storing 8 kinds of orthogonal function data corresponding to 16 divisions. In accordance with a field signal  84  and the read count  100 , the orthogonal function memory  122  outputs orthogonal function data  102  containing values of 8 kinds of orthogonal functions. Numeral  123  denotes a line block counter, and numeral  124  denotes a line block signal. By taking the read V signal  81  as a reference, the line block counter  123  conducts count operation with respect to the read H signal  82  while taking 8 lines as the unit and outputs the counted value as the line block signal  124 . FIG. 30 is a diagram illustrating operation of the orthogonal function memory  122 . FIGS. 31A to  31 C are timing diagrams illustrating operation of the line block counter  123 . FIGS. 32A to  32 F are timing diagrams illustrating operation of the column electrode driver  53 . 
     FIG. 33 is a block diagram of the row function generation circuit  50 . Numeral  125  denotes a horizontal clock,  126  a liquid crystal clock,  128  a partial count value, and  129  a partial clock. They are generated by the column signal generation circuit  46 . Numeral  127  denotes a partial counter. The partial counter  127  is reset by the horizontal clock  125  and repetitively counts up to eight by using the liquid crystal clock  126 . The partial counter  127  outputs the counted value as the partial count value  128  and generates the partial clock  129  having a period of counting up to eight. Numeral  130  denotes a block counter, and  131  denotes a block value. The block counter  130  is reset by the horizontal clock  125 . The block counter counts by using the partial clock  129  and outputs the counted value as the block value  131 . Numeral  132  denotes a comparator, and  133  denotes a comparator output. The comparator  132  compares the line block output  124  with the block value  131 . When they coincide with each other, the comparator  132  makes the comparator output  133  “high” . Number  134  denotes a P-S circuit. The orthogonal function data  102  containing 8 kinds of orthogonal functions are inputted to the P-S circuit  134 . In accordance with the partial count value  128 , the P-S circuit outputs one kind at a time. Numeral  135  denotes serial orthogonal data outputted from the P-S circuit  134 . Numeral  136  denotes a selector. When the comparator outputs  133  is “high”, the selector  136  outputs serial orthogonal data. Otherwise, the selector  136  outputs “0”. 
     First of all, outline of operation of the second embodiment will be described by referring to FIG.  17 . Thereafter, operation of respective blocks shown in FIG. 17, which is the block diagram of the liquid crystal display apparatus, will be described in detail by referring to FIGS. 18 to  34 . 
     As for the inputted display data  35 , data corresponding to one screen to be displayed during one frame interval are transmitted serially. The frame memory controller  40  converts the display data  35  to 4-bit parallel data and writes the 4-bit parallel data successively into the frame memory  44 . The controller  40  reads 4-bit parallel display data  35  stored one frame before from the frame memory  44  four times with a period equivalent to one fourth of the frame period of the input. According to the read timing, the controller  40  generates the read V signal  81 , read H signal  82 , read display signal  83 , field signal  84 , and reference clock having the same period as that of the DCLK on the basis of the inputted H signal  36 , V signal  37 , DCLK  38 , and display signal  39 . The controller  40  outputs the read V signal  81 , read H signal  82 , read display signal  83 , field signal  84 , and reference clock to the column signal generation circuit  46  via the data control signal  43 . The field signal  84  indicates the number of times of reading up to four, and has a value of “1” to “4”. They are referred to as the first field to the fourth field, respectively. On the basis of the signal on the data control signal  43  and the frame memory read data  45 , the generation circuit  46  generates liquid crystal data  47  and the column signal control signal  48  and outputs them to the column electrode driver  53 . The generation circuit  46  takes in the frame memory read data  45  corresponding to 8 lines, reads out one dot data simultaneously from every 8 lines, conducts computation on the 8-line data thus read out and orthogonal function data, and generates the liquid crystal data  47 . In this computation, computation of data of the first field with the orthogonal function of W1 is conducted as shown in FIG.  16 . Computation of data of the second field with the orthogonal function of W2 is conducted. Computation of data of the third field with the orthogonal function of W3 is conducted. Computation of data of the fourth field with the orthogonal function of W4 is conducted. The row function generation circuit  50  controls the row electrode driver  57  so that the driving voltage of the orthogonal function and “0” shown in FIG. 16 may be supplied to respective row electrode signals. In order to attain synchronization with the orthogonal function of computation in the generation circuit  46 , the generation circuit  50  generates row data  51  by using the function signal bus  49 . 
     Details of operation of respective blocks will hereafter be described. 
     Timing of the inputted display data  35  of FIG.  17  is shown in FIGS. 18A to  18 F. The display data  35  having 240 lines in the longitudinal direction. During one frame interval equivalent to one period of the V signal  37  (herein 16 ms), data of 240 lines arrive. One line is represented in one period of the H signal  36 . During an effective interval indicated by the “high” level of the display signal  39  in the one period, data of 640 dots successively arrive in series. As for the display data  35 , therefore, one screen is formed by 640 dots in the lateral direction and 240 lines in the longitudinal direction. The display data are converted to 4-bit parallel data. The resultant 4-bit parallel data are written into the frame memory  44 , and read out with a period equivalent to one fourth of the original period as shown in FIG.  19 B. 
     Read operation and write operation of the frame memory  44  will now be described. The frame memory  44  can be formed by the configuration as shown in FIG.  20 . When the frame R/W signal  72  is “high”, data should be written into the memory A as shown in FIG.  21 C. Therefore, the selector A selects the AW reset  64  and AW clock  65 , outputs them as the memory-A reset  75  and memory-A clock  76 , and makes the memory AR/W signal “high”. As a result, the memory A resets the address by using the AW reset  64  having the same timing as the V signal  37  has, and thereafter writes the frame memory write data  41  existing during the “high” interval of the display signal  39  by using the AW clock  65 . Here, the AW clock  65  is a clock signal synchronized with the frame memory write data  41 , i.e., having a period equivalent to one fourth of the period of the DCLK  38 . The AW clock  65  becomes the clock output for only data existing during the “high” interval of the display signal  39 . When this write operation is being conducted, the selector-B  74  selects the BR reset  70  and BR clock  71  as the memory-B reset  78  and memory-B clock  79  and keeps the memory-B R/W signal at the “low” level. As shown in FIG. 21C, therefore, the memory B conducts read operation in synchronism with the read V signal having a frequency which is four times as high as that of the V signal  37 . In order to read data at a speed which is four times as fast as that of writing, the BR clock  71  has a period equivalent to one fourth of the period of the write clock, i.e., equivalent to the period of the DCLK  38 . When the frame memory R/W signal  72  is “low”, the selector-A  73  and selector-B  74  select the AR reset  66 , AR clock  67 , BW reset  68  and BW clock  69 , make the memory-A R/W signal  77  and memory-B R/W signal  80  respectively “low” and “high”, and cause read operation and write operation to be conducted respectively with respect to the memory-A  62  and memory-B  63 . As heretofore described, the operation of the controller  40  and frame memory  44  causes the display data  35  shown in FIG. 18C to be written into the frame memory  44 . With a delay of one frame interval, the data are read out four times with a period equivalent to one fourth of the original period as shown in FIG.  19 B. Although not illustrated in FIGS. 19A to  19 F, the frame memory read data  45  is in synchronism with the read clock having the same period as the inputted DCLK  38  has, and this read clock is included in the data signal control bus  43 . 
     Detailed operation of the column signal generation circuit  46  will now be described. The frame memory read data  45  are 4-bit parallel data and are written into the line memory-A  92  or line memory-B  93  by the write circuit  85 . As shown in FIG. 23A, the write circuit  85  generates a line address  88 . The line address  88  is obtained by counting the read H signal  82  while taking the read V signal  81  as the reference and repetitively assumes the value of 1 to 8. In addition, the write circuit  85  causes the AW signal  91  to repetitively become “high” and “low” every 8 lines. The AW signal  91  is a signal indicating the line memory into which the frame memory read data  45  should be written. When the AW signal  91  is “high”, writing data into the line memory-A  92  is indicated. When the AW signal  91  is “low”, writing data into the line memory-B  93  is indicated. 
     Assuming now that the AW signal  91  is “high”, operation of writing data into the line memory-A  92  will now be described by referring to FIG.  24  and FIGS. 25A to  25 F. When the AW signal  91  is “high”, the write address decoder  109  shown in FIG. 24 enables write operation successively with respect to eight line memories, i.e., the line- 1  memory  106  to line- 8  memory  108  on the basis of the value of the line address  88 . That is to say, for each line memory, the write address is reset by the AW reset  113  which is identical with the read H signal  82  as shown in FIG.  25 A. By the AW clock  114  which is the clock synchronized with data existing during the “high” interval of the read display signal  83 , the A data  86  are successively written into the line memory line by line. The line memory-B  93  can be realized by the same configuration as that of FIG.  24 . However, the write address decoder included in the line memory-B  93  enables each write signal in accordance with the line address  88  when the AW signal  91  is “low”. When the AW signal  91  is “low” (i.e., when data are written into the line memory-B  93 ), read operation of the line memory-A  92  is conducted by using the read circuit  94 . 
     This read operation will now be described by referring to FIG.  26  and FIGS. 27A to  27 I. In the line- 1  memory  106  to line- 8  memory  108 , the read address is reset by the AR reset  116  and thereafter data are read successively by the AR clock  117  at the rate of one bit from every line memory. At this time, the read circuit  94  generates the AR reset  116  four times while the AW signal  91  is “low” as shown in FIG. 17E, i.e., every two periods of the read H signal  82 . Furthermore, the read count  118  is increased from 1 to 4 at this time. In one period of the AR reset  116 , data of 640 dots are successively read out by the AR clock  117  and outputted as the A read data  97  of 8-line data. This operation is true of the frame memory B as well. When the AW signal is “high”, the read circuit  94  outputs the BR clock and BR reset onto the B read control bus to conduct read operation. As understood from FIGS. 25A to  25 E, the AW reset  113  and AW clock  114  are outputted only when the line memory-A  92  is conducting write operation. In the same way, the BW reset and BW clock are also outputted only when the line memory-B  93  is conducting write operation. It is the same with the read reset and read clock. The 8-line data  99  of the data read out are inputted to the computation circuit  103  and subjected to computation together with the orthogonal function data  102  in the EX-OR  119  as shown in FIG.  28 . The number of “1”s in the resultant output is decoded and outputted as the liquid crystal data  47 . At this time, the orthogonal function data  102  for computation is generated by the function generation circuit  101  shown in FIG.  29 . 
     In accordance with the field signal  84  and read count  100 , the orthogonal function memory  122  generates orthogonal function data  102  on the basis of relations shown in FIG.  30 . That is to say, orthogonal function data of division time K 1  to K 4  corresponding to W 1  of FIG. 16 are generated when the field signal  84  is “1”. When the field signal is “2”, orthogonal function data of division time K 5  to K 8  corresponding to W 2  are generated. When the field signal is “3”, orthogonal function data of division time K 9  to K 12  corresponding to W 3  are generated. When the field signal is “4”, orthogonal function data of division time K 13  to K 16  corresponding to W 4  are generated. 
     As for the line block counter  123 , the frame memory read data  45  are once written into the line memory and thereafter read out as shown in FIGS. 31A to  31 C, and hence the frame memory read data  45  are delayed by time corresponding to 8 lines. Therefore, the line block counter  123  counts from one up to 30 at timing delayed by 8 lines with respect to the read V signal  81 . (240 lines are divided into 30 parts each having 8 lines.) That is to say, the line block signal  124  outputted from this line block counter  123  indicates the block (block  1  to  30  each containing 8 lines) of the line read out from the line memory and presently computed in the computation circuit  103 . The column signal control signal  48  contains the horizontal clock  125  and liquid crystal clock  126 . Respective signals are generated by the read circuit  94 . The horizontal clock  125  has a period, which is equal to the period of the AR reset  116  and which is twice the period of the read H signal  82 . The liquid crystal clock  126  has a period equivalent to that of the read clock. The horizontal clock  125  and liquid crystal clock  126  can be represented by OR operation of the AR reset  116  and BR reset and OR operation of the AR clock  117  and BR clock, respectively. 
     The column electrode driver  53  latches successively the liquid crystal data  47  by the liquid crystal clock  126 . In response to the horizontal clock  125  after latch of data corresponding to 640 dots, the driver  53  selects one kind out of 9 kinds of voltage as the columnn electrode signal on the basis of information of liquid crystal data  47  of respective dots and outputs it. That is to say, the liquid crystal data  47  is converted into voltage with a delay of one period of the horizontal clock  125  as shown in FIGS. 32A to  32 F, and the resultant voltage is supplied to the liquid crystal display panel  61 . Characters  1 -k 1 ,  1 -k 2 , . . . denote results of computation of the orthogonal function with division time k 1 , k 2 , . . . on display data of the first block (the first row to the eighth row). 
     Operation of the row function generation circuit  50  will now be described. The generation circuit  50  controls the row electrode driver  57  so that the orthogonal function may be outputted with respect to the line which is being subjected to computation in the column signal generation circuit  46 . The generation circuit  50  can be realized by the configuration shown in FIG.  33 . As shown in FIG. 33, the partial counter  127  is reset by the horizontal clock  125 . The partial counter  127  repetitively counts from one up to 8 and outputs the count as the partial count value  128 . In addition, the partial counter  127  causes the block counter  130  to count the liquid crystal clocks  129  having a period of counting up to 8. That is to say, the row data control signals for controlling the driver  57  contains the horizontal clock  135  and liquid crystal clock  126 . Therefore, the row data  51  other than those having the same block value  131  as the line block signal  124  has are set to “0”. The comparator  132  and the selector  136  function for this purpose. When the line block signal  124  has coincided with the block value  131 , the orthogonal function data  102  which have been used for the computation in the generation circuit  46  are outputted as row data  51  bit by bit via the P-S circuit  174 . As a result, it becomes possible to provide only rows of the computed blocks with the orthogonal function data and provide other rows with “0”. 
     Owing to the operation heretofore described, it becomes possible to control the computation for column electrodes and application of voltage to row electrodes and it becomes possible to drive liquid crystal display panel with distributed division time. In the present embodiment, frame memory read operation is conducted four times during the period of the write operation. However, this is not restrictive, but read operation may be conducted x times. Furthermore, the number of lines per block is 8. However, the number of lines per block may be y in the same way as the first embodiment. 
     In the circuit configuration of the second embodiment, line memories are used in the generation circuit  46  as shown in FIG.  22 . However, this is not restrictive, but the second embodiment may also be inplemented in a configuration which does not use line memories. This modification will now be described. In the modification of the liquid crystal display apparatus, writing the display data into the frame memory  44  and reading the frame memory read data  45  therefrom are controlled by the frame memory controller  40 . FIGS. 34A to  34 F are timing diagrams illustrating the operation of reading data from the frame memory  44 . FIG. 35 is a block diagram of the column signal generation circuit  46 . In FIG. 35, numeral  140  denotes a data converter for making data rearrangement of the frame memory read data  45 . Other blocks are identical with those of the second embodiment and they conduct the same operation. FIGS. 36A to  36 F are timing diagrams illustrating the operation of the data converter  140 . The operation of this modification will hereafter be described by referring to drawings. Inputted display data  35  and timing signal are inputted at timing shown in FIGS. 18A to  18 F. The inputted display data  35  are written into the frame memory  44  by the frame memory controller  40 . By using the inputted timing signals, i.e., the H signal  36 , V signal  37 , DCLK  38 , and display signal  39 , the controller  40  generates signals of the frame memory control signal  42 . These operations are identical with those of the second embodiment. The display data  35  written into the frame memory  44  are read out by the controller  40  and supplied to the column signal generation circuit  46  as the frame memory read data  45 . In accordance with the timing of this read operation, the controller  40  generates reference clocks having the same periods as those of the read V signal  81 , read H signal  82 , read display signal  83 , field signal  84  and DLCK  38  on the data control signal  43 . This read operation will hereafter be described. In the same way as the second embodiment, data are read from the memory-A  62  or memory-B  63 , which is included in the frame memory of FIG.  20  and which is not being subjected to write operation, four times during the period of the V signal  37  equivalent to the frame period of input as shown in FIGS. 34A to  34 F. Therefore, the read V signal  81  has four periods during one frame interval of the input and forms the first to fourth fields indicated by the field signal  84 . During one field interval, the read H signal  82  has 30 periods. During one period, display data for 8 lines are read out from the frame memory  44 . In the first period of the read H signal  82 , therefore, data of the first to eighth lines are read by 4 bits in the horizontal direction as shown in FIG. 34E to form the frame memory read data  45 . In FIG. 34E, L 1 , L 2 , . . . , L 8  denote data of the first line, second line, . . . , eighth line, respectively. 
     In this modification, the order of reading the frame memory read data  45  is changed from that of the second embodiment. With the exception of difference in period of the read H signal  82  caused therefrom, the operation of the modification is identical with that of the second embodiment. 
     The frame memory read data  54  are supplied to the generation circuit  46  together with the signal on the data control signal  43 . The circuit  46  can be realized by the configuration shown in FIG.  35 . As shown in FIGS. 36A to  36 F, the data converter  140  converts the frame memory read data  45  containing data for 8 lines each having 4 bits in the horizontal direction to 8-line data  99  containing 8 bits having one bit in the horizontal direction for each of 8 lines. As shown in FIG. 35, the 8-line data  99  are supplied to the computation circuit  103  and converted to the liquid crystal data  47 . Operation of the computation circuit  103  is similar to that of the second embodiment. Even if line memories are not used, the same operation as that of the second embodiment can be implemented. 
     As represented by a liquid crystal display apparatus  143  shown in FIG. 37, the liquid crystal display apparatus of the embodiments heretofore described is often connected in use with a display controller  141  of system apparatus, which is a display control circuit of an information processing apparatus such as a personal computer, work station, or word processor generating display data, via an interface signal  142 . The interface signal used at this time is shown in FIGS. 38A to  38 F. This is the input signal used in the above described embodiments, and includes the V signal  37 , H signal  36 , display data  35 , display signal  39  and DCLK  38 . The V signal  37  is a signal indicating the interval for sending display data of one screen to the liquid crystal display apparatus  143 . One period thereof is referred to as one frame. The H signal  36  indicates the interval for sending data of display data for one line. One period thereof is referred to as one horizontal interval. As for the display data  35 , data of one screen are serially send to the liquid crystal display apparatus  143  bit by bit in accordance with the above described timing. Although not illustrated, the DCLK  38  is a clock synchronized with the display data. The display signal  39  is a signal indicating data which are included in the display data  35  and which should be displayed on the liquid crystal display apparatus. In FIGS. 38A to  38 F, data which are not displayed and referred to as retrace data are present only in the horizontal direction (as represented by data preceding data “1” of the illustrated display data  35  and data succeeding data “ 640 ”). However, this is not restrictive, but retrace line data of several lines may also be used. 
     The interface of the information processing apparatus is not restricted to this. For example, by providing the frame memory controller, frame memory, column signal generation circuit, row function generation circuit and the like used in each embodiment in the display controller  141  of system apparatus, the interface signal  142  as shown in FIGS. 39A to  39 F or FIGS. 40A to  40 F can also be used. 
     FIGS. 39A to  39 F are timing diagrams showing an example of the interface signal  142  in case where the frame memory controller and frame memory of the second embodiment are provided in the display controller  141  of system apparatus. This signal includes the frame memory read data  45  and data control signal  43  shown in FIGS. 19A to  19 F. Although not illustrated, a clock synchronized with the read data  45  is also needed. Although the read data  45  are 4-bit parallel data, this is not restrictive. As for the number of parallel bits, one bit serial stream or an arbitrary plurality of bits may be used. In case of parallel transmission, it is also conceivable to add a clock having a data period of one dot as the interface signal for the purpose of simplifying timing design of the processing circuit of the liquid crystal display apparatus side. 
     FIGS. 40A to  40 F are timing diagrams showing an example of the interface signal  142  in case where the frame memory controller and frame memory of the second embodiment are provided in the display controller  141  of system apparatus. This signal includes the frame memory read data  45  and data control signal  43  shown in FIGS. 34A to  34 F. Although not illustrated, a clock synchronized with the read data  45  is also needed. Although the read data  45  are 4-bit parallel data in FIGS. 39A to  39 F, this is not restrictive. As for the number of parallel bits, one bit serial stream or an arbitrary plurality of bits may be used. As for readout in the line direction as well, it is also possible to send 8-bit data in order by sending, for example, 8-bit data of the first line, then 8-bit data of the second line, 8-bit data of the third line, and so on. That is to say, the features here is that data of one horizontal period are not sent in order, but data of a plurality of lines are sent alternately. In case of parallel transmission, it is also conceivable to add a clock having a data period of one dot as the interface signal for the purpose of simplifying timing design of the processing circuit of the liquid crystal display apparatus side. 
     The feature of the interface signal in the above described two embodiments is that data of the same screen are sent a plurality of times. Four times and other timing are not restrictive. As compared with the data signal control bus  43  of the second embodiment, there is no field signal. However, this can be easily generated from the V signal and read V signal. 
     An example of the interface signal  142  in case where the column signal generation circuit and row function generation circuit are provided in the display controller  141  of system apparatus will now be described. Taking FIG. 17 as an example, the interface signal  142  of this case includes the liquid crystal data  47 , row data  51  and the column data control signal  48  and row data control signal  52 . Features at this time are that the liquid crystal data are the result of computation of display data of a plurality of lines with an orthogonal function applied to the plurality of lines and the interface for the row electrode driver includes not only the timing signal but also the row data  51  for controlling the operation thereof. Furthermore, such configuration that only the row function generation circuit is provided in the liquid crystal apparatus  143  is also conceivable. At this time, the function signal  49  joins in the interface signal  142  instead of the row data  51  and the row data control signal  52 . The signal of the function signal is formed by, for example, the orthogonal function data  102  indicating data of the orthogonal function to be computed with display data of a plurality of lines as shown in the second embodiment, the line block signal  124 , the horizontal clock  125 , and the liquid crystal clock  126 . It should be noted in this case that there is orthogonal function data  102  used for the computation of the liquid crystal data  47  as the interface signal  142 . Furthermore, the above described timing signal is not restrictive, but a timing signal capable of converting the orthogonal function data  102  to row data  51  for driving the row electrodes driver  57  and capable of generating the signal of the row data control signal  52  suffices. 
     An embodiment in case where the function described before by referring to the embodiments is provided in the display controller  141  of system apparatus will now be described by referring to drawing. FIG. 41 is a block diagram of an example of the display controller  141  of system apparatus. Numeral  144  denotes a CPU which is a central arithmetic unit,  145  and an address bus,  146  a data bus,  147  a display controller,  148  a display memory bus,  149  a display memory for storing display data,  150  display palette data,  151  a display timing control signal bus,  152  a palette circuit, and  153  display data .The interface signal  142  at this time has timing shown in FIGS. 18A to  18 F. (DCLK is not illustrated.) By using the display controller  147 , the CPU  144  indicates the write or read position of the display memory  149  via the address bus and conducts data write or read position via the data bus. Thereby, the CPU  144  can write a picture to be written in the display memory and read it from the display memory  149 . The display controller  147  mediates the write and read operation conducted with respect to the display memory  149  by the CPU  144  and reads data from the display memory  149  to send data to be displayed to the display apparatus. Furthermore, the display controller  147  generates the display timing control signal  151 . Data read out from the display memory  149  by the display controller  147  become the display palette data  150 , and become the display data  153  via the palette circuit  152 . Typically, the palette circuit  152  converts the display palette data  150  to color information. Since it is now supposed that monochrome display is used, the palette data  150  are used as the display data  153  as they are. 
     FIG. 42 shows an embodiment of a display controller of system apparatus in case the interface signal shown in FIGS. 39A to  39 F is used. As compared with the above described case where the functions of the frame memory controller and frame memory are provided in the system apparatus as they are, the capacity of the memory for storing the display data can be reduced to ⅔. FIG. 42 is a block diagram of an embodiment of a display controller of system apparatus. As compared with the conventional configuration, how the display controller  147  reads data from the display memory  149  is changed and in addition a buffer memory for storing the data thus read out is provided. As shown in FIG. 20, the frame memory described before uses two memories each storing data for one screen. In the present embodiment, however, a buffer  154  stores data corresponding to one screen. Numeral  155  denotes buffer data. FIG. 43 is a block diagram of the buffer  154 . Numeral  156  denotes a selector which switches the palette data  150  or stored data. Numeral  157  denotes a buffer memory read/write circuit,  158  a data changeover signal,  159  a memory control signal,  160  memory data, and  161  memory read data. Numeral  162  denotes a memory for storing display data for one screen. In order to control writing and reading with respect to the memory  162 , the read/write circuit  157  generates the memory address and the memory control signal  159 , which is used for memory write and read operation, by using the display timing control signal  151 . FIGS. 44A to  44 I are timing diagrams illustrating the palette data  150 . As shown in FIGS. 44A to  44 I, the display controller  147  of FIG. 42 reads out data corresponding to one screen from the display memory  149  during the first period (the first field) of the read V signal having a period (one field interval) equivalent to one fourth of one frame interval and sends the data for one screen as the palette data  150 . During the subsequent second field to the fourth field, the display controller  147  does not read out data from the display memory. During one field period, the read H signal has 260 periods. In the tenth period to 249th period of the read H signal, the palette data  150  have data of the first line to 240th line. In FIG. 44E, this is represented by L 1  to L 240 . The read display signal is a signal which becomes “high” when the palette data  150  become the displayed data. As for palette data  150 , data of 640 dots represented by “1” to “640” in one period of the read H signal become serial data. In the first field, such palette data  150  are selected as the buffer data  155  by the selector  156 . In addition, the palette data  150  is the first field are written into the memory  162  by the read/write circuit  157 . In the second field and succeeding fields, written data are read out from the memory  162  by the read/write circuit  157  at the same timing as that of the palette data  150  to become the memory read data  161 . At this time, data for one screen are read during one field. In the second to fourth fields, the memory read data  161  are selected to fourth buffer data  155  by the selector  156 . Therefore, the buffer data  155  become the display data  153  via the palette circuit  152  and becomes identical with the frame memory read data shown in FIG.  39 E. By using the display timing control signal  151 , the read/write circuit  157  generates various control signals. However, this will not be described here in detail. It would be evident that they can be easily generated from the timing signals shown in FIGS. 44A to  44 I and dot clocks used as the reference signal of palette data. 
     In the present embodiment, one frame interval during which data for one screen have been read out is divided into a plurality of field intervals. During one field included therein, display data are read from the display memory  149 , used as the display data  153  as they are, and in addition stored in the memory  162 . In the remaining fields, data stored in the memory  162  are read out at the rate of one screen per field and used as the display data  153 . As compared with the embodiments described before, therefore, the capacity of the memory  162  can be equivalent to that for one screen. 
     In order to illustrate the operation of reading data from the display memory  149  conducted by the display controller  147  in case the interface signal shown in FIGS. 40A to  40 F is used in the present embodiment, FIGS. 45A to  45 I show timing of the palette data  150 . As shown in FIGS. 45A to  45 I, data for one screen are read in the first field by the display controller  147  to become the palette data  150 . As for the palette data  150 , data for one screen are read during 30 periods of the read H signal, and data corresponding to 8 lines are read during one period. In LL 1  shown in FIG. 45E, therefore, data of 8 lines ranging from the first line to the eighth line are read. In LL 2 , data of the ninth line to 16th line are read. In LL 30 , data of the 233rd line to 240th line are read. During one period of the read H signal, data for 8 lines are read at the rate of one dot per line. This is repeated. (In FIG. 45H, L 1 , L 2 , . . . , L 8  denote the first line, the second line, . . . , the eighth line, and “1” to “640” denote the first dot to the 640th dot.) 
     A third embodiment of the liquid crystal display apparatus according to the present invention will now be described. The liquid crystal display apparatus of the present embodiment is basically identical with that shown in FIG.  5 . In this example, however, the column signal generation circuit  17  has the block diagram shown is FIG.  46  and generates the column data  16  by computing the display data  1  with the row function data  23  outputted by the row function generation circuit  22 . In addition, the column signal generation circuit  17  outputs an overflow signal  206  to the row function generation circuit  22 . The liquid crystal panel has 240 rows (N=240). The column electrode driver  18  is capable of generating voltages of 64 levels. Data for one row are taken in one division interval. The row electrode driver  24  takes in function values corresponding to the number of rows in one division interval from the row function data  23 , and thereafter simultaneously outputs voltages depending upon the function values to the liquid crystal panel  28  via the row electrodes  25 ,  26 , . . . ,  27 . This operation of taking in the row function data  23  is also conducted during one division interval, and it is in synchronism with the operation of taking in data and outputting data conducted by the column electrode driver  18 . 
     FIG. 46 is a block diagram showing details of the column signal generation circuit  17 . Numeral  302  denotes a write circuit,  204  a frame memory,  309  a read circuit, and  310  data for one column. The write circuit  302  takes in the display data  1  and writes the display data successively into the frame memory  204 . The read circuit  309  reads display data for one column from the frame memory  204  and outputs the display data as data  310  for one column. Numeral  311  denotes a computation circuit,  202  an overflow detector,  315  a voltage converter,  314  the number of coincident values, and  332  original column data. The computation circuit  311  computes the data  310  for one column with the row function data  23  and outputs the number  314  of coincident values. If the number  314  of coincident values is between a predetermined upper limit value and a predetermined lower limit valve, the detector  202  accepts the number  314  of coincident values as it is, and outputs it as the original column data  332 . If the number  314  of coincident values exceeds the predetermined upper limit value or lower limit value, the detector  202  outputs a logic 1 as the overflow signal  206 . If the number  314  of coincident values is between the upper limit valve and lower limit value, the overflow signal  206  becomes a logic “0”. The voltage converter  315  converts the original column data  332  to the column data  16 . Details of the computation circuit  311  and the overflow detector  202  will be described later. 
     In the frame memory  204 , display data corresponding to one frame are stored. Details of the computation circuit  311  are identical with those of FIG. 11 or  28 . The EX-OR circuit derives exclusive OR of the display data for one column and the row function data  23  bit by bit. The decoder counts logic 0s resulting from the computation and outputs the count as the number  314  of coincident values. 
     FIG. 47 is a diagram showing details of the overflow detector  202 . Numeral  426  denotes an upper limit overflow detector,  427  an upper limit overflow signal,  428  a lower limit overflow detector,  429  a lower limit overflow signal,  430  a clipping circuit, and  431  an OR circuit. The detector  426  causes the upper limit overflow signal  427  to become a logic 1 when the number  314  of coincident values has exceeded the predetermined upper limit value and causes the signal  427  to become a logic 0 when the number  314  of coincident values has not exceeded the predetermined upper limit value. The detector  428  causes the lower limit overflow signal  429  to become a logic 1 when the number  314  of coincident values has become smaller than the predetermined lower limit value and causes the signal  429  to become a logic 0 when the number  314  of coincident values has not become smaller than the predetermined lower limit value. The clipping circuit  430  outputs the upper limit value as the original column data  332  when the upper limit overflow signal  427  has been outputted, whereas the circuit  430  outputs the lower limit value as the original column data  332  when the lower limit overflow signal  429  has been outputted. Otherwise, the number  314  of coincident values is outputted as it is as the original column data  332 . The OR circuit  431  derives logical sum of the upper limit overflow signal  427  and lower limit overflow signal  429 , and causes the overflow signal  206  to become a logic 1 when either of them is a logic 1. 
     FIG. 48 is a diagram showing details of the row function generation circuit  22 . Numerals  433 ,  435 ,  437  and  439  denote orthogonal function generation circuits. Numerals  434 ,  436 ,  438  and  440  denote orthogonal function data outputted by respective orthogonal function generation circuits. In the present embodiment, four kinds of orthogonal function data are generated. Numeral  441  denotes a selector,  442  a selector controller, and  443  a select signal. Four kinds of orthogonal function data  434 ,  436 ,  438  and  440  outputted by respective generation circuits  433 ,  435 ,  437  and  439  are shown in FIGS. 49,  50 ,  51  and  52 , respectively. The selector  441  selects one out of the orthogonal function data  434 ,  436 ,  438  and  440  and outputs it as the row function data  23 . The selector controller  442  generates the select signal  443  in accordance with the overflow signal  206  and determines the selection operation of the selector  441 . 
     Operation of an embodiment having the configuration heretofore described will now be described. In the column signal generation circuit  17 , the write circuit  302  writes the inputted display data  1  into the frame memory  204  successively as P( 1 , 1 ), P( 1 , 2 ), P( 1 , 3 ), . . . , P( 1 ,M), P( 2 , 1 ), P( 2 , 2 ), . . . , P( 2 ,M), . . . , P(N, 1 ), P(N, 2 ), . . . , P(N,M). That is to say, the display data  1  are serially transmitted in the so-called dot sequential manner, and hence they are written into the frame memory  204  in order. Then the read circuit  309  reads out in a lump the display data for one column written into the frame memory  204 . That is to say, for the jth column, N display data P(i,j), P( 2 ,j), . . . , P(N,j) are simultaneously read out as the display data  310  for one column.  310 . The display data  310  for one column are inputted to the computation circuit  311 . On the other hand, the row function data  23  are generated by the row function generation circuit  22  shown in FIG.  48 . In the present embodiment, the generation circuit  22  has four kinds of orthogonal function generation circuits  433 ,  435 ,  437  and  439  which are different from each other. The orthogonal function generation circuits need not be limited to four kinds, but the number of kinds may be increased or decreased as occasion demands. One out of the orthogonal function data  434 ,  436 ,  438  and  440  outputted by the four kinds of generation circuits  433 ,  435 ,  437  and  439  is selected by the selector  441  and inputted to the computational circuit  311  as the row function data  23 . Each of the generation circuits  433 ,  435 ,  437  and  439  generates N orthogonal functions h( 1 ), h( 2 ) . . . , h(N). For the purpose of explanation, examples of respective orthogonal function data  434 ,  436 ,  438  and  440  in case where N=5 are shown in FIGS. 49,  50 ,  51  and  52 , respectively. FIG. 49 shows five orthogonal function data of the orthogonal function data  434  outputted by the orthogonal function generation circuit  433 . In the same way, FIGS. 50,  51  and  52  show five orthogonal function data of the orthogonal function data  436 ,  438  and  440 , respectively. Each of the orthogonal function data  434 ,  436 ,  438  and  440  is formed by arbitrarily taking out 5 divisions from the Walsh function having 8 divisions shown in FIG.  4  and assigning them to the orthogonal functions h( 1 ), h( 2 ), . . . , h( 5 ). Even if N orthogonal functions are formed by arbitrarily taking out divisions from the same function system such as the Walsh function and arranging the divisions, they are referred to as “orthogonal functions which are different from each other” so long as the way of taking out and arranging the divisions is different. Furthermore, the basic orthogonal function system is not limited to the Walsh function, but may be any function system satisfying the orthogonality condition. The Walsh function has binary values “+1” and “−1”. In the following description, therefore, “+1” and “−1” are defined respectively as a logic “0” and a logic “1”. The selector  441  for selecting one out of four kinds of orthogonal function data which are different from each other operates under instructions from the selector controller  442 . If a logic “1” of the overflow signal  206  is inputted, the selector controller  442  outputs the selector control signal  443  so that orthogonal function data different from that presently selected by the selector  441  may be selected. To be concrete, the selector controller  442  has a counter for counting logic “1s” of the overflow signal  206 . Whenever a logic “1” of the overflow signal  206  is inputted, the counter counts and the orthogonal function data  434 ,  436 ,  438  and  440  are successively selected. This is not restrictive. Alternatively, a random number may be generated whenever a logic “1” of the overflow signal  206  is inputted so that orthogonal function data may be switched according to the random number. Details of the occurrence of the overflow signal  206  and the effect of switching the orthogonal function data will be described later. 
     Operation of the computation circuit  311 , which receives the row function data  23  thus generated and the display data  310  corresponding to one column already described and which computes the number  314  of coincident values, will now be described. The computation circuit  311  conducts computation according to equation ( 22 ). The computation of equation ( 22 ) counts logic coincidences between P(i,j) and W(i,t), and represents the count as the number D of coincident values. Details of the operation of the computation circuit  311  which actually conducts computation according to the equation ( 22 ) will now be described. The display data  310  corresponding to one column and the row function data  23  are inputted to the EX-OR circuit respectively bit by bit. The EX-OR circuit conducts exclusive OR operation between P(i,j) and W(i,t). In the exclusive OR operation, the result becomes a logic “0” when the input logics coincide with each other whereas the result becomes a logic “1” when the input logics do not coincide .The subsequent decoder counts logic “0s” each indicating logic coincidence included in the output of the EX-OR circuit and outputs the count as the number  314  of coincident values. Since N=240, the number  314  of coincident values can assume a value ranging from “0” to “240”. Then the number “314” or coincident values is inputted to the overflow detector  202  shown in FIG.  46 . Details of operation of the detector  202  will now be described by referring to FIG.  47 . As described above, the number  314  of coincident values can assume a value ranging from “0” to “240”. However, the column electrode driver  18  can generate only 64 levels. Therefore, the detector determines whether the value of the number  314  of coincident values is at least “89” and “152” or less (i.e., whether the value of the number  314  of coincident values is in a range of 64 levels around N/2=120). When this range is exceeded, the detector  202  yields a logic “1” as the output of the overflow signal  206 . Otherwise, the detector  202  yields a logic “0”. The upper limit overflow detector  426  determines whether the number  314  of coincident values has exceeded “152”. When “152” is exceeded, the upper limit overflow signal  427  becomes a logic “1”. Otherwise, the upper limit overflow signal  427  becomes a logic “0”. The lower limit overflow detector  428  determines whether the number  314  of coincident values has become smaller than 89. When the number  314  of coincident values has become smaller than “89”, the lower limit overflow signal  429  becomes a logic “1”. Otherwise, the lower limit overflow signal  429  becomes a logic “0”. The upper limit overflow signal  427 , the lower limit overflow signal  429 , and the number  314  of coincident values are inputted to the clipping circuit  430 . When both the upper limit overflow signal  427  and the lower limit overflow signal  429  are logic “0s,” the number  314  of coincident values is outputted as it is as the original column data  332 . When the upper limit overflow signal  427  is a logic “1”, the value of the original column data  332  is set to “152”. When the lower limit overflow signal  429  is a logic “1”, the value of the original column data  332  is set to “89”. In this way, the original column data  332  can assume a value in 64 levels ranging from “89” to “152”. On the other hand, the logical sum of the upper limit overflow signal  427  and the lower limit overflow signal  429  is derived and outputted as the overflow signal  206 . When the number  314  of coincident values has exceeded the 64-level range between “89” and “152”, therefore, the overflow signal  206  becomes a logic “1”. Otherwise, the overflow signal  206  becomes a logic “0”. When the number  314  of coincident values is “50”, for example, the value of the original column data  332  becomes “89” and the overflow signal  206  becomes a logic “1”. Then the original column data  332  is converted to the column data  16  by the voltage converter  315 . By regarding the original column data  332  as D, the voltage converter  315  converts the original column data  332  to g(j) in accordance with equation ( 22 ) and outputs g(j) as the column data  16 . The column electrode driver  18  takes in the column data  16  corresponding to one row, and thereafter outputs data of one row simultaneously to the liquid crystal panel  18  via the column electrodes  19 ,  20 , . . .  21 . 
     The row function data generated generation circuit  22  shown in FIG. 48 has four kinds of orthogonal functions beforehand, one of which is selected. However, an alternative method is also conceivable. This method is shown in FIG.  53 . In FIG. 53, five divisions are arbitrarily selected from the Walsh function having 8 divisions and outputted as the row function data. With reference to FIG. 53, numeral  444  denotes an orthogonal function generation circuit,  445  orthogonal function data,  446  a switch matrix controller,  447  a switch matrix control signal, and  448  a switch matrix. The row function generation circuit  22  conducts operation of arbitrarily making selections out of one kind of orthogonal function data and making rearrangement in the switch matrix  448 . Turning on or off in each switch is controlled by the switch matrix controller  446 . Whenever the overflow signal  206  becomes a logic “1”, the controller  446  changes over the switch matrix control signal  447  and successively outputs different row function data  23 . The signal patterns of the controller  446  may be stored in ROM beforehand and successively used. Alternatively, the signal patterns of hte controller  446  may be generated as random numbers. It is sufficient that the row function generation circuit  22  shown in FIG. 53 has only one orthogonal function generation circuit  444 . 
     When the number  314  of coincident values has exceeded the range of at least “89” and “152” or less (i.e., the range of 64 levels around N/2=120), the column signal generation circuit  17  outputs the overflow signal  206  as heretofore described. Thereby, row function data different from the row function data  23  presently outputted by the row function generation circuit  22  are outputted. Even if display contents are constant as in a still picture and overflow occurs, therefore, a different row function is subsequently used. As a result, the number D of coincident values has value distribution conforming to normal distribution, and degradation of display quality due to lowering of column voltage can be avoided. 
     A modification of the present invention will now be described. The same components as those of the third embodiment are denoted by like characters. The detailed configuration of the column signal generation circuit  17  is shown in FIG.  54 . In FIG. 54, numeral  453  denotes a clipping circuit. When the number  314  of coincident values has exceeded a predetermined upper limit value, the clipping circuit  453  outputs the upper limit value as the original column data  332 . When the number  314  of coincident values has become smaller than a predetermined lower limit value, the clipping circuit  453  outputs the lower limit value as the original column data  332 . When the number  314  of coincident values is within a predetermined range, the clipping circuit  453  outputs the number  314  of coincident values as it is as the original column data  332 . A variant of the row function generation circuit  22  will now be described. Instead of the selector controller  442  of FIG. 48, a counter is used. Whenever a frame signal is inputted, this is counted and the selector  441  is changed over. Thereby orthogonal function data are successively changed over frame by frame. The configuration of the row function generation circuit  22  shown in FIG. 48 is not restrictive, but the switch matrix as shown in FIG. 53 may be used. 
     In the operation of this variant heretofore described, overflow detection described with reference to the third embodiment is not conducted, but the orthogonal function data are changed over frame by frame no matter whether overflow occurs or not. That is to say, the row function generation circuit  22  generates a different kind of orthogonal function for every frame period. Even if display contents are constant as in a still picture and overflow occurs, therefore, a different row function is used in the next frame. No matter whether overflow occurs or not, the row function is changed over one after another, As a result, the number of coincident values has value distribution conforming to normal distribution, and degradation of display quality due to lowering of column voltage can be avoided. 
     As heretofore described, the present invention makes it possible to realize a new liquid crystal driving method which can be applied to the case where a still picture is displayed as in a personal computer and which does not degrade the display quality even for fast responding TN liquid crstal displays.