Patent Publication Number: US-2009228538-A1

Title: Multi input coding adder, digital filter, signal processing device, synthesizer device, synthesizing program, and synthesizing program recording medium

Description:
TECHNICAL FIELD 
     The present invention relates to a multi-input coding adder, and more particularly, to a multi-input coding adder which can carry out an operation that is equivalent to an operation of a multi-input multiplier and adder which multiply a plurality of inputs by constant multipliers, respectively, and adds the plural multiplication results together by a smaller circuit. 
     BACKGROUND ART 
     A circuit which multiplies inputs by constants, and calculates the sum of the plural outputs is used in various signal processing and in digital filters, and it has a lot of applications. 
     The above-described circuit is constituted by constant multipliers, a multi-input adder, and the like, and miniaturization and speeding up are demanded. 
     Up until now, a lot of patent applications are filed on the constructions of constant multipliers and multi-input adders (for example, refer to Patent Document 1, Patent Document 2, and Patent Document 3). 
       FIG. 9  is a diagram illustrating a construction of a multi-input multiplier and adder according to a prior art example. In  FIG. 9 , reference numeral  20   a ,  20   b ,  20   c , . . . ,  20   n  denote partial product generators, respectively. Numeral  92  denotes a multi-input adder circuit, and numerals  93   a ,  93   b ,  93   c , . . . ,  93   n  denote two-input adder blocks which constitute the multi-input adder circuit  92 . The multi-input multiplier and adder shown in  FIG. 9  is a circuit which multiplies the input signals by constant multipliers respectively, and adds the plural multiplication outputs obtained by the multiplications together. 
     For multiplying the input signal by a constant multiplier, a logical product operation is usually used to obtain respective partial products. The partial product generator circuits  20   a ,  20   b ,  20   c ,  20   n  generate partial products of the respective inputs and the constant multipliers for each bit. The two-input adder blocks  93   a ,  93   b ,  93   c ,  93   n  are constituted by providing a plurality of two-input one-output adders, respectively, and by employing these in a plurality of stages, the sum of the outputs of the partial product generators  20   a ,  20   b ,  20   c ,  20   n  is obtained. The number of the adders of the two-input one-output adders in the final stage two-input adder block  2   n  is 1. 
     In addition,  FIG. 10  shows an example of a multi-input multiplier and adder which has an input number of 4. The circuit shown in  FIG. 10  is a usual FIR filter. In  FIG. 10 , numerals  21   a ,  21   b ,  21   c , and  21   d  denote multiplier circuits, respectively, and numeral  5   a ,  5   b , and  5   c  denote adder circuits, respectively. 
     The multiplier circuits  21   a ,  21   b ,  21   c , and  21   d  multiply four inputs by a coefficient  1 , a coefficient  2 , a coefficient  3 , and a coefficient  4 , respectively, and outputs the results, respectively. The adder circuits  5   a ,  5   b , and  5   c  are two-input one-output adders, respectively, and these obtain the sum of the outputs of the multiplier circuits  21   a ,  21   b ,  21   c , and  21   d.    
     Patent Documents 1: Japanese Patent No. 3558436 
     Patent Documents 2: Japanese Published Patent Application No.Hei.5-233226 
     Patent documents 3: Japanese Published Patent Application No.Hei.10-124298 
     DISCLOSURE OF THE INVENTION 
     Problems to be Solved by the Invention 
     The conventional multi-input coding adder circuit having constant multipliers has a problem in that when there is an increase in the number of inputs, there occurs an increase in the number of the partial product generator circuits and also an increase in the number of stages of the addition blocks. Herein, a partial product generator circuit requires, when, for example, the input has j bits and the coefficient has k bits, j×k pieces of AND circuits, and with an increase in the inputs, the circuit scale increases to a great extent. 
     The present invention is directed to solving the problems in the above-described conventional technique, and has for its object to provide a multi-input coding adder circuit which can reduce its circuit scale in its circuit construction, and further to provide a synthesizer device, a synthesizing program, and a synthesizing program recording medium for that multi-input coding adder circuit. 
     Measures to Solve the Problems 
     In order to solve the above-described problems, according to claim  1  of the present invention, there is provided a multi-input coding adder, being an operator which multiplies a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together to output the added result, comprising: a multi-input encoder which, comprising a plurality of encoder parts each of which accomplishes a function corresponding to generation of a partial product in a multiplication, each of the plural inputs to which encoder is an input of each said encoder part, and which encoder has plural outputs each of which is the multi-input output of each said encoder part, and a multi-input adder circuit which adds the plural outputs of said multi-input encoder, which are the multi-bit output of each said encoder part. 
     Thereby, by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, it is possible to realize reduction in a circuit scale, and to realize an operator which can perform an operation that is equivalent to the operation by a conventional multi-input multiplier and adder with a miniaturized circuit construction. 
     According to claim  2  of the present invention, there is provided a multi-input coding adder circuit as defined in claim  1 , wherein: said multi-input adder circuit comprises a multi-input adder which receives the plural outputs of said multi-input encoder as its inputs, which are the multi-bit output of each of said encoder parts of said multi-input encoder, and adds these inputs together. 
     Thereby, by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, it is possible to realize reduction in a circuit scale, and to obtain a small sized multi-input coding adder. 
     According to claim  3  of the present invention, there is provided a multi-input coding adder as defined in claim  1 , wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to the plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises: an inverter for inverting each bit of said input signal; an adder circuit which adds a constant to the output of said inverter; a selection circuit for selecting either of said input signal and the output signal of said adder circuit according to said coefficient pattern to output the selected result; and a bit-shift circuit which carries out a bit-shift of the output signal of said selection circuit. 
     Thereby, it is possible to realize reduction in a circuit scale for the respective encoder parts which constitute the multi-input encoder, and thereby to obtain a small-sized multi-input coding adder. 
     According to claim  4  of the present invention, there is provided a multi-input coding adder as defined in claim  1 , wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises: an inverter for inverting each bit of said input signal; an adder circuit which adds a constant to the output of said inverter; a bit-shift circuit which carries out a bit-shift of the output signal of said adder circuit. 
     Thereby, it is possible to realize reduction in a circuit scale for the respective encoder parts which constitute the multi-input encoder, and thereby to obtain a small-sized multi-input coding adder. 
     According to claim  5  of the present invention, there is provided a multi-input coding adder circuit as defined in claim  1 , wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises a bit-shift circuit which carries out a bit-shift of said input signal. 
     Thereby, it is possible to realize reduction in a circuit scale for the respective encoder parts which constitute the multi-input encoder, and thereby to obtain a small-sized multi-input coding adder. 
     According to claim  6  of the present invention, there is provided a multi-input coding adder circuit as defined in claim  1 , wherein: each said encoder part constituting said multi-input encoder employs a Booth-algorithm. 
     Thereby, the reduction in a circuit scale for the respective encoder parts can be realized, and thereby, a small-sized multi-input coding adder can be obtained. 
     According to claim  7  of the present invention, there is provided a multi-input coding adder circuit as defined in claim  2 , wherein: said multi-input adder is a Wallace Tree adder. 
     Thereby, the reduction in a circuit scale for the multi-input adder can be realized, and thereby, a small-sized multi-input coding adder can be obtained. 
     According to claim  8  of the present invention, there is provided an operator as a multi-input coding adder, being an operator which multiplies a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together, comprising: a multi-input encoder which, comprising a plurality of encoder parts each of which accomplishes a function corresponding to generation of a partial product in a multiplication, each of the plural inputs to which encoder is an input of each said encoder part, and which encoder has plural outputs each of which is the multi-input output of each said encoder part, and a multi-input adder circuit which adds the plural outputs of said multi-input encoder, which are the multi-bit output of each said encoder part, and a constant. 
     Thereby, by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, it is possible to realize reduction in a circuit scale, and to realize an operator which can perform an operation that is equivalent to the operation by a conventional multi-input multiplier and adder with a miniaturized circuit construction. 
     According to claim  9  of the present invention, there is provided a multi-input coding adder circuit as defined in claim  8  wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to the plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises: an inverter for inverting each bit of said input signal; an adder circuit which adds a constant to the output of said inverter; a selection circuit for selecting either of said input signal and the output signal of said adder circuit according to said coefficient pattern to output the selected result; and a bit-shift circuit which carries out a bit-shift of the output signal of said selection circuit. 
     Thereby, the reduction in a circuit scale for the respective encoder parts which constitute the multi-input encoder can be realized, and thereby a small sized multi-input coding adder can be obtained. 
     According to claim  10  of the present invention, there is provided a multi-input coding adder, being an operator which multiplies a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together to output the added result, comprising: a multi-input encoder which, comprising a plurality of encoder parts each of which accomplishes a function corresponding to generation of a partial product in a multiplication, each of the plural inputs to which encoder is an input of each said encoder part, and which encoder has plural outputs each of which is the multi-input output of each said encoder part, and a column position adjusting circuit which, with receiving the multi-bit outputs of the respective encoder parts which constitute said multi-input encoder as its inputs, carries out an adjustment of the column positions of said respective inputs. 
     Thereby, by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, it is possible to realize reduction in a circuit scale, and to realize an operator which can perform an operation that is equivalent to the operation by a conventional multi-input multiplier and adder with a miniaturized circuit construction. 
     According to claim  11  of the present invention, there is provided a multi-input coding adder as defined in claim  10 , wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises: an inverter for inverting each bit of said input signal; an adder circuit which adds a constant to the output of said inverter; a selection circuit for selecting either of said input signal and the output signal of said adder circuit according to said coefficient pattern to output the selected result; and a bit-shift circuit which carries out a bit-shift of the output signal of said selection circuit. 
     Thereby, it is possible to realize reduction in a circuit scale for the respective encoder parts which constitute the multi-input encoder, and thereby to obtain a small-sized multi-input coding adder. 
     According to claim  12  of the present invention, there is provided a digital filter that is provided with a means for multiplying a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together, wherein: said means for multiplying a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together is constituted by a multi-input coding adder as defined in claim  1 . 
     Thereby, a digital filter can be realized by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, thereby enabling reduction in a circuit scale, and resulting in a digital filter of a miniaturized circuit construction. 
     According to claim  13  of the present invention, there is provided a signal processing device comprising: said multi-input coding adder circuit according to claim  1 , and performing a signal processing including multiplying said plural inputs by fixed multipliers, respectively, and adding all the multiplication results together. 
     Thereby, a signal processing device can be realized by employing a small sized multi-input encoder and a multi-input adder circuit without employing a partial product generator circuit, thereby enabling reduction in a circuit scale, and resulting in a signal processing circuit of a miniaturized circuit construction. 
     According to claim  14  of the present invention, there is provided a synthesizer device for synthesizing a multi-input coding adder circuit, which is being an operator which multiplies a plurality of inputs by fixed multipliers, respectively, and adds all the multiplication results together, by execution of a program by a computer, which operator comprising: a multi-input encoder which, comprising a plurality of encoder parts each of which accomplishes a function corresponding to generation of a partial product in a multiplication, each of the plural inputs to which encoder is an input of each said encoder part, and which encoder has plural outputs which are the multi-bit output of each said encoder part, and a multi-input adder circuit which adds the plural outputs of said multi-input encoder, which are the multi-bit output of each said encoder part of said multi-input encoder. 
     Thereby, it is possible to realize a synthesizer device which can automatically synthesizes a small-sized multi-input coding adder, which employs a small-sized multi-input encoder and a multi-input adder without employing a partial product generator circuit. 
     According to claim  15  of the present invention, there is provided a synthesizer device for synthesizing a multi-input coding adder circuit, as defined in claim  14 , wherein: each said encoder part constituting said multi-input encoder includes a plurality of encoder units which generate respectively partial products which respectively correspond to the plural coefficient patterns which are obtained by partitioning the bit pattern of the fixed multiplier into each plural bits, and at least one of said plural encoder units comprises: an inverter for inverting each bit of said input signal; an adder circuit which adds a constant to the output of said inverter; a selection circuit for selecting either of said input signal and the output signal of said adder circuit according to said coefficient pattern to output the selected result; and a bit-shift circuit which carries out a bit-shift of the output signal of said selection circuit. 
     Thereby, it is possible to reduce the circuit scale of the respective encoder parts which constitute the multi-input encoder of the above-described multi-input coding adder synthesized, and to realize a synthesizer device which can automatically synthesize a small-sized multi-input coding adder. 
     According to claim  16  of the present invention, there is provided a synthesizing program for synthesizing a multi-input coding adder, comprising: synthesizing a multi-input coding adder as defined in claim  1  by being executed by a computer. 
     Thereby, it is possible to obtain a synthesizing program which can automatically synthesizes a small-sized multi-input coding adder which employs a small-sized multi-input encoder and multi-input adder, without employing a partial product generator circuit. 
     According to claim  17  of the present invention, there is provided a synthesizing program recording medium for a multi-input coding adder, comprising: having stored a synthesizing program for synthesizing a multi-input coding adder as defined in claim  16 . 
     Thereby, it is possible to obtain a synthesizing program recording medium which can automatically synthesizes a small-sized multi-input coding adder which employs a small-sized multi-input encoder and a multi-input adder, without employing a partial product generator circuit. 
     EFFECTS OF THE INVENTION 
     According to a multi-input coding adder circuit of the present invention, since a small sized multi-input encoder and a multi-input adder circuit are employed without employing a partial product generator circuit when constituting a circuit, it is possible to realize an operator which can perform an operation that is equivalent to the operation by a conventional multi-input multiplier and adder with a miniaturized circuit construction. 
     According to a synthesizer device for a multi-input coding adder, a synthesizing program, and a synthesizing recording medium of the present invention, since a small sized multi-input encoder and a multi-input adder circuit are employed without employing a partial product generator circuit, it is possible to obtain a synthesizer device, a synthesizing program, and a synthesizing program recording medium which can perform synthesis of a miniaturized multi-input coding adder. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a construction of a multi-input coding adder  10  according to a first embodiment of the present invention. 
         FIG. 2  is a block diagram illustrating a construction of the encoder part  11   a  in the multi-input encoder  11  of the first embodiment. 
         FIG. 3  is a block diagram illustrating a construction of the encoder unit  11   b  in the encoder part  11   a  in the multi-input encoder  11  of the first embodiment. 
         FIG. 4  is a block diagram illustrating other construction examples of the encoder unit  11   b - 2  and  11   b - 3  in the encoder part  11   a  in the multi-input encoder  11  of the first embodiment. 
         FIG. 5  is a block diagram illustrating a construction of a multi-input coding adder  50  according to a second embodiment f the present invention. 
         FIG. 6  is a block diagram illustrating a construction of the encoder part  51   a  in the multi-input encoder  51  of the second embodiment. 
         FIG. 7  is a block diagram illustrating a construction of a multi-input coding adder  70  according to a third embodiment f the present invention. 
         FIG. 8  is a block diagram illustrating a construction of the encoder part  71   a  in the multi-input encoder  17  of the third embodiment. 
         FIG. 9  is a diagram illustrating a construction of a conventional multi-input multiplier and adder. 
         FIG. 10  is a diagram illustrating an example of a conventional multi-input multiplier and adder. 
         FIG. 11  is a diagram illustrating an operation employing a secondary Booth-algorithm. 
         FIG. 12  is a diagram illustrating a partial product which is generated according to a bit pattern in the secondary Booth-algorithm. 
         FIG. 13  is a diagram illustrating a construction of the encoder part  51   a  in the multi-input encoder  51  of the second embodiment. 
         FIG. 14  is a diagram illustrating a construction of the encoder part  71   a  in the multi-input encoder  71  of the third embodiment. 
     
    
    
     DESCRIPTION OF REFERENCE NUMERALS 
     
         
           11 ,  51 ,  71  . . . multi-input encoder 
           11   a ,  51   a , and  71   a  . . . encoder part 
           11   b ,  51   b ,  71   b  . . . encoder unit 
           12 ,  52 , and  72  . . . multi-input adder circuit 
           2   a ,  2   b ,  2   c ,  2   n  . . . two-input adder circuit block 
           3  . . . inverter 
           4 ,  54  . . . constant 
           5 ,  5   a ,  5   b ,  5   c  . . . adder circuit 
           6  . . . selection circuit 
           7  . . . coefficient pattern 
           8 ,  8   a ,  8   b  . . . bit-shift circuit 
           9  . . . column position adjustment circuit 
           10   a ,  10   b ,  10   c ,  10   d  . . . partial product generator circuit 
           11   a ,  11   b ,  11   c , and  11   d  . . . multiplier circuit 
       
    
     BEST MODE TO EXECUTE THE INVENTION 
     Hereinafter, embodiments of the present invention will be described with reference to the drawings. 
     First Embodiment 
     A multi-input coding adder according to a first embodiment of the present invention will be described with reference to  FIGS. 1 ,  2 ,  3 ,  4 ,  11 , and  12 . 
       FIG. 1  is a block diagram illustrating the multi-input coding adder of the first embodiment of the present invention. In  FIG. 1 , reference numeral  11  denotes a multi-input encoder and numeral  12  denotes a multi-input adder circuit. 
     The multi-input encoder  11  makes the plural inputs  1   a ,  1   b ,  1   c ,  1   n  subjected to encoding by the respective encoder parts  11   a , and outputs plural encoded signals  2   a ,  2   b ,  2   c , . . . ,  2   n , respectively. 
     The multi-input adder circuit  12  receives the plural outputs  2   a ,  2   b ,  2   c , . . . ,  2   n  which are outputted from the respective encoder parts  11   a  in the multi-input encoder  11  as its inputs, and calculates the total sum of those. As the multi-input adder circuit  12 , one which is provided with plural stages of two-input adder blocks similarly as in the multi-input adder circuit  92  in the conventional multi-input multiplier and adder shown in  FIG. 9  can be employed. Further, by employing such as a multi-input Wallace Tree adder circuit as the multi-input adder circuit  12 , it is possible to realize miniaturization of the addition circuit. 
       FIG. 2  is a block diagram illustrating a construction of the respective encoder parts  11   a  in the multi-input encoder  11 . In  FIG. 2 , the encoder part  11   a  is further constituted by plural encoder units  11   b , where each of the respective encoder units  11   b  encodes the input signal for each one bit or for each several bits, and outputs an encoded signal  2   a  comprising plural bits. 
       FIG. 3  is a block diagram illustrating an example of construction of an encoder unit  11   b  in each of the encoder parts  11   a  which constitute the multi-input encoder  11 . In  FIG. 3 , numeral  3  denotes an inverter, numeral  4  denotes a constant, numeral  5  denotes an adder circuit, numeral  6  denotes a selection circuit, numeral  7  denotes a coefficient pattern, and numeral  8  denotes a bit-shift circuit. 
     The inverter  3  is operated to generate an inverted signal for each bit of the input signal, and a constant  4  is added to the output of the inverter  3  by the addition circuit  5 . Here, the value of the constant  4  is “1”, and by the inverter  3 , the constant  4 , and the addition circuit  5 ,  2 &#39;s complement (sign inversion) of the input is obtained. 
     Next, either of the input signal  1   a  or the output signal  5   a  of the adder circuit  5  is selected by the selection circuit  6  according to the coefficient patter  7  which is obtained by partitioning the fixed multiplier, and the result is multiplied by “0” or “1” to output the obtained signal. Further, the bit-shift circuit  8  outputs the output signal  6   a  of the section circuit  6  with varying the bit-shift amount thereof. 
     In the encoder unit  11   b  in the example shown in  FIG. 3 , a secondary Booth-algorithm is employed. 
     Usually, according to the Booth-algorithm, signals of 0 times, +k times, and −k times of the input are outputted according to the bit patterns which are obtained by partitioning the multiplier into each n bits. Here, k is an integer from 1 to n−1. According to the secondary Booth-algorithm, partial products are generated each for 2 bits of the multiplier. However, since 1 bit overlaps, partial products of 0, +X, and +2X for the input signal X are generated corresponding to the successive 3 bits bit patterns of the multiplier Y, as shown in  FIG. 12 . Then, the partitioning into three bits is carried out with assuming that the lowest column of the multiplier has “0” at its further lower column. The generation of negative numbers is carried out such that the respective bits of X are inverted and “0” is added thereto, since the multiplicand X is in an expression of 2&#39;s complement. Further, the generation of 2X is realized by one-bit shifting. 
       FIG. 11  is a diagram illustrating an operation employing a secondary Booth-algorithm in a case where the input X as the multiplicand is 4 bit (x 3 , x 2 , x 1 , x 0 ) and the fixed multiplier Y is (y 3 , y 2 , y 1 , y 0 ) The multiplied value of the input X and the fixed multiplier Y is calculated by that the fixed multiplier Y is divided into each three bits with “0” being added to the lower column than the lowest column thereof, the resulted respective bit patterns are symbolized as r 0  and r 1 , and these partial products r 0 (x 3 , x 2 , x 1 , x 0 ) and r 1 (x 3 , x 2 , x 1 , x 0 ) are added together. 
     More particularly, the construction and operation of the encoder part  11   a  in a case where the fixed multiplier Y is 4 bits of (0101) will be described. In a case where the fixed multiplier Y is (1010), if “0” is added to a lower bit than the lowest bit of the fixed multiplier Y and the partitioning into three bits is performed, coefficient patterns (100), (101) from the lower bit side are obtained. Therefore, the encoder part  11   a  is constituted by two encoder units  11   b , i.e., the lower bit side encoder unit  11   b  which has a coefficient pattern  7  of (100) and the upper bit side encoder unit  11   b  which has a coefficient pattern  7  of (101). In the lower bit side encoder unit  11   b  having the coefficient pattern  7  of (100), in order to generate a partial product of −2X for the input X, the output signal  5   a  of the adder circuit  6  is selected by the selection circuit  6 , it is multiplied by “1” to be outputted, and the bit-shift circuit  8  outputs the output signal  6   a  of the selection circuit  6  with bit-shifting it by one-bit. On the other hand, in the upper bit side encoder unit  11   b  which has the coefficient pattern  7  of (101), in order to generate a partial product of −X for the input X, the output signal  5   a  of the adder circuit  5  is selected by the selection circuit  6 , it is multiplied by “1” to be outputted, and the bit-shift circuit  8  outputs the output signal  6   a  of the selection circuit  6  as it is without bit-shifting the same. 
     By employing an encoder unit  11   b  which employs Booth-algorithm in the multiplication with a fixed multiplier, it is possible to constitute a multi-input coding adder  10  shown in  FIG. 1  with a miniaturized circuit, without employing a partial product generator circuit employing a logical product operation. 
       FIGS. 4(   a ) and  4 ( b ) are block diagrams illustrating other construction examples  11   b - 2  and  11   b - 3  of the encoder unit  11   b  in each encoder part  11   a  which constitute the multi-input encoder  11 . 
     In the encoder unit  11   b - 2  shown in  FIG. 4(   a ), numeral  3  denotes an inverter, numeral  4  denotes a constant, numeral  5  denotes an adder circuit, and numeral  8   a  denotes a bit-shift circuit. 
     In encoder unit  11   b - 3  shown in  FIG. 4(   b ), numeral  8   b  denotes a bit-shift circuit. 
     The operations of the respective circuits such as the inverter  3  in the encoder unit  11   b - 2  shown in  FIG. 4(   a ) and the encoder unit  11   b - 3  shown in  FIG. 4(   b ) are the same as the operations of the respective circuits in the encoder unit  11   b  shown in  FIG. 3 . 
     Since when the secondary Booth-algorithm is employed, which of the partial products of “0”, ±X, and ±2X for the input X is generated is previously determined according to the coefficient pattern of the multiplier, the encoder unit  11   b  shown in  FIG. 3  may be replaced by the encoder unit  11   b - 2  shown in  FIG. 4(   a ), or by the encoder unit  11   b - 2  shown in  FIG. 11   b - 3  according to the bit pattern of the multiplier. By constituting the encoder unit  11   b  of the encoder part  11   a  shown in  FIG. 2  by the encoder unit  11   b - 2  shown in  FIG. 4(   a ) or the encoder unit  11   b - 3  shown in  FIG. 4(   b ) according to the coefficient pattern of the multiplier, it is possible to construct the respective encoder units as those which do not include circuits which are not used, thereby realizing the miniaturization of the circuit. 
     Besides, the multi-input coding adder according to the first embodiment may be realized by a specified use hardware. Or, in place of realized by a specified use hardware, it may be realized by a synthesizer device which comprises a general purpose computer and synthesizes a multi-input coding adder of this embodiment by execution of a program. When the multi-input coding adder of this embodiment is realized by a synthesizer device, a synthesizing program which, when executed by a computer, synthesizes a multi-input coding adder of this embodiment may be recorded in an information recording medium such as CD so that when the program is read out from the recording medium storing that program and is executed, the multi-input coding adder of this embodiment should be synthesized. 
     Further, the multi-input coding adder of this first embodiment may be employed so as to constitute a signal processing device which performs a signal processing including a processing that multiplies the plural inputs by fixed multipliers respectively and adds all the multiplication results. Further, it is also possible to employ it as a means which multiplies the plural inputs by fixed multipliers respectively and adds all the multiplication results, in a digital filter which is provided with means which multiplies the plural inputs by fixed multipliers respectively and adds all the multiplication results. 
     In this way, according to the multi-input coding adder of this first embodiment, by constructing as described above, i.e., by constructing, without employing partial product generator circuits, a circuit that can perform equivalent functions to those circuits employing a small-sized multi-input encoder and a multi-input adder circuit, it is possible to realize reduction in circuits and further to realize an operator which can perform operations equivalent to those in the conventional multi-input multiplication and adder circuit, with a small-sized circuit configuration. 
     Second Embodiment 
     A multi-input coding adder according to a second embodiment of the present invention will be described with reference to  FIGS. 5 ,  6 , and  13 . 
       FIG. 5  is a block diagram illustrating a multi-input coding adder according to this second embodiment. 
     In  FIG. 5 , numeral  50  denotes a multi-input coding adder of the second embodiment, numeral  51  denotes a multi-input encoder, numeral  51   a  denotes an encoder part in the multi-input encoder  51 , numeral  52  denotes a multi-input adder circuit, and numeral  54  denotes a constant. In addition,  FIG. 13  is a diagram illustrating a construction of the encoder part  51   a  in the multi-input encoder  51  of the second embodiment. In  FIG. 13 , the encoder part  51   a  is further constituted by plural encoder units  51   b , where each of the respective encoder units  51   b  encodes the input signal for each one bit or for each several bits, and outputs an encoded signal  2   a  comprising plural bits. 
     In  FIG. 5 , the difference of this second embodiment from the first embodiment shown in  FIG. 1  resides in that a constant  54  is added at the input of the multi-input adder circuit  52 . 
     In this second embodiment, the multi-input adder circuit  52  calculates the total sum of the plural encode signals  2   a ,  2   b ,  2   c , . . . ,  2   n  which are plural outputs of the multi-input encoder  51  and the constant  54 . 
     Next, the construction of the encoder units  51   b  which constitute the encoder part  51   a  in the multi-input encoder  51 , in the construction of the multi-input coding adder  50  of this second embodiment shown in  FIG. 5  will be described. 
       FIG. 6  is a block diagram illustrating an example of construction of the encoder unit  51   b  which constitutes the encoder part  51   a  in the multi-input encoder  51  in this second embodiment. 
     In  FIG. 6 , numeral  3  denotes an inverter, numeral  6  denotes a selection circuit, numeral  7  denotes a coefficient pattern, and numeral  8  denotes a bit-shift circuit. 
     The difference of the encoder unit  51   b  in this second embodiment shown in  FIG. 6  from the encoder unit  11   b  in the first embodiment shown in  FIG. 3  resides in that the constant  4  and the adder circuit  5  in the encoder unit  11   b  shown in  FIG. 3  are omitted in the encoder unit  51   b  shown in  FIG. 6 . 
     While in the first embodiment, the constant  4  and the addition circuit  5  are provided inside the encoder unit  11   b , in this second embodiment, the constant addition in the plural encoder units  11   b  by the constant  4  and the addition circuit  5  are collectively replaced by a constant, i.e., a constant  54  shown in  FIG. 5  to be used for addition. 
     In this second embodiment as described above, by collecting the constant additions in the respective encoder units  51   b  as a constant addition  54  and making it as an input to the multi-input adder circuit  52 , the respective encoder units  51   b  are not required to have constants and adder circuits therein respectively, and thereby the circuit scale can be further reduced. 
     In this way, according to the multi-input coding adder of this second embodiment, by constructing as described above, i.e., by constructing a circuit employing a small-sized multi-input encoder and a multi-input adder, without employing partial product generator circuits, it is possible to realize reduction in circuits, and further to realize an operator that can perform an operation that is equivalent to that in the conventional multi-input multiplication and adder circuit, with a miniaturized circuit configuration. 
     Third Embodiment 
     A multi-input coding adder circuit according to a third embodiment of the present invention will be described with reference to  FIGS. 7 ,  8 , and  14 . 
       FIG. 7  is a block diagram illustrating a multi-input coding adder  70  according to this third embodiment. 
     In  FIG. 7 , numeral  70  denotes a multi-input coding adder of this third embodiment, numeral  71  denotes a multi-input encoder, numeral  71   a  denotes an encoder part in the multi-input encoder  71 , numeral  79  denotes a column position adjustment circuit, and numeral  72  denotes a multi-input adder circuit. In addition,  FIG. 14  is a block diagram illustrating a construction of each encoder part  71   a  in the multi-input encoder  71 . In  FIG. 14 , the encoder part  71   a  is further constituted by plural encoders  71   b , where each of the respective encoders  71   b  encodes the input signal for each one bit or for each several bits, and outputs an encoded signal  2   a  comprising plural bits. 
     In  FIG. 7 , the difference of this third embodiment from the first embodiment which is shown in  FIG. 1  resides in that a column position adjustment circuit  79  is provided in the multi-input encoder  71 . 
     Next, the construction of the encoder parts  71   a  in the multi-input encoder  71 , in the construction of the multi-input coding adder  70  of the third embodiment shown in  FIG. 7  will be described. 
       FIG. 8  is a block diagram illustrating an example of construction of the encoder  71   b  which constitutes the encoder part  71   a  in the multi-input encoder  71  in this third embodiment. 
     In  FIG. 8 , numeral  3  denotes an inverter, numeral  4  denotes a constant, numeral  5  denotes an adder circuit, numeral  6  denotes a selection circuit, and numeral  7  denotes a coefficient pattern. 
     The difference of the encoder unit  71   b  in this third embodiment shown in  FIG. 8  from the encoder unit  11   b  in the first embodiment shown in  FIG. 3  resides in that the bit-shift circuit  8  in the encoder unit  11   b  shown in  FIG. 3  is omitted in the encoder unit  71   b  shown in  FIG. 8 . 
     In this third embodiment, in place of the bit-shift circuit  8  is omitted in the encoder unit as shown in  FIG. 8 , the column position adjustment circuit  79  is added in the multi-input encoder  71 , as shown in  FIG. 7 . 
     The bit-shifting by the bit-shift circuit  8  shown in  FIG. 3  corresponds to adjusting the column position in the multi-input adder circuit  12 , and the column position adjustment circuit  79  adjusts the column positions of the plural outputs from the respective encoder parts  71   a  respectively, to output the results to the multi-input adder circuit  72 . This column position adjustment circuit  79  has unique column adjustment positions when the multiplier is a fixed multiplier having a fixed pattern. This circuit only designates the paths of addition operation (column positions) in the multiplication, which would arise no addition of extra circuits. 
     In such third embodiment, by adjusting the column positions of the outputs of the respective encoder parts  71   a  by the column position adjustment circuit  79 , the respective encoder units  71   b  can be made those which include no bit-shift circuits therein, and thereby, the circuit scale can be further reduced. 
     In this way, according to the multi-input coding adder of this third embodiment, by constructing as described above, i.e., by constructing a circuit employing a small-sized multi-input encoder and a multi-input adder, without employing partial product generator circuits, it is possible to realize reduction in circuits, and further to realize an operator which can perform an operation that is equivalent to that in the conventional multi-input multiplication and adder circuit, with a miniaturized circuit configuration. 
     While in the above embodiments, as encoders, those which are constituted by employing a secondary Booth-algorithm are employed, encoders used in the present invention are not limited to those which utilize secondary Booth-algorithm, but those which utilize other algorithms such as tertiary Booth-algorithm may be employed. 
     APPLICABILITY IN INDUSTRY 
     According to the multi-input coding adder of the present invention, by employing a small-sized multi-input encoder and a multi-input adder circuit, it is possible to realize a small-sized multi-input multiplication and addition circuit, and it is very useful as a multi-input multiplication and addition circuit which performs various signal processing or used in a digital filter. In addition, it is applicable in fundamental operation devices for all kinds of digital signal processing as those used in optical recording and reproduction devices or in various uses for such as communications.