Abstract:
A multivalued subtractor for processing a multiplication of a first data and a second data, which are one of binary logic and multivalued logic, includes a first and second input circuit. The first input circuit includes parallel inputs for binary logic and multivalued logic, and receives the first data. The first input circuit also outputs a first set of bit data representing the first data. Similarly, the second input circuit includes parallel inputs for binary logic and multivalued logic, and receives the second data. The second input circuit also outputs a second set of bit data representing the second data. A subtracting circuit, connected to the first and said second input circuits, subtract the second set of bit data from the first set of bit data. A output circuit, connected to the subtracting circuit, converts the output of the subtracting circuit into data in binary logic and multivalued logic, in parallel, and outputs converted data in binary logic and multivalued logic, in parallel.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a multivalued subtracter which may apply to various data processings such as image processing or signal processing for communication or a microprocessor. 
     2. Description of the Related Art 
     In general, a subtracter is a kind of arithmetic and logic unit and is a dedicated circuit for subtraction. 
     In recent days, computer-equipped instruments containing logic operating units such as a microprocessor are used in society. These computer-equipped instruments include a personal computer, a point of sales (POS) terminal and a cash register. In such instruments, a subtracter is built-in for executing various logic operations, and the operating performance of the subtracter is likely to increase through the effect of various methods. 
     The subtracter known by the inventors of the present application, however, provides more operating gate stages as the processing of bit signals becomes faster and faster. More operating gate states result in delaying a signal by a greater amount, thereby making the subtraction unstable. The known subtracter has such a disadvantage. 
     Furthermore, the known instruments based on binary electronics are requested to have faster and more highly functional electronic components as the amount of data to be processed is made larger and larger. The binary electronics technique, however, provides limited information processing capability. Hence, the technique cannot cope with a quantity of data larger than a certain level. This means that the operating capability given by the binary electronics technique cannot achieve the capability which is now being requested. This is another disadvantage. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a multivalued subtracter which is capable of executing subtraction at fast speed without having to increase the circuit in scale and sharing a multivalued bit signal. 
     In carrying out the object, a multivalued subtracter includes: an apparatus for processing a subtraction between a first data and a second data, each of said first and second data being in one of binary logic and multivalued logic, comprising: first input means having parallel inputs of binary logic and multivalued logic for receiving said first data, and for outputting a first set of bit data representing said first data; second input means having parallel inputs of binary logic and multivalued logic for receiving said second data, and for outputting a second set of bit data representing said second data; subtracting means connected to said first input means and said second input means for subtracting said second set of bit data from said first set of bit data; and output means, connected to said subtracting means, for converting output of said subtracting means into data in binary logic and multivalued logic, in parallel, and for outputting converted data in binary logic and multivalued logic, in parallel. 
     As will be understood from the arrangement and operation, the multivalued subtracter according to the present invention enables enhancement of a subtracting speed if the processing amount of bit signals to be executed at one time is increased, without having to enlarge the circuit in scale. Further, the multivalued subtracter has a lower number of circuit components, thereby lowering the power consumption. Since the number of signals to be processed can be reduced, the number of wires mounted on an LSI circuit is reduced. This results in making it possible to implement high integration, thereby sharing binary signals and multivalued signals, such as a binary signal, a ternary signal and a quaternary signal in the multivalued circuit of this invention. 
     Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1a is a circuit diagram showing a partial arrangement of a ternary subtracter according to a first embodiment of the present invention; 
     FIG. 1b is a circuit diagram showing the other part of the ternary subtracter shown in FIG. 1a; 
     FIG. 2 is a circuit diagram showing an arrangement of a ternary binary I/O circuit which may apply to the ternary subtracter shown in FIGS. 1a and 1b; 
     FIG. 3 is a circuit diagram showing an arrangement of a ternary binary I/O circuit which may apply to the ternary subtracter shown in FIGS. 1a and 1b; 
     FIG. 4 is a circuit diagram showing an arrangement of a ternary subtracter according to a second embodiment of the present invention; 
     FIG. 5 is a circuit diagram showing an arrangement of a binary I/O circuit with two values which may apply to the ternary subtracter shown in FIG. 1 or FIG. 4; 
     FIG. 6 is a circuit diagram showing an arrangement of a binary I/O circuit with two values which may apply to the ternary subtracter shown in FIG. 1 or FIG. 4; 
     FIG. 7 is a circuit diagram showing an arrangement of a binary I/O circuit with two values which may apply to the ternary or a quaternary subtracter; 
     FIG. 8a is a circuit diagram showing a partial arrangement of a quaternary subtracter according to a third embodiment of the present invention; 
     FIG. 8b is a circuit diagram showing the other part of the quaternary subtracter shown in FIG. 8a; 
     FIG. 9 is a circuit diagram showing an arrangement of a binary I/O circuit with four values which may apply to the quaternary subtracter shown in FIGS. 8a and 8b; 
     FIG. 10 is a circuit diagram showing an arrangement of a binary I/O circuit with four values which may apply to the quaternary subtracter shown in FIGS. 8a and 8b; 
     FIG. 11 is a circuit diagram showing a binary I/O circuit with two values which may apply to the quaternary subtracter shown in FIGS. 8a and 8b; 
     FIG. 12 is a circuit diagram showing an arrangement of a binary I/O circuit with two values which may apply to the quaternary subtracter shown in FIGS. 8a and 8b; and 
     FIG. 13 is a circuit diagram showing an arrangement of an operator using the multivalued subtracter according to the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Hereafter, the description will be oriented to a multivalued subtracter according to an embodiment of the present invention as referring to the drawings. 
     FIGS. 1a and 1b are a circuit diagram showing an arrangement of a ternary subtracter according to an embodiment of the present invention. The ternary subtracter shown in FIGS. 1a and 1b is arranged to have I/O elements 10 to 19, logical AND circuit elements (referred to as AND elements) 20 to 35, multivalued functional elements 36 to 75, I/O elements 76 and 77, AND elements 78 to 83, logical OR circuit elements (referred to as OR elements) 84 to 88, I/O elements 89 and 90, and a one-bit delay circuit 91. 
     Next, each component will be discussed in detail. 
     The I/O element 10 inputs a ternary signal X and outputs a binary signal X 0 . The I/O element 11 inputs a ternary signal X and outputs a binary signal X 1/2 . The I/O element 12 inputs a ternary signal X and outputs a binary signal X 1 . 
     The I/O element 18 inputs a ternary signal Y and outputs a binary signal Y 0 . The I/O element 14 inputs a ternary signal Y and outputs a binary signal Y 1/2 . The I/O element 15 inputs a ternary signal Y and outputs a binary signal Y 1 . 
     The I/O element 16 inputs a binary signal x and outputs a binary signal x 0 . The I/O element 17 inputs a binary signal x and outputs a binary signal x 1 . 
     The I/O element 18 inputs a binary signal y and outputs a binary signal Y 0 . The I/O element 19 inputs a binary signal y and outputs a binary signal Y 1 . 
     The AND element 20 inputs the binary signals X 0 , Y 0 , x 0  and y 0  and outputs a logical product of them. The AND element 21 inputs the binary signals X 0 , Y 1/2 , x 0  and y 0  and outputs a logical product of them. The AND element 22 inputs the binary signals X 0 , Y 1 , x 0  and Y 0  and outputs the logical product of them. 
     The AND element 28 inputs the binary signals X 0 , Y 0 , x 0  and Y 1  and outputs a logical product of them. The AND element 24 inputs the binary signals X 1/2 , Y 0 , x 0  and Y 0  and outputs a logical product of them. The AND element 25 inputs the binary signals X 1/2 , Y 1/2 , x 0  and y 0  and outputs the logical product of them. 
     The AND element 28 inputs the binary signals X 1/2 , Y 1 , x 0  and Y 0  and outputs a logical product of them. The AND element 27 inputs the binary signals X 1/2 , Y 0 , x 0  and y 1  and outputs a logical product of them. The AND element 28 inputs the binary signals X 1 , Y 0 , x 0  and y 0  and outputs the logical product of them. 
     The AND element 29 inputs the binary signals X 1 , Y 1/2 , x 0  and y 0  and outputs a logical product of them. The AND element 30 inputs the binary signals X 1 , Y 1 , x 0  and y 0  and outputs a logical product of them. The AND element 31 inputs the binary signals X 1 , Y 0 , x 0  and y 1  and outputs the logical product of them. 
     The AND element 32 inputs the binary signals X 0 , Y 0 , x 1  and y 0  and outputs a logical product of them. The AND element 33 inputs the binary signals X 0 , Y 1/2 , x 1  and Y 0  and outputs a logical product of them. The AND element 34 inputs the binary signals X 0 , Y 1 , x 1  and y 0  and outputs the logical product of them. The AND element 35 inputs the binary signals X 0 , Y 0 , x 1  and y 1  and outputs the logical product of them. 
     The multivalued functional element 36 inputs an output signal sent from the AND element 20 and outputs a binary threshold value. The multivalued functional element 37 inputs an output signal sent from the AND element 20 and outputs a binary threshold value. 
     The multivalued functional element 38 inputs an output signal sent from the AND element 21 and outputs a binary threshold value. The multivalued functional element 39 inputs an output signal sent from the AND element 21 and outputs a binary threshold value. The multivalued functional element 40 inputs an output signal sent from the AND element 21 and outputs a binary threshold value. The multivalued functional element 41 inputs an output signal sent from the AND element 21 and outputs a binary threshold value. 
     The multivalued functional element 42 inputs an output signal sent from the AND element 22 and outputs a binary threshold value. The multivalued functional element 43 inputs an output signal sent from the AND element 22 and outputs a binary threshold value. The multivalued functional element 44 inputs an output signal sent from the AND element 22 and outputs a binary threshold value. The multivalued functional element 45 inputs an output signal sent from the AND element 22 and outputs a ternary threshold value. 
     The multivalued functional element 46 inputs an output signal sent from the AND element 23 and outputs a binary threshold value. The multivalued functional element 47 inputs an output signal sent from the AND element 28 and outputs a binary threshold value. The multivalued functional element 48 inputs an output signal sent from the AND element 23 and outputs a ternary threshold value. 
     The multivalued functional element 49 inputs an output signal sent from the AND element 24 and outputs a ternary threshold value. 
     The multivalued functional element 50 inputs an output signal sent from the AND element 25 and outputs a binary threshold value. The multivalued functional element 51 inputs an output signal sent from the AND element 25 and outputs a binary threshold value. 
     The multivalued functional element 52 inputs an output signal sent from the AND element 26 and outputs a binary threshold value. The multivalued functional element 53 inputs an output signal sent from the AND element 26 and outputs a binary threshold value. The multivalued functional element 54 inputs an output signal sent from the AND element 26 and outputs a binary threshold value. The multivalued functional element 55 inputs an output signal sent from the AND element 26 and outputs a binary threshold value. 
     The multivalued functional element 56 inputs an output signal sent from the AND element 27 and outputs a binary threshold value. The multivalued functional element 57 inputs an output signal sent from the AND element 27 and outputs a binary threshold value. The multivalued functional element 58 inputs an output signal sent from the AND element 27 and outputs a binary threshold value. The multivalued functional element 59 inputs an output signal sent from the AND element 27 and outputs a ternary threshold value. 
     The multivalued functional element 60 inputs an output signal sent from the AND element 28 and outputs a binary threshold value. The multivalued functional element 61 inputs an output signal sent from the AND element 28 and outputs a ternary threshold value. 
     The multivalued functional element 62 inputs an output signal sent from the AND element 29 and outputs a ternary threshold value. 
     The multivalued functional element 63 inputs an output signal sent from the AND element 30 and outputs a binary threshold value. The multivalued functional element 64 inputs an output signal sent from the AND element 30 and outputs a binary threshold value. 
     The multivalued functional element 65 inputs an output signal sent from the AND element 31 and outputs a binary threshold value. The multivalued functional element 66 inputs an output signal sent from the AND element 31 and outputs a binary threshold value. The multivalued functional element 67 inputs an output signal sent from the AND element 31 and outputs a binary threshold value. The multivalued functional element 68 inputs an output signal sent from the AND element 31 and outputs a binary threshold value. 
     The multivalued functional element 69 inputs an output signal sent from the AND element 32 and outputs a binary threshold value. The multivalued functional element 70 inputs an output signal sent from the AND element 32 and outputs a binary threshold value. 
     The multivalued functional element 71 inputs an output signal sent from the AND element 33 and outputs a binary threshold value. The multivalued functional element 72 inputs an output signal sent from the AND element 33 and outputs a ternary threshold value. 
     The multivalued functional element 73 inputs an output signal sent from the AND element 34 and outputs a ternary threshold value. 
     The multivalued functional element 74 inputs an output signal sent from the AND element 35 and outputs a binary threshold value. The multivalued functional element 79 inputs an output signal sent from the AND element 35 and outputs a binary threshold value. 
     The I/O element 76 inputs a borrow signal C and outputs a binary borrow signal C 0 . The I/O element 77 inputs a borrow signal C and outputs a binary borrow signal C 1 . 
     The AND element 78 inputs an output signal from any one of the multivalued functional elements 38, 42, 46, 52, 56 and 65 and a binary borrow signal C 0  from the I/O element 76 and outputs a logical product of them. 
     The AND element 79 inputs an output signal from any one of the multivalued functional elements 36, 39, 43, 47, 50, 53, 57, 63, 66 and 74 and a binary borrow signal C 1  from the I/O element 77 and outputs a logical product of them. 
     The OR element 84 inputs the logical product from the AND element 78 and the logical product from the AND element 79 and outputs a logical sum of them. 
     The delay circuit 91 inputs the logical sum from the OR element 84 and outputs a binary borrow signal C&#39;. The binary borrow signal C&#39; is further divided into two borrow signals C&#39; 1  and C&#39; 2  before outputting. 
     The AND element 80 inputs an output from any one of the multivalued functional elements 44, 48, 49, 58, 60, 62, 71 and 73 and a binary borrow signal C 0  from the I/0 element 76 and outputs a logical product of them. The AND element 81 inputs an output from any one of the multivalued functional elements 40, 45, 54, 59, 61, 67, 69 and 72 and a binary borrow signal C 1  from the I/O element 77 and outputs a logical product of them. The OR element 85 inputs the logical products from the AND elements 80 and 81 and outputs a subtracted output Z, that is, the logical sum of these logical products. The subtracted output Z is applied to the I/O elements 89 and 90. 
     The AND element 82 inputs an output from any one of the multivalued functional elements 41, 55, 88 and 70 and a binary borrow signal C 0  from the I/0 element 76 and outputs a logical product of them. The AND element 83 inputs an output from any one of the multivalued functional elements 37, 51, 64 and 75 and a binary borrow signal C 1  from the I/O element 77 and outputs a logical product of them. The OR element 86 inputs the logical products from the AND elements 82 and 83 and outputs a subtracted output Z&#39;, that is, the logical sum of these logical products. 
     The I/O element 89 inputs the subtracted output Z and outputs the subtracted output Z 1 . The I/O element 90 inputs the subtracted output Z and outputs the subtracted output Z 1/2 . 
     The OR element 87 inputs the subtracted output Z 1  from the I/O element 89 and the subtracted output Z&#39; from the OR element 88 and outputs the logical sum of them, that is, a subtracted output Z 2 . The OR element 88 inputs the subtracted output Z 1/2  from the I/O element 90 and the subtracted output Z&#39; from the OR element 86 and outputs a logical sum of them, that is, a subtracted output Z 1 . 
     The multivalued functional element may be a quantizing functional element. The quantizing functional element uses as an operating principle the wave theory of electrons and the quantum-mechanical quality that electrons hold energy merely at scattered spots. This element has a multivalued logic and is often referred to as a micro-structural element, a quantumlevel element, or a quantum-wave element. 
     Two-bit parallel binary input signals x and X shown in FIG. 1 are obtained by the binary input circuit shown in FIG. 2. 
     The binary input circuit shown in FIG. 2 is composed of NOT circuit elements (referred to as NOT elements) 92 and 93, AND elements 94 to 97, and an OR element 98. 
     Next, the description will be oriented to the operation of the binary input circuit shown in FIG. 2. 
     The NOT element 92 inputs the binary signal X 2  and outputs a NOT signal of the signal X 2 . The NOT element 93 inputs the binary signal X 1  and outputs a NOT signal of the signal X 1 . 
     The AND element 94 inputs an output signal from the NOT element 92 and the binary signal X 1  and outputs a logical product of them. The AND element 95 inputs an output signal from the NOT element 98 and the binary signal X 2  and outputs a logical product of them. The AND element 96 inputs the binary signals X 2  and X 1  and outputs a logical product of them, that is, a binary signal x. The AND element 97 inputs the logical product from the AND element 94 and a ternary threshold value 1/2 and outputs a logical product of them. The OR element 98 inputs the logical products from the AND elements 97 and 95 and outputs a logical sum of them, that is, a ternary signal X. 
     The binary input signals y and Y shown in FIG. 1 are obtained from the binary input circuit shown in FIG. 3. 
     The binary input circuit shown in FIG. 3 is composed of NOT elements 99 and 100, AND elements 101 to 104 and an OR element 105. 
     Next, the description will be oriented to the operation of the binary input circuit shown in FIG. 3. 
     The NOT element 99 inputs the binary signal Y 2  and outputs the NOT signal of the signal Y 2 . The NOT element 100 inputs the binary signal Y 1  and outputs the NOT signal of the signal Y 1 . 
     The AND element 101 inputs an output signal from the NOT element 99 and the binary signal Y 1  and outputs a logical product of them. The AND element 102 inputs an output signal from the NOT element 100 and the binary signal Y 2  and outputs a logical product of them. The AND element 103 inputs the binary signals Y 2  and Y 1  and outputs a logical product of them, that is, a binary signal y. 
     The AND element 104 inputs the logical product from the AND element 101 and a ternary threshold value 1/2 and outputs a logical sum of them. The OR element 105 inputs the logical products from the AND elements 104 and 102 and outputs a logical sum of them, that is, a ternary signal Y. 
     Table 1 lists codes allocated to two-bit parallel binary input signals X 2 , X 1 , Y 2  and Y 1 , ternary output signals X, x, Y and y, and borrow signals C 2 , C 1  and C. 
     
                       TABLE 1______________________________________X.sub.2X.sub.1      Y.sub.2             Y.sub.1                 x     X    y     Y    C.sub.2                                           C.sub.1                                                C______________________________________0    0     0      0   0     0    0     0    0   0    00    1     0      1   0     1/2  0     1/2  --     --1    0     1      0   0     1    0     1    --     --1    1     1      1   1     0    1     0    1   1    1                 (1/2   0)  (1/2   0)______________________________________ 
    
     The expressions (1) and (2) indicate logical expressions corresponding to the Table 1. 
     
         X=1/2X.sub.2 X.sub.1 +X.sub.2 X.sub.1, x=X.sub.2 X.sub.1 (or x=1/2X.sub.2 X.sub.1)                                                  (1) 
    
     
         Y=1/2Y.sub.2 Y.sub.1 +Y.sub.2 Y.sub.1, y=Y.sub.2 Y.sub.1 (or y=1/2Y.sub.2 Y.sub.1)                                                  (2) 
    
     Chart 1 lists logics provided in the ternary subtracter. Chart 2 lists borrow outputs used in the ternary subtracter. 
     
         ______________________________________CHART 1C.sub.0           C.sub.1x.sub.0         x.sub.1                 x.sub.0    x.sub.1X.sub.0   X.sub.1/2            X.sub.1                   X.sub.0                       X.sub.0                           X.sub.1/2                                X.sub.1                                    X.sub.0______________________________________y.sub.0Y.sub.0      1    2    3   3        1   2   &lt;Z&#39;, Z&gt;Y.sub.1/2       3          1    2   2   3        1Y.sub.1       2     3         1   1   2    3y.sub.1Y.sub.0       1     2    3            1    2   3______________________________________ 
    
     
         ______________________________________CHART 2C.sub.0           C.sub.1x.sub.0         x.sub.1                 x.sub.0    x.sub.1X.sub.0   X.sub.1/2            X.sub.1                   X.sub.0                       X.sub.0                           X.sub.1/2                                X.sub.1                                    X.sub.0______________________________________y.sub.0Y.sub.0                    3                &lt;C&#39;&gt;Y.sub.1/2       3                   3   3Y.sub.1       3     3             3   3    3y.sub.1Y.sub.0       3     3    3        3   3    3   3______________________________________ 
    
     Chart 2 
     Symbols added to the multivalued functional elements shown in FIG. 1 indicate physical functions listed in Table 2. Several kinds of logical elements may apply to these multivalued functional elements. 
     
                       TABLE 2______________________________________Symbol       Function______________________________________ ##STR1##         ##STR2## ##STR3##         ##STR4##______________________________________ 
    
     TABLE 2 
     These logical elements may apply to the binary input circuit shown in FIGS. 2 and 3 as well as a ternary logical circuit (equivalent circuit, OR circuit, AND circuit and so forth) composing the ternary subtraction shown in FIG. 1. 
     Table 3 lists re.mary subtracted outputs &lt;Z&#39;, Z&gt; and binary subtracted outputs &lt;Z 2 , Z 1  &gt; and codes allocated for them. 
     
                       TABLE 3______________________________________Z&#39;      Z               Z.sub.2                         Z.sub.1______________________________________0       0               0     00       1/2             0     10       1               1     01       0               1     1______________________________________ 
    
     In FIG. 1a, x 0  and x 1  are indicated by the equivalent circuits. In this case, since x 0  and x 1  are binary signals, they may be output signals of the x bar and the x. This holds true to y 0  and y 1  in FIG. 1a. 
     As indicated in the Table 1, in place of (1, 0) for (x, X), (1/2, 0) may be allocated and in place of (1, 0) for (y, Y), (1/2,0) may be allocated. 
     In this embodiment, for (1/2, 0), the similar synthesis may be executed. Hence, the description about this case is not herein. In the chart 1, a blank portion is &#34;0&#34;, &#34;1&#34; is 1/2, &#34;2&#34; is 1, and &#34;3&#34; is (10). Based on these values, the ternary subtracter shown in FIGS. 1a and 1b is arranged. 
     In the borrow outputs listed in the Chart 2, a blank is &#34;0&#34;. The value of &#34;3&#34; is &#34;1&#34;. On these values, the ternary subtracter shown in FIGS. 1a and 1b is arranged. 
     FIG. 4 is a circuit diagram showing an arrangement of a ternary subtracter according to a second embodiment of the present invention. The essential arrangement of the ternary subtracter shown in FIG. 4 is the same as that of the ternary subtracter shown in FIG. 1, except the input arrangements of AND elements 220 to 235. 
     Later, the description will be oriented to the inputs of the AND elements 220 to 235 shown in FIG. 4. The other part is the same as that shown in FIG. 1. Hence, the description about the part is left out. 
     The AND element 220 inputs binary signals X 0 , Y 0 , x 0  and y 0  and outputs a logical product of these signals. The AND element 221 inputs binary signals X 0 , Y1/2, and x 0  and outputs a logical product of these signals. The AND element 222 inputs binary signals X 0 , Y 1  and x 0  and outputs a logical product of these signals. 
     The AND element 223 inputs binary signals X 0 , Y 0 , x 0  and y 1  and outputs a logical product of these signals. The AND element 224 inputs binary signals X 1/2 , Y 0  and y 0  and outputs a logical product of these signals. The AND element 225 inputs binary signals X 1/2  and Y 1/2  and outputs a logical product of these signals. 
     The AND element 226 inputs binary signals X 1/2  and Y 1  and outputs a logical product of these signals. The AND element 227 inputs binary signals X 1/2 , Y 0  and Y 1  and outputs a logical product of these signals. The AND element 228 inputs binary signals X 1 , Y 0  and y 0  and outputs a logical product of these signals. 
     The AND element 229 inputs binary signals X 1  and Y 1/2  and outputs a logical product of these signals. The AND element 280 inputs binary signals X 1  and Y 1  and outputs a logical product of these signals. The AND element 281 inputs binary signals X 1 , Y 0  and Y 1  and outputs a logical product of these signals. 
     The AND element 282 inputs binary signals X 0 , Y 0 , x 1  and y 0  and outputs a logical product of these signals. The AND element 238 inputs binary signals X 0 , Y 1/2  and x 1  and outputs a logical product of these signals. The AND element 284 inputs binary signals X 0 , Y 1  and x 1  and outputs a logical product of these signals. 
     The AND element 235 inputs binary signals X 0 , Y 0 , x 1  and y 1  and outputs a logical product of these signals. 
     The ternary subtracter shown in FIG. 4 may use a binary input and a binary output circuits shown in FIGS. 5 to 7. 
     In FIGS. 2 and 3, the binary input signal is converted into a ternary output signal. In FIGS. 5 to 7, the input is binary. Thus, the binary output can be obtained. 
     The logics listed in Charts 3 and 4 are the substantially same as the logics of the above-mentioned subtracter, except that the used signals are x 0  X 0 , X 1/2 , X 1 , x 1  X 0  and the used signals are y 0  Y 0 , Y 1/2 , Y 1 , Y 1  Y 0 . 
     
         ______________________________________Chart 3C.sub.0            C.sub.1x.sub.0 X.sub.0      X.sub.1/2             X.sub.1                   x.sub.1 X.sub.0                        x.sub.0 X.sub.0                             X.sub.1/2                                  X.sub.1                                      x.sub.1 X.sub.0______________________________________y.sub.0Y.sub.0       1    2   3    3         1   2    &lt;Z&#39;,Y.sub.1/2       3           1   2    2    3        1    Z&gt;Y.sub.1       2      3        1    1    2    3y.sub.1Y.sub.0       1      2    3             1    2   3______________________________________ 
    
     
         ______________________________________Chart 4C.sub.0           C.sub.1x.sub.0 X.sub.0     X.sub.1/2            X.sub.1                  x.sub.1 X.sub.0                       x.sub.0 X.sub.0                            X.sub.1/2                                 X.sub.1                                     x.sub.1 X.sub.0______________________________________y.sub.0    Y.sub.0                     3                  &lt;C&#39;&gt;    Y.sub.1/2      3                    3    3    Y.sub.1      3      3             3    3    3y.sub.1    Y.sub.0      3      3    3        3    3    3   3______________________________________ 
    
     The Charts 3 and 4 lists logical expressions, on which the ternary subtracter shown in FIG. 4 may be arranged. The output signals X 0 , x 1 , X 1/2 , X 1  and x 0  shown in FIG. 5 are used as the binary input signals X 0 , x 1 , X 1/2 , X 1  and x 0  of the ternary subtracter shown in FIG. 1 or 4. Likewise, the output signals Y 0 , Y 1 , Y 1/2 , Y 1  and Y 0  shown in FIG. 6 may be used as the binary input signals Y 0 , y 1 , Y 1/2 , Y 1  and Y 0 . In FIG. 7, C 1  and C 0  may be replaced with the output signals of the equivalent circuits C O  and C 1 . The binary signal and the ternary signal are not used at one time. However, both of these signals may be used in combination. 
     FIGS. 8a and 8b are a circuit diagram showing an arrangement of a quaternary subtracter according to a third embodiment of the present invention. In the following description about the quaternary subtracter, the quantizing functional elements (referred to as quantizing elements) will be used as its multivalued functional elements. 
     The quaternary subtracter shown in FIGS. 8a and 8b is arranged to have I/O elements 210 to 217, AND elements 220 to 235, quantizing elements 236 to 275, I/O element 276 and 277, AND elements 278 to 281, OR elements 282 and 283, I/O elements 284 to 286, OR elements 287 and 288, and a one-bit delay circuit 289. 
     Next, each component will be described. 
     The I/O element 210 inputs a quaternary signal X and outputs a binary signal X 0 . The I/O element 211 inputs a quaternary signal X and outputs a binary signal X 1/3 . The I/O element 212 inputs a quaternary signal X and outputs a binary signal X 2/3 . The I/O element 213 inputs a quaternary signal X and outputs a binary signal X 1 . 
     The I/O element 214 inputs a quaternary signal Y and outputs a binary signal Y 0 . The I/O element 215 inputs a quaternary signal Y and outputs a binary signal Y 1/3 . The I/O element 216 inputs a quaternary signal Y and outputs a binary signal Y 2/3 . The I/O element 217 inputs a quaternary signal Y and outputs a binary signal Y 1 . 
     The AND element 220 inputs the binary signals X 0  and Y 0  and outputs a logical product of them. The AND element 221 inputs the binary signals X 0  and Y 1/3  and outputs a logical product of them. The AND element 222 inputs the binary signals X 0  and Y 2/3  and outputs a logical product of them. The AND element 223 inputs the binary signals X 0  and Y 1  and outputs a logical product of them. 
     The AND element 224 inputs the binary signals X 1/3  and Y 0  and outputs a logical product of them. The AND element 225 inputs the binary signals X 1/3  and Y 1/3  and outputs a logical product of them. The AND element 226 inputs the binary signals X 1/3  and Y 2/3  and outputs a logical product of them. The AND element 227 inputs the binary signals X 1/3  and Y 1  and outputs a logical product of them. 
     The AND element 228 inputs the binary signals X 2/3  and Y 0  and outputs a logical product of them. The AND element 229 inputs the binary signals X 2/3  and Y 1/3  and outputs a logical product of them. The AND element 230 inputs the binary signals X 2/3  and Y 2/3  and outputs a logical product of them. The AND element 281 inputs the binary signals X 2/3  and Y 1  and outputs a logical product of them. 
     The AND element 232 inputs the binary signals X 1  and Y 0  and outputs a logical product of them. The AND element 233 inputs the binary signals X 1  and Y 1/3  and outputs a logical product of them. The AND element 234 inputs the binary signals X 1  and Y 2/3  and outputs a logical product of them. The AND element 235 inputs the binary signals X 1  and Y 1  and outputs a logical product of them. 
     The quantizing element 236 inputs an output signal from the AND element 220 and outputs a binary threshold value. The quantizing element 237 inputs an output signal from the AND element 220 and outputs a binary threshold value. 
     The quantizing element 238 inputs an output signal from the AND element 221 and outputs a binary threshold value. The quantizing element 289 inputs an output signal from the AND element 221 and outputs a binary threshold value. The quantizing element 240 inputs an output signal from the AND element 221 and outputs a binary threshold value. The quantizing element 241 inputs an output signal from the AND element 221 and outputs a quaternary threshold value. 
     The quantizing element 242 inputs an output signal from the AND element 222 and outputs a binary threshold value. The quantizing element 243 inputs an output signal from the AND element 222 and outputs a binary threshold value. The quantizing element 244 inputs an output signal from the AND element 222 and outputs a quaternary threshold value. The quantizing element 245 inputs an output signal from the AND element 222 and outputs a quaternary threshold value. 
     The quantizing element 246 inputs an output signal from the AND element 228 and outbuts a binary threshold value. The quantizing element 247 inputs an output signal from the AND element 223 and outputs a binary threshold value. The quantizing element 248 inputs an output signal from the AND element 228 and outputs a quaternary threshold value. 
     The quantizing element 249 inputs an output signal from the AND element 224 and outputs a quaternary threshold value. 
     The quantizing element 250 inputs an output signal from the AND element 225 and outputs a binary threshold value. The quantizing element 251 inputs an output signal from the AND element 225 and outputs a binary threshold value. 
     The quantizing element 252 inputs an output signal from the AND element 228 and outputs a binary threshold value. The quantizing element 258 inputs an output signal from the AND element 226 and outputs a binary threshold value. The quantizing element 254 inputs an output signal from the AND element 226 and outputs a binary threshold value. The quantizing element 255 inputs an output signal from the AND element 226 and outputs a quaternary threshold value. 
     The quantizing element 256 inputs an output signal from the AND element 22 and outputs a binary threshold value. The quantizing element 25 inputs an output signal from the AND element 22 and outputs a binary threshold value. The quantizing element 258 inputs an output signal from the AND element 22 and outputs a quaternary threshold value. The quantizing element 259 inputs an output signal from the AND element 227 and outputs a quaternary threshold value. 
     The quantizing element 260 inputs an output signal from the AND element 228 and outputs a quaternary threshold value. The quantizing element 261 inputs an output signal from the AND element 228 and outputs a quaternary threshold value. 
     The quantizing element 262 inputs an output signal from the AND element 229 and outputs a quaternary threshold value. 
     The quantizing element 263 inputs an output signal from the AND element 230 and outputs a binary threshold value. The quantizing element 264 inputs an output signal from the AND element 230 and outputs a binary threshold value. 
     The quantizing element 265 inputs an output signal from the AND element 231 and outputs a binary threshold value. The quantizing element 266 inputs an output signal from the AND element 231 and outputs a binary threshold value. The quantizing element 267 inputs an output signal from the AND element 231 and outputs a binary threshold value. The quantizing element 268 inputs an output signal from the AND element 231 and outputs a quaternary threshold value. 
     The quantizing element 269 inputs an output signal from the AND element 232 and outputs a binary threshold value. The quantizing element 270 inputs an output signal from the AND element 232 and outputs a quaternary threshold value. 
     The quantizing element 271 inputs an output signal from the AND element 233 and outputs a quaternary threshold value. The quantizing element 272 inputs an output signal from the AND element 233 and outputs a quaternary threshold value. 
     The quantizing element 273 inputs an output signal from the AND element 234 and outputs a quaternary threshold value. 
     The quantizing element 274 inputs an output signal from the AND element 235 and outputs a binary threshold value. The quantizing element 275 inputs an output signal from the AND element 235 and outputs a binary threshold value. 
     The I/O element 276 inputs a borrow signal C and outputs a binary borrow signal C O . The I/O element 277 inputs the borrow signal C and outputs a binary borrow signal C 1 . 
     The AND element 278 inputs an output signal from any one of the quantizing elements 288, 242, 246, 252, 256 and 265 and the binary borrow signal C O  from the I/O element 276 and outputs a logical product of them. The AND element 279 inputs an output signal from any one of the quantizing elements 286, 289, 248, 247, 250, 258, 257, 268, 266 and 274 and the binary borrow signal C 1  from the I/O element 277 and outputs a logical product of them. The OR element 282 inputs the logical products from the AND elements 278 and 279 and outputs a logical sum of them. 
     The delay circuit 289 inputs the logical sum from the OR element 282 and outputs a binary borrow signal C&#39;. The binary borrow signal C&#39; is divided into two borrow signals C&#39; 1  and C&#39; 2  before outputting. 
     The AND element 280 inputs an output signal from any one of the quantizing elements 240, 244, 248, 249, 254, 258, 260, 262, 267, 269, 271 and 278 and the binary borrow signal C O  from the I/0 element 276 and outputs a logical product of them. The AND element 281 inputs an output signal from any one of the quantizing elements 287, 241, 245, 251, 255, 259, 261, 264, 268, 270, 272 and 275 and the binary borrow signal C 1  from the I/O element 277 and outputs a logical product of them. The OR element 288 inputs the logical products from the AND elements 280 and 281 and outputs a logical sum of them, that is, a subtracted output Z. The subtracted output Z is applied to the I/O elements 284, 285 and 286. The I/O element 284 inputs the subtracted output Z and outputs a subtracted output Z 2/3 . The I/O element 285 inputs the subtracted output Z and outputs a subtracted output Z 1 . The I/O element 286 inputs the subtracted output Z and outputs a subtracted output Z 1/3 . 
     The OR element 287 inputs the subtracted output Z 2/3  from the I/O element 284 and the subtracted output Z 1  from the I/O element 285 and outputs a logical sum of them, that is, a subtracted output Z 2 . The OR element 288 inputs the subtracted output Z 1  from the I/O element 285 and the subtracted output Z 1/3  from the I/O element 286 and outputs a logical sum of them, that is, the subtracted output Z 1 . 
     The quaternary signal X shown in FIG. 8a can be obtained by the binary input circuit shown in FIG. 9. The binary input circuit is composed of NOT elements 290, 291, AND elements 292 to 296 and an OR element 297. 
     Next, the description will be oriented to the operation of the binary input circuit shown in FIG. 9. 
     The NOT element 290 inputs the binary signal X 2  and outputs the NOT signal. The NOT element 291 inputs the binary signal X 1  and outputs the NOT signal. 
     The AND element 292 inputs the output signal from the NOT element 290 and the binary signal X 1  and outputs a logical product of them. The AND element 29 inputs the output signal from the NOT element 291 and the binary signal X 2  and outputs a logical product of them. 
     The AND element 294 inputs the binary signals X 2  and X 1  and outputs a logical product of them. The AND element 295 inputs the logical product from the AND element 292 and a quaternary threshold value 1/3 and outputs a logical product of them. The AND element 296 inputs the logical product from the AND element 292 and a quaternary threshold value 2/3 and outputs a logical product of them. 
     The OR element 297 inputs the logical product from the AND element 295 and the logical product from the AND element 296, and the logical product from AND element 294 and outputs a logical sum of them, that is, the quaternary signal X. 
     The quaternary signal Y shown in FIG. 8a can be obtained by the binary input circuit shown in FIG. 10. The binary input circuit is composed of NOT elements 298, 299, AND elements 300 to 304 and an OR element 305. 
     Next, the description will be oriented to the operation of the binary input circuit shown in FIG. 10. 
     The NOT element 298 inputs the binary signal Y 2  and outputs the NOT signal. The NOT element 299 inputs the binary signal Y 1  and outputs the NOT signal. 
     The AND element 300 inputs the output signal from the NOT element 298 and the binary signal Y 1  and outputs a logical product of them. 
     The AND element 301 inputs the output signal from the NOT element 299 and the binary signal Y 2  and outputs a logical product of them. The AND element 302 inputs the binary signals Y 2  and Y 1  and outputs a logical product of them. The AND element 303 inputs the logical product From the AND element 300 and a quaternary threshold value 1/3 and outputs a logical product of them. The AND element 304 inputs the logical product from the AND element 301 and a quaternary threshold value 2/3 and outputs a logical product of them. 
     The OR element 305 inputs the logical product From the AND element 303, the logical product from the AND element 304 and the logical product from the AND element 302 and outputs a logical sum of them, that is, a quaternary signal Y. 
     Table 4 lists codes allocated for two-bit parallel binary input signals X 2 , X 1 , Y 2  and Y 1 , quaternary output signals X and Y, and borrow signals C 2 , C 1  and C. 
     
                       TABLE 4______________________________________X.sub.2  X.sub.1        Y.sub.2 Y.sub.1                    X      Y    C.sub.2                                      C.sub.1                                          C______________________________________0      0     0       0   0      0    0     0   00      1     0       1   1/3    1/3  --      --1      0     1       0   2/3    2/3  --      --1      1     1       1   1      1    1     1   1______________________________________ 
    
     Expressions (3) and (4) indicate logical expressions corresponding to the Table 4. 
     
         X=1/3X.sub.2 X.sub.1 +2/3X.sub.2 X.sub.1 +X.sub.2 X.sub.1  (3) 
    
     
         Y=1/3Y.sub.2 Y.sub.1 +2/3Y.sub.2 Y.sub.1 +Y.sub.2 Y.sub.1  (4) 
    
     Chart 5 lists logics provided in the quaternary subtracter. Chart 6 lists borrow outputs. 
     
         ______________________________________CHART 5C.sub.0          C.sub.1X.sub.0 X.sub.1/3          X.sub.2/3                  X.sub.1                      X.sub.0                           X.sub.1/3                                X.sub.2/3                                      X.sub.1______________________________________Y.sub.0     1      2     3   3         1     2   &lt;Z&gt;Y.sub.1/33             1     2   2    3          1Y.sub.2/32      3            1   1    2    3Y.sub.11      2      3              1    2     3______________________________________ 
    
     
         ______________________________________CHART 6C.sub.0          C.sub.1X.sub.0 X.sub.1/3          X.sub.2/3                  X.sub.1                      X.sub.0                           X.sub.1/3                                X.sub.2/3                                      X.sub.1______________________________________Y.sub.0                      3                   &lt;C&#39;&gt;Y.sub.1/33                       3    3Y.sub.2/33      3                3    3    3Y.sub.13      3      3         3    3    3     3______________________________________ 
    
     The symbols added to the quantizing elements shown in FIG. 8 stand for physical functions listed in Table 5. 
     
                       TABLE 5______________________________________Symbol       Function______________________________________ ##STR5##         ##STR6## ##STR7##         ##STR8## ##STR9##         ##STR10##______________________________________ 
    
     Several kinds of logical elements may apply to the quantizing elements shown in FIG. 8. These logical elements may apply to the binary input circuit shown in FIGS. 9 and 10 as well as the quaternary logic circuit (equivalent circuit, OR circuit, AND circuit and so forth) composing the quaternary subtracter shown in FIG. 8. 
     Table 6 lists the quaternary subtracted output &lt;Z&gt; and the binary subtracted output &lt;Z 2 , Z 1  &gt; and a relation among codes. 
     
                       TABLE 6______________________________________Z                Z.sub.2                  Z.sub.1______________________________________0                0     01/3              0     12/3              1     01                1     1______________________________________ 
    
     In FIG. 4, x 0  and x 1  are denoted by the equivalent circuits. Since the binary signal is used in this case, x and a bar x may be used as an output signal. This holds true to y 0  and y 1 . 
     In the logics listed in the Chart 5, the blank is &#34;0&#34; The value of &#34;1&#34; is 1/3. The value of &#34;2&#34; is 2/3. The value of &#34;3&#34; is 1. On these values, the quaternary subtracter shown in FIG. 8 is arranged. 
     In the borrow output listed in the Chart 6, the blank is &#34;0&#34;. The value of &#34;3&#34; is 1. On these values, the quaternary subtracter shown in FIG. 8 is arranged. 
     The circuits shown in FIGS. 11 and 12 use binary inputs and binary outputs. 
     The output signals X 0 , X 1/3 , X 2/3 , and X 1  shown in FIG. 11 may be used as binary input signals X 0 , X 1/3 , X 2/3  and X 1  used in the quaternary subtracter shown in FIG. 8. This holds true to the output signals Y 0 , Y 1/3 , Y 2/3  and Y 1  shown in FIG. 12. The binary signal arid the quaternary signal cannot be used at one time. However, these signals may be used in combination. 
     FIG. 13 is a circuit diagram showing an arrangement of an operator arranged to have a multivalued converter 318, a multivalued operating unit 319, a binary converter 320, a multivalued signal input unit 321, and a multivalued signal output unit 322. 
     To use only the ternary input signal, what is required is only to input the ternary signal from the multivalued input unit 321. For the multivalued operator 319, the ternary subtracter shown in FIG. 1 or 4 may be used. To use only the quaternary input signal, what is required is only to input the quaternary signal from the multivalued signal input unit 321. For the multivalued operator 319, the quaternary subtracter shown in FIG. 8 may be used. 
     In addition to a way of use described above, it is possible to combine the I/0 signals with the binary signal and the multivalued signal in a various manner as shown in FIG. 13. 
     According to the above-mentioned embodiment, the subtracting speed is allowed to be doubled. Though the clock frequency is reduced in half, the subtracting speed may be kept. This means the power consumption of the subtracter is lowered. Further, keeping the circuit in scale means reduction of logical elements or circuit elements composing the subtracter in number, thereby making it possible to lower the power consumption. 
     If the processing amount of bit signals to be executed at a time is increased, the multivalued logics and the multivalued functional elements allow a rapid subtracting speed to be realized without having to increase the subtracter circuit in scale. 
     Many widely different embodiments of the present invention may be constructed without departing from the spirit and scope of the present invention.