Exclusive-OR circuit
BACKGROUND OF THE INVENTION 
     The present invention relates to an exclusive-OR circuit adapted for use, for example, in a circuit for driving a pulse motor. 
     The most fundamental exclusive-OR circuit is composed, as shown in FIG. 1, of inverters N1, N2, AND gates A1, A2 and an OR gate O. 
     The output OUT of the exclusive-OR circuit thus constructed can be represented as below by using inputs A and B. 
     
         OUT=AB+AB=A⊕B 
    
     FIG. 2 shows an exclusive-OR circuit which employs integrated-injection logic (I 2  L) circuits operating fundamentally as an inverter. 
     The inputs A and B are respectively inverted by I 2  L gates G1 and G2 having multiple-collector outputs. A first output of gate G1 is short-circuited with the output of a gate G3 having its input connected to a first output of gate G2 to provide a wired-AND function. The logical formula at the connecting point of the outputs of gates G1 and G3 is represented as below. 
     
         X=AB 
    
     Similarly, a second output of gate G2 is short-circuited with the output of a gate G4 having its input connected to a second output of gate G1 to provide a wired-AND function. 
     The logical formula at the connecting point of the outputs of gates G2 and G4 is represented as below. 
     
         Y=AB 
    
     I 2  L gates G5, G6, G7 form an OR circuit. Therefore, the logical formula at the output is given by 
     
         OUT=AB+AB 
    
     The logical multiplication function and the logical sum function of the circuit of FIG. 2 are achieved by employing the property of a logic current of open collector output type. The I 2  L gate is an example of the open-collector-output logic circuits. 
     As described above, the conventional exclusive-OR circuit necessitates five logic gates G3 to G7. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an exclusive-OR circuit which can be composed of a lesser number of elements. 
     The above object of the present invention is achieved by using two flip-flop circuits, as two input signal sources, each of which provides complementary outputs necessary to provide an exclusive-OR function. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 and 2 show circuit diagrams of conventional exclusive-OR circuits; 
     FIG. 3A shows a circuit diagram of an exclusive-OR circuit according to an embodiment of the present invention; 
     FIG. 3B shows a practical arrangement of the exclusive-OR circuit of FIG. 3A using the integrated-injection logic gates; 
     FIG. 4 shows a circuit diagram of 4-phase pulse generating circuit using the exclusive-OR circuit of the invention; 
     FIG. 5 is a timing chart of the pulse generating circuit of FIG. 4; 
     FIG. 6 is a circuit diagram of a flip-flop circuit composed of integrated-injection logic gates; 
     FIG. 7A is a circuit diagram of another embodiment of the present invention; 
     FIG. 7B is a practical arrangement of the circuit in FIG. 7A; 
     FIG. 8 is a circuit diagram of still another embodiment of the invention; and 
     FIG. 9 is a circuit diagram of still another embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 3A shows one embodiment of the exclusive-OR circuit according to the present invention. The outputs of flip-flop circuits FF1, FF2 are used as inputs of the exclusive-OR circuit. Since each of the flip-flop circuits provides a pair of complementary outputs, the gates G3, G4 of FIG. 2 can be eliminated. 
     The flip-flop circuits FF1, FF2 are composed of open collector circuits, e.g., I 2  L gates. The output Q A  of flip-flop circuit FF1 is short-circuited with the output Q B  of flip-flop circuit FF2 to form a wired-AND circuit. On the other hand, the output Q A  of flip-flop circuit FF1 is short-circuited with the output Q B  of flip-flop circuit FF2 to provide a wired-AND circuit. The outputs of two wired-AND circuits are supplied to an OR circuit which is composed of gates G8, G9, G10. Accordingly, it is evident that the circuit in FIG. 3A provides the exclusive-OR function similar to the circuit in FIG. 2. 
     The exclusive-OR circuit using flip-flops is advantageously adapted for a circuit for driving a pulse motor, because flip-flop circuits are used in the drive circuit. FIG. 3B shows a practical arrangement of the circuit of FIG. 3A which is composed of I 2  L gates. 
     FIG. 4 shows a 4-phase pulse generating circuit which employs the above exclusive-OR circuit and may be used, for example, as a circuit for driving a 4-phase pulse motor. In FIG. 4, FF1, FF2 represent flip-flop circuits which employ I 2  L circuits, 11 the above exclusive-OR circuit, and 12 a non-inverting buffer circuit. 
     The flip-flop circuit FF1 is driven by a clock signal CL, and the flip-flop circuit FF2 is driven by the output Q A  of the flip-flop circuit FF1. The outputs of the exclusive-OR circuit 11 and the flip-flop circuit FF2 produce outputs OP1 to OP4 through buffer circuits 12. 
     The output signals OP1 to OP4 are represented as below. 
     
         OP1=Q.sub.A ⊕Q.sub.B 
    
     
         OP2=Q.sub.B 
    
     
         OP3=Q.sub.A +Q.sub.B 
    
     
         OP4=Q.sub.B 
    
     FIG. 5 shows the timing chart of the respective signals of the circuit in FIG. 4. The outputs OP1 to OP4 are four-phase pulse signals displaced by 90° in phase from each other, which are used to drive a four-phase pulse motor. 
     FIG. 6 shows a practical arrangement of the flip-flop circuits FF1, FF2, which are composed of gates G11 to G17. 
     FIGS. 7A and 7B show another embodiment of the invention. This embodiment uses input signals A and B, and an inverted signal is produced by a gate G18. Namely, A·B is inverted by gate G18 to produce A·B. Further, A·B·A and A·B·B are supplied to an OR circuit which is composed of gates G19, G20, G21 to provide the exclusive-OR function. 
     This circuit is composed on the basis of a modification of the logic formula AB+AB as shown below. ##EQU1## 
     FIG. 7B shows a practical arrangement of the circuit in FIG. 7A. 
     The above formulae are further modified as below. 
     
         ABA+ABB=AB(A+B)=AB×(AB) 
    
     FIG. 8 shows an exclusive-OR circuit which is based on this modification. Namely, the product of the output Q A  of the flip-flop FF1 and the output Q B  of the flip-flop FF2 is supplied to a gate G22. On the other hand, the product of the output Q A  of the flip-flop FF1 and the output Q B  of the flip-flop FF2 is supplied to a gate G23. The outputs of the gates G22, G23 are wired-ANDed to provide the exclusive-OR function. 
     FIG. 9 shows a circuit providing an exclusive-OR function with gates G24, G25 added to the circuit in FIg. 8 and with inputs A and B. Namely, this circuit can be composed of only four gates.