A Constructing Theory of Multiple-Valued Logic Functions based on the Exclusive-OR Minimization Technique and Its Implementation

Exclusive-OR 최소화 기법에 의한 다치논리 함수의 구성 및 실현

The sum-of-product type MVL (Multiple-valued logic) functions can be directly transformed into the exclusive-sum-of-literal-product(ESOLP) type MVL functions with a substitution of the OR operator with the exclusive-OR(XOR) operator. This paper presents an algorithm that can reduce the number of minterms for the purpose of minimizing the hardware size and the complexity of the circuit in the realization of ESOLP-type MVL functions. In Boolean algebra, the joinable true minterms can form the cube, and if some cubes form a cube-chain with adjacent cubes by the insertion of false cubes(or, false minterms), then the created cube-chain can become a large cube which includes previous cubes. As a result of the cube grouping, the number of minterms can be reduced artificially. Since ESOLP-type MVL functions take the MIN/XOR structure, a XOR circuit and a four-valued MIN/XOR dynamic-CMOS PLA circuit is designed for the realization of the minimized functions, and PSPICE simulation results have been also presented for the validation of the proposed algorithm.