A multiple-valued logic synthesis using the Kleenean coefficients

This paper presents a new multiple-valued sum-of-products expression structure and shows its minimization to reduce the number of implicants needed in the minimal sum-of-products expressions. The new expression is introduced as the MAX-of-MIN's expression of Kleenean coefficients and one or more literals, where Kleenean coefficients are defined as the logic formulas built from MIN, constants and variables xi and x~i~. It shows a minimization of the above expressions based on binary Quine McCluskey algorithm. The result of computer simulation shows that a saving of approximately 9% on the average can be had for some random functions. A result for some arithmetic functions shows that the minimal solutions of MOD radix SUM, MAX and MIN functions require much fewer implicants than those of the standard sum-of-products expressions.<>