On low cost realization of multiple-valued logic functions

This paper evaluates the number of product terms needed in the minimal sum-of-products expressions for extended product and sum operators based on Shannon expansion. We show definitions of a product-type and a sum-type function. According to the definitions, we list all product-type and sum-type functions by investigating all three-valued two-variable functions. Using the functions, we examine the numbers of product terms needed in the minimal sum-of-product expressions for any three-valued two-variable functions and show that the MODSUM-of-MINs expressions require fewest product terms of the all. On investigating all four-valued sum-of-products expressions, it is shown that MODSUM-of-MINs expressions require the fewest product terms. Furthermore, on investigating the expressions with the weak conditions for the product-type function. We find some expressions requiring fewer product terms than the MODSUM-of-MINs expressions