Use of gray decoding for implementation of symmetric functions

Abstract

This paper discusses reduction of the number of product terms in representation of totally symmetric Boolean functions by Sum of Products (SOP) and Fixed Polarity Reed-Muller (FPRM) expansions. The suggested method reduces the number of product terms, correspondingly, the implementation cost of symmetric functions based on these expressions by exploiting Gray decoding of input variables. Although this decoding is a particular example of all possible linear transformation of Boolean variables, it is efficient in the case of symmetric functions since it provides a significant simplification of SOPs and FPRMs. Mathematical analysis as well as experimental results demonstrate the efficiency of the proposed method.