Compound Synthesis of Threshold-Logic Network for the Realization of General Boolean Functions

Abstract

This paper deals with the problem of compound synthesis of threshold-logic network, or of realizing a general Boolean function with a number of threshold-logic elements. Some basic theorems concerning the expression of a general Boolean function as a combination of a number of threshold functions are presented. The general structure of a network of m threshold-logic elements is analyzed in light of the basic theorems and properties of threshold functions. The properties of isobaric threshold functions are discussed and are utilized for compound synthesis. Methods for decomposing a function into a sum or product of unate functions and into a sum or product of threshold functions are developed. A synthesis procedure conforming with the general structure of a network of threshold-logic elements is given. A simplified synthesis procedure, which needs less cut and trial than the original procedure and is, therefore, more practical, is also presented. Some special situations are discussed. Examples are worked out to show the decomposition of functions, and to illustrate the synthesis method.