Synthesis of Multiple-Valued Logic Networks Based on Tree-Type Universal Logic Module

This correspondence presents a theoretical study on the synthesis of multiple-valued logic networks based on tree-type universal logic modules (T-ULM’s). The mathematical notation of T-ULM is introduced. On the basis of the mathematical properties, an algorithm for synthesizing an arbitrary logic function of n variables with a smaller number of modules is presented. In this algorithm, only true and constant inputs are allowed at input terminals. The algorithm consists of two parts. The first one is a functional decomposition, and the other one is the proper order of the expansion which is the problem of finding the most incomplete tree structure. Thus it is established that the systematic and nonexhaustive procedure of the algorithm gives a suboptimal solution for the reduction of the number of T-ULM’s.