Threshold logic: A simplified synthesis by a recursive method

Despite the numerous threshold logic synthesis methods developed in the past decade, the logic designer is still handicapped by the technological independent characterization of these methods. Hence, it has long been the desire for the logic designer to have a simple, efficient threshold-logic synthesis method, analogous to conventional Boolean synthesis using ANDs, ORs, or combinations of ANDs and ORs. The scope of this paper is to describe the theoretical basis of a direct and efficient synthesis method for a threshold function(s) from its Boolean expression. A set of recursive formulas of weight and threshold is thus derived. This method is capable of handling a relatively large number of Boolean variables, whether the Boolean expression is a single threshold function or compound threshold functions. The minimal realization of the Boolean threshold function can also be obtained. Another noted advantage of this recursive synthesis method is to give a clearer picture by permitting the investigator to examine every intermediate step while the final solution is being attained.