A Method for Simplifying Boolean Functions

This article presents an iterative technique for simplifying Boolean functions. The method enables the user to obtain prime implicants by simple operations on a set of decimal numbers which describe the function. This technique may be used for functions of any number of variables. At the present time, although several design aids have been introduced, 1 2 3 the synthesis of switching circuits remains a highly developed art, the theory being of only limited value to the circuit designer. In particular, that part of the design process involving the simplification of Boolean functions having large numbers of variables still presents a major problem. Probably the best method currently available for the solution of such problems is the Quine-McCluskey T a b u l a r M e t h o d , which consists of the exhaustive comparison of terms of the standard sum for adjacencies -- terms which differ in only one variable. This technique, besides being a long, tedious one, determines all possible prime implicants of the given function. T h u s a second problem is generated -- selecting the essential prime implicants from among those found. This in itself is often a difficult procedure, for which specific methods have been developed. 1 The m e t h o d to Ih» described in this paper i« a simple, iterative technique for determining the prime implicants of a Boolean function. All of the essential prime implicants are found with this method, and in general, some or all of the nonessential prime implicants ore automatically eliminated, materially simplifying the final search for the essential prime implicants.