Some Methods for Simplifying Switching Circuits Using “Don't Care” Conditions

Abstract

Several methods for simplifying switching circuits using “don't-care” conditions are suggested. One of the methods uses the following procedure: Let the given circuit be represented by the truth function F . Let the given “don't-care” conditions be denoted by D = 0. (For example, if x ₁ = 1 and x ₂ = 0 represent the combination of input signals which never takes place, then D = x ₁ x ₂ .) Generate all the irredundant disjunctive and conjunctive forms which are equivalent to F whenever D = 0. From these forms, the simplest ones may then be chosen according to a given measure of simplicity. They correspond to the simplest two-level AND/OR or OR/AND switching circuits which, under the “don't-care” conditions, perform the same function as the given circuit. Several methods for generating the equivalent irredundant forms are suggested. They are generalizations of those due to Quine, Ghazala and Mott, and may be programmed for use on computers. Alternative simplification methods are also given.