Extending Quine-McCluskey for Exclusive-Or logic synthesis

Abstract

Various forms of Boolean minimization have been used within electronic engineering degrees as a key part of the syllabus. Typically, Karnaugh maps and Quine-McCluskey methods are the principal exhaustive search techniques for digital minimization at the undergraduate level as they are easy to use and simple to understand. Despite the popularity of these methods, they are not well suited to typical digital circuits. Simple examples of such circuits are parity, adders, gray code generators, and so on. The common factor among these is the Exclusive-Or logic gate. This problem is exacerbated by the increasing importance of Exclusive-Or in modern design. This paper proposes an extension to the Quine-McCluskey method which successfully incorporates Exclusive-Or gates within the minimization process. A number of examples are given to demonstrate the effectiveness of this approach. This technique is easy to master as it can be considered to be an extension to the Quine-McCluskey method.