A Comparison of the Methods of Boolean-Equation Solving and Input-Domain Constraining for Handling Type-2 Problems of Digital Circuit Design

Abstract

With the advent of digital computers, several prominent problems of digital circuit design emerged. A particular class of these problems, (called Type-2 problems) can be divided into two subclasses depending on whether an honest translator is possible or a sneaky translator is warranted. The case of an honest translator is simply an inverse problem of logic in which knowledge of the vectorial function Z(X) is utilised to produce its inverse vectorial function X(Z). Though an old method of solving type-2 problems was known almost half a century ago, two modern methods are now possible, namely the method of Boolean-equation solving and the method of input-domain constraining. The purpose of this paper is to expose and illustrate these two novel methods, with a stress on comparing them together and demonstrating their superiority to (as well as agreement with) the old conventional method. This purpose is achieved by way of three typical classical examples for which conventional solutions are somewhat tedious and cumbersome, while modern solutions are simple and insightful. Throughout these examples, the Karnaugh map is effectively utilised, either in its conventional version or in its variable-entered version. The Boolean-equation-solving method seems to involve certain unwarranted steps that might be possibly skipped. However, its utility can be extended beyond type-2 problems.