Parametric General Solutions of Boolean Equations Via Variable–Entered Karnaugh Maps

Abstract

A new method for obtaining a compact parametric general solution of a system of Boolean equations is presented. The method relies on the use of the variable-entered Karnaugh map (VEKM) to implement various steps of the solution procedure and to ensure minimization of the expressions obtained. It is highly efficient as it requires the construction of natural maps that are significantly smaller than those required by classical methods. Moreover, the method is applicable to general Boolean equations and is not restricted to the two- valued case. As an offshoot, the paper contributes some pictorial insight on the representation of “big” Boolean algebras and functions. It also predicts the correct number of particular solutions of a Boolean equation, and produces a comprehensive list of particular solutions, if desired. Details of the method are carefully explained and further demonstrated via an illustrative example.