Algorithms for Verifying Variants of Boolean Algebra Equations and Expressions

Abstract

The word, Boolean, was derived from the name of a British mathematician, George Boole, as a result of his classical work on logic. Boolean algebra can be defined as a set, whose members have two possible values, with two binary operators and one unary operator, satisfying the properties of commutativity, associativity, distributivity, existence of identity and complement. Boolean algebra has important applications to the design of computer hardware and software. Techniques, like Karnaugh maps, Boolean algebra theorems and laws can be used to simplify and reduce complex Boolean algebra expressions, while truth table can be used to confirm that the reduced Boolean algebra expression is the same as the original, complex Boolean algebra expression. Generating the truth table manually is tedious, especially when the Boolean algebra equation or expression has many Boolean variables. This paper presents three variants of Boolean algebra, and novel algorithms that can be used to verify Boolean algebra equations and evaluate Boolean algebra expressions.