ABSTRACT
This chapter begins with a presentation of the axioms and theorems of Boolean algebra — the axioms are referred to as postulates. The minimization of logic functions can be realized by applying the principles of Boolean algebra. In 1854, George Boole introduced a systematic treatment of the logic operations AND, OR, and NOT, which is called Boolean algebra. The chapter discusses various techniques for minimizing a Boolean function. A Boolean function is an algebraic representation of digital logic. Each term in an expression represents a logic gate and each variable in a term represents an input to a logic gate. The number of terms and variables that are necessary to generate a Boolean function can be minimized by algebraic manipulation. A Karnaugh map provides a geometrical representation of a Boolean function. The Quine-McCluskey algorithm is a tabular method of obtaining a minimal set of prime implicants that represents the Boolean function.
