Boolean algebra is mathematics of logic. It is one of the most basic tools available to the logic designer and thus can be effectively used for simplification of complex logic expressions. Other useful and widely used techniques based on Boolean theorems include the use of Karnaugh maps in what is known as the mapping method of logic simplification and the tabular method given by Quine–McCluskey. In this chapter, we will have a closer look at the different postulates and theorems of Boolean algebra and their applications in minimizing Boolean expressions. We will also discuss at length the mapping and tabular methods of minimizing fairly complex and large logic expressions.
Boolean algebra, quite interestingly, is simpler than ordinary algebra. It is also composed of a set of symbols and a set of rules to manipulate these symbols. However, this is the only similarity between the two. The differences are many. These include the following: