Introduction

This unit is very closely linked with Unit 1. It was C.E.Shannon, the founder of information theory, who observed an analogy between the functioning of switching circuits and certain operations of logical connectives. In 1938 he gave a technique based on this analogy to express and manipulate simple switching circuits algebraically. Later, the discovery of some new solid state devices (called electronic switches or logic gates) helped to modify these algebraic techniques and, thereby, paved a way to solve numerous problems related to digital systems algebraically.

In this unit, we shall discuss the symbolic logic techniques which are required for the algebraic understanding of circuits and computer logic. We shall introduce you to Boolean algebras with the help of certain examples based on objects you are already familiar with. You will see that such algebras are apt for describing operations of logical circuits used in computers.

Also we have discussed the linkages between Boolean expressions and logic circuits.

And,  you will read about how to express the overall functioning of a circuit mathematically in terms of certain suitably defined functions called Boolean functions. In this section we shall also consider a simple circuit design problem to illustrate the applications of the relationship between Boolean functions and circuits.

Objectives

After reading this unit, you should be able to:

• define and give examples of Boolean algebras, expressions and functions;
• give algebraic representations of the functioning of logic gates;
• obtain and simplify the Boolean expression representing a circuit;
• construct a circuit for a Boolean expression;
• design and simplify some simple circuits using Boolean algebra techniques