Principles of switching algebra

In order to describe, analyse and design digital circuits it is first necessary to become familiar with the underlying basic mathematics of the subject. The development of an algebra for reasoning about ‘logical’ problems by Boole [1] and others in the nineteenth century was utilized by Shannon [2] in 1938 to establish the mathematical tools needed to describe the operation of logic circuits. The ever-increasing use of digital circuits since that time is based not only upon new manufacturing techniques but on the fact that suitable theoretical methods exist to support circuit design. In this chapter we review relevant mathematical theory [3], including Boolean algebras, in such a way that any engineer may readily appreciate and apply it to the design of digital systems. In addition, much of the basic terminology used in later chapters will be defined. A number of different techniques for representing logic functions will be introduced, together with their possible areas of application.