6 Classical Logic, Gates, and Circuits

In this chapter we briefly study classical computation, presenting the ideas in roughly chronological order. We start with boolean functions and logic, first introduced by George Boole in the late nineteenth century. In the 1930s, Claude Shannon studied boolean algebra and realized that boolean functions could be described using electrical switches. The electrical components that correspond to boolean functions are called logic gates. Composing boolean functions becomes the study of circuits involving these gates. We will begin by studying boolean functions in terms of logic; then we will show how to translate everything into circuits and gates. The material, up to this point, is now considered standard and is contained in every introductory computer science text. But after this we look at some ideas that are usually not part of the standard introduction.