8 - Logic gates

Abstract

In digital circuits, extensive use is made of switching circuits. A switch is either on or off with these states being denoted by the digits 1 or 0. A logic circuit is considered as a collection of switching circuits. In this chapter, the basic mathematics necessary to analyze and synthesize such circuits is introduced. The mathematics involved is named after George Boole, who first developed the modern ideas of the mathematics concerned with the manipulation of logic statements. In this chapter, Boolean algebra is approached by means of the analysis of switching circuits. The main objective of this chapter is to teach how to represent switching systems by logic gates, how to represent the action of such gates by truth tables, how to describe switching logic by Boolean statements, and how to manipulate Boolean statements by the use of the rules of Boolean algebra.