Fundamentals of Digital Logic and Microcontrollers, 6th Edition

Chapter 3Boolean Algebra and Digital Logic Gates

This chapter describes fundamentals of logic operations, Boolean algebra, minimization techniques, and implementation of basic digital circuits.

Digital circuits contain hardware elements called gates that perform logic operations on binary numbers. Devices such as transistors can be used to perform the logic operations. Boolean algebra is a mathematical system that provides the basis for these logic operations. George Boole, an English mathematician, introduced this theory of digital logic. The term Boolean variable is used to mean the two-valued binary digit 0 or 1.

3.1 Basic Logic Operations

Boolean algebra uses three basic logic operations namely, NOT, OR, and AND. These operations are described next.

3.1.1 NOT Operation

The NOT operation inverts or provides the ones complement of a binary digit. This operation takes a single input and generates one output. The NOT operation of a binary digit provides the following result:

Therefore, NOT of a Boolean variable A, written as A (or A′) is 1 if and only if A is 0. Similarly, A is 0 if and only if A is 1. This definition may also be specified in the form of a truth table:

The truth table contains the inputs and outputs of a digital logic circuit. The truth table is used to verify ...