# 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 ...

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