Introduction

Boolean Algebra

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This is an introduction to Boolean algebra tutorial.

About

Mathematician George Boole invented the Boolean Algebra. This algebra deals with the rules by which logical operations are carried out. So, a digital circuit in this system is represented as input and output symbols and the function of the circuit is expressed as a Boolean relationship between the symbols.

Terms

  • Binary Number System
  • Binary Constant
  • Binary Variable
  • Basic Logical Operation
  • Boolean Function

Binary Number System

It is a number system consisting of only two digits 0 and 1. It is also called the base 2 number system. All the numbers in this system is expressed in 0s and 1s.

Example: Decimal number (8)10 is written as (1000)2 in binary.

Binary Constant

A binary value that will not change is called a binary constant.

Binary Variable

A binary variable is a symbolic name assigned to a binary value.

Example: A = 1010

Here, A is a variable having binary value 1010.

Basic Logical Operation

Following are the basic logical operation.

  • OR operation (+)
  • AND operation (.)
  • NOT operation (')

The Logical OR operation (+)

Logical OR operation of two boolean variables A and B is written as X = A + B

It is also called logical addition.

The following table contains the input and output of the logical OR operation.

So, if any one of the input is 1 then the output is 1, otherwise it is 0.

The Logical AND operation (.)

Logical AND operation of two boolean variables A and B is written as X = A . B

It is also called logical multiplication.

The following table contains the input and output of the logical AND operation.

So, if both the input is 1 then the output is 1, otherwise it is 0.

The Logical NOT operation (')

Logical NOT operation performs inverse operation and converts 1 into 0
and 0 into 1.

The following table contains the input and output of the logical NOT operation.

So, if the input is 1 then the output is 0 and if the input is 0 then the output is 1.

Boolean Function

A boolean function is an algebraic expression formed using binary constants, binary variables and basic logical operators.

Example: Boolean Function
F = A + 1

where, A is a binary variable
+ is a Basic Logical Operator (OR)
and, 1 is a binary constant.

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