Boolean Algebra


Boolean Algebra is used to analyze and simplify the digital (logic) circuits. It uses only the binary numbers i.e. 0 and 1. It is also called as Binary Algebra or logical Algebra. Boolean algebra was invented by George Boole in 1854.

Rule in Boolean Algebra

Following are the important rules used in Boolean algebra.


  • Complement of a variable is represented by an overbar (-). Thus, complement of variable B is represented as B Bar. Thus if B = 0 then B Bar = 1 and B = 1 then B Bar = 0.



Boolean Laws

There are six types of Boolean Laws.

Commutative law


Commutative Law


Associative law

This law states that the order in which the logic operations are performed is irrelevant as their effect is the same.

Associative Law

Distributive law

Distributive law states the following condition.

Distributive Law

AND law



OR law


OR Law


This law uses the NOT operation. The inversion law states that double inversion of a variable results in the original variable itself.


Important Boolean Theorems

Following are few important boolean Theorems.

Boolean function/theorems Description

Boolean Functions

Boolean Functions and Expressions, K-Map and NAND Gates realization

De Morgan's Theorems

De Morgan's Theorem 1 and Theorem 2