BOOLEAN ALGEBRA | Boolean Theorems |Commutative law | Associative law| Distributive law | DeMorgan’s theorems

BOOLEAN ALGEBRA

Boolean algebra was first introduced by George Boole in 1854. It defines different types of logical operations and works with variables called Boolean variables. The value of the Boolean variables can be either TRUE/HIGH or FALSE/LOW. The digital systems work on binary inputs and produce binary output. In binary system, a TRUE or HIGH state is represented as logic 1 and a FALSE or LOW state is represented as logic 0 in positive logic. In negative logic, a HIGH state is represented by logic 0 and a LOW state is represented by logic 1. 

The basic laws of Boolean algebra are :- 

A + 0 = A A · 0 = 0

A + 1 = 1 A · 1 = A

A + A = A A · A = A

A + A = 1 A · A = 0

Basic laws of Boolean algebra

Boolean Theorems

Boolean algebra supports three basic laws of simple algebra. These laws are stated as follows:


1. Commutative law :-  

A + B = B + A 

A · B = B · A

2. Associative law :- 

A + (B + C) = (A + B) + C 

A · (B · C) = (A · B) · C

3. Distributive law :- 

A · (B + C) = A · B + A · C 

A + B · C = (A + B) · (A + C)

DeMorgan’s theorems are also very important Boolean theorems, which are extensively used in simplifying the

Boolean expressions. These are as follows :-

AND Gate  ,OR Gate,NOT Gate,XOR Gate,NAND Gate, NOR Gate

Universal Gates | NAND Gate | NOR Gate