Laws of Boolean Algebra

Laws of Boolean Algebra

There are six types of Boolean algebra laws. They are:

• Commutative law
• Associative law
• Distributive law
• AND law
• OR law

Commutative Law

Any binary operation which satisfies the following expression is referred to as a commutative operation. Commutative law states that changing the sequence of the variables does not have any effect on the output of a logic circuit.

• A. B = B. A
• A + B = B + A

Associative Law

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

• ( A. B ). C = A . ( B . C )
• ( A + B ) + C = A + ( B + C)

Distributive Law

Distributive law states the following conditions:

• A. ( B + C) = (A. B) + (A. C)
• A + (B. C) = (A + B) . ( A + C)

AND Law

These laws use the AND operation. Therefore they are called AND laws.

• A .0 = 0
• A . 1 = A
• A. A = A
• A.A¯=0

OR Law

These laws use the OR operation. Therefore they are called OR laws.

• A  + 0 = A
• A + 1 = 1
• A + A = A
• A+A¯=1