What is boolean algebra and boolean algebra roles.

Boolean Algebra is used to analyze and simplify digital logic circuits. It uses only binary numbers i.e. 0 and 1.  It is also called 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.

★ The variable used can have only two values. Binary 1 for high and binary 0 for low

★ The complement of a variable is represented by using ( ' ).

Thus, the complement of the variable B is represented as B'. Thus if B = 0 then B' = 1 and B = 1 then B' = 0.

★ ORing of variables is represented by a plus (+) sign between them.

For example, the direction of A, B, C is represented as A + B + C.

★ Logical endings of two or more variables are denoted by writing a dot between them e.g. A.B.C. Or sometimes dot can be written as ABC.

Boolean Laws:

There are 6 types of Boolean rules.

Commutative law :

Any binary operation that satisfies the following expression is called a commutative operation.

1.    A.B = B.A 
2.     A+B = B+A 

Commutative law states that changing the sequence of variables has no effect on the output of a logic circuit.

Associative law :

This law states that the order in which logic operations are performed is irrelevant because they have the same effect.

1.   (A.B).C = A.(B.C)
2.   (A+B)+C = A+(B+C)

Distributive law :

The distribution law states the following situation.

  A.(B+C) = A.B + A.C

AND law:

These laws use the AND operation. That's why they are called AND laws.

1.  A.0 = 0
2.  A.1 = A
3.  A.A = A
4.  A.A' = 0

OR law:

These laws use the OR operation. That's why they are called OR laws.

1. A+0 =A 
2. A+1 = 1
3. A+A = A
4. A+A' = 1

INVERSION law:-

This law uses the NOT operation. The inversion rule states that duplicating a variable will result in the same variable as the original.

 A'' = A

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