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.
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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