# Boolean Algebra

In Boolean algebra, only two states of variables (0 and 1) are allowed. The variables (

*A*,*B*,*C*â€¦) of Boolean Algebra are subjected to following three operations:**OR operation**Represented by (+) sign.

**Fig. 40**

Boolean expression,

*Y*=*A*+*B*When switch

*A*or*B*is closed, bulb glows.**AND operation**Represented by (Â·) sign.

Boolean expression,

*Y*=*A*Â·*B*When switches

*A*and*B*both are closed, bulb glows.

**Fig. 41**

**NOT operation**Represented by bar over the variables

Boolean expression,

**Fig. 42**

# Basic Boolean postulates and laws

- Boolean postulates: 0
*+ A = A*,*Â· A = A*,*A*= 1, 0 Â·*A*= 0, - Â—Identity law:
*A*+*A*=*A*,*A*Â·*A*=*A* - Â—Negation law:
- Â—Commutative law:
*A*+*B*=*B*+*A*,*A*Â·*B*=*B*Â·*A* - Â—Associative law: (
*A+B*) + C =*A*+ (*B*+*C*)*,**(**A*Â·*B*) Â·*C*=*A*Â· (*B*Â·*C*) - Â—Distributive law:
*A*Â· (*B+C*) =*A Â· B + A Â· C**(**A*+*B*) Â· (*A*+*C*) =*A + BC* - Â—Absorption laws:
*A*+*A*Â·*B*=*A*,*A*Â· (*A*+*B*) =*A* - Boolean identities: ,

**De Morganâ€™s theorem**It states that the complement of the whole sum is equal to the product of individual complements and vice versa, i.e., and .