BOOLEAN ALGEBRA

DEFINITIONS:Boolean algebra is in fact an algebric structure defined on

a set of elements with two binary operators ‘+’ and ‘.’Provided the following postulates are satisfied.

A. (a) closure with respect to the operator ‘+’.

(b) closure with respect to the operator ‘.’ .

B. (a) an identity element with respect to ‘+’ designated

x+0=0+x=x (c) an identity element with respect to ‘.’ Designated

x.1=1.x=x

FUNDAMENTALS OF BOOLEAN ALGEBRA:

The variables used in Boolean equation have unique characteristics and assume only one of the two possible values , i.e. either a 1 or a 0.The following rules of logical addition, multiplication, negation also define the OR gate And and NOT operations respectively.

LOGICAL ADDITION:

0+0=0 OR operations:0+1=11+0=1 x y x+y

1+1=1 0 0 0

0 1 11 0 1

1 1 1LOGICAL MULTIPLICATIONS:

0.0=00.1=01.0=01.1=1

AND operation

x y x.y

0 0 00 1 01 0 01 1 1

Logical negation

1’=00’=1

NOT operations:

X x’

1 00 11