1. 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=1
1+0=1 x y x+y

2. 1+1=1
0 0 0
0 1 1
1 0 1
1 1 1
LOGICAL MULTIPLICATIONS:
0.0=0
0.1=0
1.0=0
1.1=1
AND operation
x y x.y
0 0 0
0 1 0
1 0 0
1 1 1
Logical negation
1’=0
0’=1
NOT operations:
X x’
1 0
0 1
1