Center for Technical Education
Digital Electronics

BOOLEAN ALGEBRA


Postulates:
AND ORNOT
0 0 = 0
0 1 = 0
1 0 = 0
1 1 = 1
 0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
 = 1
= 0
Algebraic Properties:

Commutative Laws:
AB = BAA + B = B + A
Associative Laws:

A (BC) = (AB)CA + (B + C) = (A + B) + C
Distributive Law:

A(B + C) = AB + AC
Theorems:

1. A + 0 = A 2.A + 1 = 1
3.A0 = 0 4.A1 = A
5.A + A =A 6.
7.AA = A 8.
9. 10.A + AB = A
11. 12.
13.(A + B) (A + C) = A + BC

DeMorgan's Theorems:

13. 14.