www.cs.amherst/~ccm/cs14/logic.html

Computer Science 14 - Boolean Logic

Note: + means OR, * means AND, × means XOR, and ¬ A means NOT A.

Some Truth Tables

OR
A B A + B
0 0 0
0 1 1
1 0 1
1 1 1
AND
A B A * B
0 0 0
0 1 0
1 0 0
1 1 1
NOT
A B ¬ A ¬ B
0 0 1 1
0 1 1 0
1 0 0 1
1 1 0 0
XOR
A B A × B
0 0 0
0 1 1
1 0 1
1 1 0

Laws of Boolean Algebra

Double Negation: ¬ ¬ A = A
Idempotent: A + A = A A * A = A
Identity: A + 0 = A A * 1 = A
Zero/One: A + 1 = 1 A * 0 = 0
Inverse: A + ¬ A = 1 A * ¬ A = 0
Commutative: A + B = B + A A * B = B * A
Associative: A + (B + C) = (A + B) + C A * (B * C) = (A * B) * C
Distributive: A * (B + C) = (A * B) + (A * C) A + (B * C) = (A + B) * (A + C)
DeMorgan's: ¬ (A + B) = ¬ A * ¬ B ¬ (A*B) = ¬ A + ¬ B

Digital Logic Gates