Digital System Design ECE331
Jens­Peter Kaps
Laws and Rules of Boolean Algebra
Commutative Law
A B=B A
A⋅B=B⋅A
Associative Law
A BC = ABC
A⋅ B⋅C = A⋅B⋅C
Distributive Law
A⋅ BC = A⋅C A⋅B
AB⋅C= A B⋅ AC 
Null Elements
A1=1
A⋅0=0
Identity
A0= A
A⋅1= A
Idempotence
A A= A
A⋅A= A
Complement
A 
A =1
A⋅
A =0
Involution

A= A
Absorption (Covering)
A A⋅B= A
A⋅ AB= A
Simplification  ⋅B= AB
A A
A⋅ 
A B= A⋅B
DeMorgan's Rule
A B= 
A⋅
B
A⋅B= 
A 
B
Logic Adjacency (Combining)
=A
A⋅B A⋅B
 = A
 AB⋅ A B
Consensus
⋅C
A⋅BB⋅C 
A⋅C = A⋅B A
 C =
 AB⋅ BC ⋅ A
 AB⋅ 
AC 
1/30/07