1. 7.1 De Morgan's Laws
Bond Chapter 7.1 Part 2

2. De Morgan’s Laws
These enable Boolean conversions to form expressions using only NOR gates/functions or NAND ones.

3. How to Convert Boolean Expressions
Three Steps:
Change the operator (AND –> OR; OR –> AND)
NOT each element
NOT the whole expression

4. Rule 1 (De Morgan's 1st Law)
A + B = A . B Or A + B = A . B = A . B

5. Rule 2 (De Morgan’s 2nd Law)
A . B = A + B Or A . B = A + B = A + B

6. Boolean Identities Identity Name AND Form OR Form Identity 1 . A = A
Null Law
0 . A = 0
1 + A = 1
Idempotence Law
A . A = A
A + A = A
Inverse Law
A . A = 0
A + A = 1
Commutative Law
A . B = B . A
A + B = B + A
Associative Law
(A . B).C = A.(B . C)
(A+B) + C = A + (B + C)
Absorption Law
A.(A + B) = A . A + A . B
= A.(1 + B)
= A . 1 = A
A + (A . B) = A.(1 + B)
= A . 1
= A
De Morgan’s Law
A . B = A + B
A + B = A . B
Double Complement Law
A = A

7. Example June 2009 Q4c Simplify: A + B + B . A = A . B + B . A