7.1 De Morgan's Laws Bond Chapter 7.1 Part 2

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

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

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

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

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

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