De Morgan’s Law
De Morgan’s Law is a fundamental rule in Boolean algebra that helps you simplify logic expressions, especially when working with complements (NOT).
The Two De Morgan’s Laws
1. First Law:
(A · B)' = A' + B'
“The complement of AND becomes OR of complements”
2. Second Law:
(A + B)' = A' · B'
“The complement of OR becomes AND of complements”
Simple way to remember
- Break the bar (complement)
- Change the operator:
- AND ↔ OR
- Complement each variable
Example
(AB + C)' = (AB)' · C' = (A' + B') · C'
Why it is useful
- Helps convert circuits using only NAND or NOR gates
- Used in simplifying logic expressions
- Very important in digital electronics and circuit design