Logic simplification using Boolean axioms
We use the axioms of Boolean algebra to convert (reduce) logical expressions to forms better suited for real hardware
Two key concepts (remember these):
- Duality (a meta-theorem— a theorem about theorems)
- All Boolean expressions have logical duals
- Any theorem that can be proven is also proven for its dual
- Replace: • with +, + with •, 0 with 1, and 1 with 0
- Leave the literals unchanged
- de Morgan’s Theorem
- Procedure for complementing Boolean functions
- Replace: • with +, + with •, 0 with 1, and 1 with 0
- Replace all literals with their complements