Boolean Algebra

Key laws:

• Identity: $A + 0 = A$, $A \cdot 1 = A$
• Null: $A + 1 = 1$, $A \cdot 0 = 0$
• Idempotent: $A + A = A$
• Complement: $A + \bar{A} = 1$, $A\bar{A} = 0$
• Absorption: $A + AB = A$
• Distributive: $A + BC = (A + B)(A + C)$

De Morgan's theorems:

$\overline{A \cdot B} = \bar{A} + \bar{B} \qquad \overline{A + B} = \bar{A} \cdot \bar{B}$

"Break the bar, change the sign." Simpler expressions mean fewer gates, less power and less delay.