Boolean algebra
A mathematical system operating on truth values using logical operations (AND, OR, NOT), laws, and identities. Boolean algebra underlies digital logic design and computer hardware. Laws simplify complex expressions enabling efficient circuit design. De Morgan's Laws and other identities enable algebraic manipulation.
Formula
De Morgan's: ¬(A ∧ B) = ¬A ∨ ¬B; ¬(A ∨ B) = ¬A ∧ ¬B
Real World
Intel's chip designers use Boolean algebra to simplify millions of logic expressions before fabricating a processor, reducing the transistor count on an i9 chip and lowering power consumption and heat output.
Exam Focus
Show each simplification law by name (e.g. 'by De Morgan's') — marks require you to identify which law you applied at each step.
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