Logic Gates & Boolean Algebra

VLSI Concept · Fundamentals

Six symbols are all digital logic is built from.

Every digital circuit, no matter how complex, reduces to combinations of a handful of basic gates: AND, OR, NOT, NAND, NOR, XOR. NAND and NOR are "universal gates" because either one alone can implement any Boolean function — which is why standard cell libraries build almost everything from them.

Universal gatesNAND and NOR can each build AND, OR, NOT, and everything else on their own.

Why it mattersStandard cell libraries are built around NAND/NOR variants because they map most efficiently to CMOS transistors.

De Morgan's LawNOT(A AND B) = NOT(A) OR NOT(B) — the algebra that lets you convert between gate types.

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