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Why NOR and NAND are universal gates

Short answer

NAND and NOR gates are universal because NOT, AND, and OR—hence any logic function—can be built using only one gate type. For example, a NOT is made by tying both inputs of a NAND (or NOR); AND is NAND followed by NOT; OR is NOR followed by NOT.

Why NOR and NAND gates are called universal gates? Explain with examples.

NAND and NOR gates are called universal gates because any logic function (AND, OR, NOT, and hence any combination) can be built using only NAND gates, or only NOR gates.

NAND gate as universal gate

FunctionUsing NAND only
NOTA' = (A·A)' (tie both inputs)
ANDAB = ((AB)')' (NAND followed by NAND as NOT)
ORA + B = (A'·B')' (NAND of A' and B')
 NOT:  A --[NAND, inputs tied]-- A'
 AND:  A,B --[NAND]--[NAND tied]-- AB
 OR:   A --[NAND tied]--+
       B --[NAND tied]--[NAND]-- A+B

NOR gate as universal gate

FunctionUsing NOR only
NOTA' = (A + A)'
ORA + B = ((A + B)')' (NOR followed by NOR as NOT)
ANDAB = (A' + B')' (NOR of A' and B')

Example: to make an OR gate from NOR gates, connect the output of a NOR gate to a second NOR gate with tied inputs.

Because NOT, AND and OR are enough to build every logic circuit, NAND and NOR are universal. They are also cheaper and smaller in ICs, which is why they are widely used.

✓ Answer checked by Claude Opus 5.5 (high effort)

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