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Universal gates; positive and negative logic

Short answer

Universal gates like NAND and NOR can realize any Boolean function. For instance, NAND alone builds NOT, AND, OR. Positive logic assigns HIGH=1, LOW=0; negative logic reverses. Because of this convention change, a gate’s logical function changes: positive AND becomes negative OR, positive NAND becomes negative NOR.

Define universal gates with example. Explain positive and negative logic.

Universal gates

A universal gate is a gate that alone can implement NOT, AND and OR, and hence any Boolean function. NAND and NOR are universal gates.

Examples with NAND only:

  • NOT: A⋅A‾=Aˉ\overline{A \cdot A} = \bar A
  • AND: NAND followed by a NAND inverter, AB‾‾=AB\overline{\overline{AB}} = AB
  • OR: Aˉ⋅Bˉ‾=A+B\overline{\bar A \cdot \bar B} = A + B

Examples with NOR only:

  • NOT: A+A‾=Aˉ\overline{A + A} = \bar A
  • OR: NOR followed by a NOR inverter
  • AND: Aˉ+Bˉ‾=AB\overline{\bar A + \bar B} = AB
 OR from NAND:
 A --[NAND]-- A' --+
 B --[NAND]-- B' --+--[NAND]-- A+B

Positive and negative logic

  • Positive logic: HIGH level = logic 1 and LOW level = logic 0 (e.g. +5 V = 1, 0 V = 0).
  • Negative logic: HIGH level = logic 0 and LOW level = logic 1.

The same circuit changes its logic name when the convention changes. A gate with output HIGH only when both inputs are HIGH is AND in positive logic but OR in negative logic; similarly positive NAND = negative NOR.

✓ Answer checked by Claude Opus 5.5 (high effort)

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