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Advanced Data Structures and Logic

NAND, NOR and Boolean simplification

  • 3 things to know
  • A2 Unit 3

Overview

Truth table of a two-input NAND gate and truth table of a two-input NOR gate.

What you need to know

Answer each one before you reveal it.

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Key term

How is an AND gate made from NAND gates?

Key term

State the truth table of a two-input NAND gate.

Key term

Write the NAND operation in Boolean notation and then apply De Morgan's law to it.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the truth table of a two-input NAND gate.

    Model answer

    NAND outputs 1 for inputs 0 and 0, 1 for 0 and 1, 1 for 1 and 0, and 0 for 1 and 1.

  2. 2

    State the truth table of a two-input NOR gate.

    Model answer

    NOR outputs 1 for inputs 0 and 0, 0 for 0 and 1, 0 for 1 and 0, and 0 for 1 and 1.

  3. 3

    Write the NAND operation in Boolean notation and then apply De Morgan's law to it.

    Model answer

    A NAND B is ¬(A·B), which De Morgan's law rewrites as ¬A + ¬B.

  4. 4

    Write the NOR operation in Boolean notation and then apply De Morgan's law to it.

    Model answer

    A NOR B is ¬(A + B), which De Morgan's law rewrites as ¬A·¬B.

  5. 5

    Why are NAND and NOR called universal gates?

    Model answer

    Every Boolean function can be built from NAND gates alone, or from NOR gates alone, so no other kind of gate is required.

  6. 6

    How is a NOT gate made from a single NAND gate?

    Model answer

    Both inputs of the NAND gate are tied to the same signal A, giving ¬(A·A), which reduces to ¬A.

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