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Boolean Logic and Simplification

Simplifying Boolean expressions

  • 3 things to know
  • Component 1

Overview

General strategy for simplifying a Boolean expression and redundant term in a Boolean expression.

What you need to know

Answer each one before you reveal it.

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Key term

Why is a Boolean expression simplified?

Key term

Simplify A.B + A.NOT B.

Key term

Simplify A + A.B.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Why is a Boolean expression simplified?

    Model answer

    A simplified expression needs fewer gates, so the circuit costs less and uses less power. Propagation delay through the circuit is also reduced.

  2. 2

    Simplify A.B + A.NOT B.

    Model answer

    The expression simplifies to A. The common factor A multiplies B OR NOT B, which equals 1.

  3. 3

    Simplify A + A.B.

    Model answer

    The expression simplifies to A. The absorption law removes the second term entirely.

  4. 4

    Simplify A.(A + B).

    Model answer

    The expression simplifies to A. The bracket adds nothing, because A must already be 1 for the AND to give 1.

  5. 5

    Simplify A + NOT A.B.

    Model answer

    The expression simplifies to A + B. The single A already covers every case in which A is 1.

  6. 6

    Simplify (A + B).(A + NOT B).

    Model answer

    The expression simplifies to A. Expansion leaves A plus further terms that all contain A.

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