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Boolean Logic and Simplification

Truth tables for combined Boolean expressions

  • 3 things to know
  • Component 1

Overview

Building the table for an expression with several operators: 2ⁿ rows for n inputs, listed in binary counting order, with an intermediate column for each part of the expression.

What you need to know

Answer each one before you reveal it.

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Key term

How is a truth table built for a compound expression?

Numbers

How many rows are needed for a truth table with four inputs?

Key term

Why are intermediate columns useful in a truth table?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How is a truth table built for a compound expression?

    Model answer

    The table lists every input combination and then adds a column for each intermediate term. The final column holds the value of the whole expression.

  2. 2

    How many rows are needed for a truth table with four inputs?

    Model answer

    Four inputs need 16 rows. The row count doubles for each extra input, following 2ⁿ.

  3. 3

    Why are intermediate columns useful in a truth table?

    Model answer

    An intermediate column records the value of one part of the expression. Errors are far easier to find than in a single long calculation.

  4. 4

    In what order are input combinations normally listed?

    Model answer

    Input combinations are listed as a binary count upwards from all zeros. Every combination then appears exactly once.

  5. 5

    State the value of A AND NOT B when A = 1 and B = 0.

    Model answer

    The output is 1. The inverse of B is 1, and 1 AND 1 gives 1.

  6. 6

    State the value of NOT (A OR B) when A = 0 and B = 1.

    Model answer

    The output is 0. A OR B gives 1, and the inversion turns that into 0.

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