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Truth Tables

FoundationHigherAQA

Revise Truth Tables for GCSE Computer Science with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA GCSE Computer Science (8525). A truth table lists every possible combination of inputs and the resulting output.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA specification. Every worksheet comes with a full mark scheme.

Foundation

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Higher

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Topic overview

A truth table lists every possible combination of inputs to a logic circuit alongside the resulting output.

The number of rows is 2 to the power of the number of inputs. Two inputs give 4 rows, three give 8, four give 16. Listing the input combinations in binary counting order — 00, 01, 10, 11 — guarantees none is missed.

For a circuit with several gates, add a column for each intermediate output as well as the final one. Working through one gate at a time and filling its whole column before moving on is far more reliable than trying to evaluate an entire row at once, and it makes any error easy to locate.

Revision notes

Number of rows

Rows = 2 to the power of the number of inputs.

Two inputs give 2² = 4 rows; three give 2³ = 8; four give 2⁴ = 16. Listing combinations in binary counting order guarantees none is missed.

Intermediate columns

For a circuit with several gates, add a column for each gate's output.

This breaks the problem into single-gate steps. Fill each column completely before moving to the next, working through the circuit from inputs to output.

Checking your work

Every row should have a value in every column.

A missing entry usually means a row was skipped. Comparing your input combinations against binary counting order catches this immediately.

Key points

  • A truth table lists all input combinations.
  • Rows = 2 to the power of the input count.
  • Two inputs give four rows.
  • Three inputs give eight rows.
  • Add a column for each intermediate output.
  • Fill each column completely before moving on.

Worked examples

Example 1

State how many rows a truth table with four inputs needs. [2 marks]

Working

Each of the four inputs can be 0 or 1, giving 2⁴ combinationsstate the calculation
2⁴ = 16 rowswork out the number

Example 2

List the four input combinations for a two-input truth table. [2 marks]

Working

In binary counting order: 00, 01give the first two combinations
then 10, 11give the remaining two

Example 3

Explain why intermediate columns are added for a circuit with several gates. [2 marks]

Working

Each column holds the output of one gate, breaking the circuit into single stepsstate the purpose
so each gate can be evaluated separately, which is more reliable and makes errors easier to findexplain the benefit

Common mistakes

  • Missing input combinations.

    Use binary counting order to list them systematically.

  • Calculating inputs × 2 instead of 2 to the power.

    Three inputs give 8 rows, not 6.

  • Evaluating a whole row at once.

    Work gate by gate, filling each column completely.

  • Omitting intermediate columns.

    They make multi-gate circuits far easier to get right.

Exam tips

  • Use 2 to the power of the input count.
  • List combinations in binary counting order.
  • Add a column per gate.
  • Fill columns, not rows.

Key terms

Truth table
A table of all input combinations and outputs.
Input combination
One possible set of input values.
Intermediate output
The output of one gate within a larger circuit.
Binary counting order
Listing combinations as 00, 01, 10, 11.

Related topics

Written and reviewed against the current AQA specification. Spotted an error? Let us know.