AQA · GCSE · Computer Science
Course version: 8525 · Version from Sept 2020
Boolean logic: Construct truth tables for the following logic gates:
A truth table lists every possible combination of inputs to a logic gate and the output produced for each combination.
Checked against the AQA 8525 specification (opens in a new tab) on .
- Point 1 of 16
Study notes
From the checked teaching notes for this specification point.
The idea
A truth table lists every possible combination of inputs to a logic gate and the output produced for each combination. To construct one, first count the inputs and work out how many rows are needed: with n inputs there are 2ⁿ combinations, so a single-input gate needs 2 rows, a two-input gate needs 4 rows and a three-input gate needs 8 rows. List the input columns in a systematic binary counting order (for example 00, 01, 10, 11) so no combination is missed or repeated. Then apply the gate's rule to each row and record the output. For a NOT gate the output is the inverse of its single input; for AND the output is 1 only when all inputs are 1; for OR the output is 1 when at least one input is 1. Check each row against the rule rather than copying a remembered pattern.
What earns the marks
- Recognises that a truth table must include every possible input combination, giving 2ⁿ rows for n inputs.
- Uses a systematic ordering of input values (binary counting) so that no combination is omitted or duplicated.
- Applies the correct rule for the named gate to each row, e.g. AND outputs 1 only when all inputs are 1.
- Records the output column consistently and correctly for every input row.
- For a NOT gate, states that the single output is the inverse of the single input (0 becomes 1 and 1 becomes 0).
Common mistakes and how to put them right
Listing input combinations in a random order and missing one.
Put it right by counting in binary (00, 01, 10, 11) so all 2ⁿ rows appear exactly once.
Giving an AND gate an output of 1 when only one input is 1.
Put it right by applying the rule that AND needs every input to be 1.
Treating NOT as a two-input gate.
Put it right by recognising NOT has one input and therefore only two rows.
Exam tips
- Count the inputs first and write down how many rows you need (2ⁿ) before drawing the table.
- Fill the input columns in binary counting order, then work through the output column row by row.
- Re-check each output against the gate's rule rather than relying on memory of a pattern.
Try the lesson
The start of the Boolean logic: Construct truth tables for the following logic gates: lesson, made from checked teaching notes for this specification point.
Have a go first
A two-input AND gate has inputs A and B. Which row of its truth table gives output 1?
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