Truth tables — Edexcel GCSE Computer Science
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Truth tables explained
A truth table lists every combination of input values and the output for each combination.
Read the full explanation
With three inputs there are 2³ = 8 rows, so list them systematically, for example A, B and C counting in binary from 000 to 111. AND gives 1 only when both operands are 1; OR gives 1 when at least one operand is 1; NOT reverses a single value. Work out the expression in stages: evaluate the bracketed part first, then combine the results. For example, with A = 1, B = 0 and C = 1, the expression (A AND B) OR NOT C gives (1 AND 0) OR NOT 1, which is 0 OR 0, so the output is 0. Check each row independently and keep the column headings clear. Pseudocode in this specification is an informal written description using imprecise English statements and does not require strict programming syntax.
Your focus
- Construct a complete truth table for an expression with up to three inputs.
- Apply AND, OR and NOT correctly to individual rows and sub-expressions.
- Use a completed truth table to determine the output for a given input combination.
Truth tables exam tips
Marking Points
- Identifies that a truth table with three inputs has 2³ = 8 rows and lists all input combinations without repetition or omission.
- Applies AND correctly, producing 1 only when both operands are 1.
- Applies OR correctly, producing 1 when at least one operand is 1.
- Applies NOT correctly, reversing a single input or sub-expression value.
- Evaluates a compound expression in the correct order, working out bracketed or NOT parts before combining with AND and OR.
- Reads the completed table to answer the problem, for example identifying the input combination that produces a given output.
Examiner Tips
- 💡Write the input columns in a fixed order such as 000, 001, 010 and so on, so no combination is missed.
- 💡Add intermediate columns for sub-expressions; this reduces errors and can earn method credit.
- 💡Recheck each row by substituting the values back into the original expression before selecting your answer.
Common Mistakes
- Missing rows in a three-input table. Correction: there are 2³ = 8 rows, so list all combinations from 000 to 111 systematically.
- Treating OR as exclusive, so that 1 OR 1 is marked 0. Correction: OR gives 1 when at least one operand is 1, so 1 OR 1 gives 1.
- Applying NOT to the whole expression when it applies only to one variable. Correction: check what the NOT symbol or word is attached to before reversing a value.
- Evaluating left to right without regard to brackets. Correction: work out bracketed sub-expressions and NOT terms first, then combine with AND and OR.