Boolean logic: Interpret the results of simple truth tables.

The idea

Interpreting a truth table means reading the completed table and explaining what it shows about the logic. For each row, the input values combine to give the output recorded. To interpret, identify which combinations of inputs produce an output of 1 and which produce 0, then describe the relationship in words or as a Boolean expression. For example, a table whose output is 1 only when both A and B are 1 describes an AND relationship, Q = A AND B. A table whose output is 1 whenever either input is 1 describes OR. A table whose output is the opposite of a single input describes NOT. When reading a table, check the number of rows matches 2ⁿ for n inputs, confirm each combination appears once, and match output values to the correct row before drawing a conclusion. Interpretation is about explaining the pattern, not just copying the numbers.

What earns the marks

• Identifies which input combinations give an output of 1 and which give 0.
• Describes the relationship between inputs and output in words, for example 'output is 1 only when both inputs are 1'.
• Matches the observed pattern to a named logic operation such as AND, OR or NOT.
• Expresses the relationship as a correct Boolean expression consistent with the table.
• Checks the table is complete (2ⁿ rows) before drawing conclusions from it.

Common mistakes and how to put them right

• Reading the wrong row when matching inputs to output.

  Put it right: Trace across a single row carefully before stating a result.

• Assuming a pattern without checking every row.

  Put it right: Confirm the description holds for all rows, not just one.

• Confusing AND and OR: AND gives 1 only when all inputs are 1, whereas OR gives 1 when at least one input is 1.

• Writing a Boolean expression that does not match the table.

  Put it right: Test the expression against each row before finalising.

Exam tips

• List the rows where the output is 1 first; this usually reveals the pattern quickly.
• State the rule in words before converting it to a Boolean expression.
• Test your proposed expression against every row of the table to confirm it matches.
• Check the row count equals 2ⁿ so you know the table is complete before interpreting.