AQA · A-Level · Physics

    Course version: 7408 · Version from Sept 2016

    Construction and deduction of a logic circuit from a truth table.

    Full specification wording

    Combinational logic (A-level only): Construction and deduction of a logic circuit from a truth table.

    A truth table lists every combination of inputs and the required output, so it fully defines a combinational function.

    Checked against the AQA 7408 specification (opens in a new tab) on .

    • Point 3 of 4
    • 2 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    A truth table lists every combination of inputs and the required output, so it fully defines a combinational function. To construct a circuit, identify each row where the output is 1, write a product term that is true only for that row (using AND gates and NOT gates for inputs that are 0), then OR the terms together. For example, output 1 for A = 0, B = 1 gives the term NOT A AND B. To deduce a truth table from a given circuit diagram, work through each gate in order, tabulating intermediate values for all input combinations until the final output column is complete. Both directions rely on the same link between rows, product terms and gates, and on checking that the finished circuit reproduces every row of the table.

    What earns the marks

    • Identify all input combinations for which the required output is 1 and treat each as one product term.
    • Combine the product terms with OR gates to form the complete expression for the output.
    • When deducing a truth table from a circuit, label intermediate gate outputs and evaluate them for every input combination.
    • Check the final column against the given truth table and correct any row that does not match.
    • Use the same systematic row-by-row method whether constructing a circuit or deducing its behaviour.

    Common mistakes and how to put them right

    • Writing a product term for rows where the output is 0 instead of 1.

      Put it right by selecting only the rows whose output is 1.

    • Forgetting to invert an input that is 0 in a selected row.

      Put it right by placing a NOT gate on that input in the product term.

    • Evaluating a circuit in the wrong order or ignoring gate precedence.

      Put it right by working stage by stage from the inputs towards the output.

    Exam tips

    • Draw a column for every intermediate gate output so your working can be followed and checked.
    • After building or deducing a circuit, test at least one row where the output is 0 as well as rows where it is 1.
    • Keep the number of gates minimal where possible, but always prioritise a circuit that matches the truth table exactly.

    Try the lesson

    The start of the Combinational logic (A-level only): Construction and deduction of a logic circuit from a truth table. lesson, made from checked teaching notes for this specification point.

    Have a go first

    A truth table for a logic circuit with inputs A and B shows that the output Q is 1 only when A = 1 and B = 0. Which Boolean expression represents this logic circuit?

    Listen

    A truth table lists every combination of inputs and the required output, so it fully defines a combinational function. To construct a circuit, identify each row where the output is 1, write a product term that is true only for that row (using AND gates and NOT gates for inputs that are 0), then OR the terms together. For example, output 1 for A = 0, B = 1 gives the term NOT A AND B. To deduce a truth table from a given circuit diagram, work through each gate in order, tabulating intermediate values for all input combinations until the final output column is complete. Both directions rely on the same link between rows, product terms and gates, and on checking that the finished circuit reproduces every row of the table. A strong answer earns marks for these points. Identify all input combinations for which the required output is 1 and treat each as one product term. Combine the product terms with OR gates to form the complete expression for the output. When deducing a truth table from a circuit, label intermediate gate outputs and evaluate them for every input combination. Check the final column against the given truth table and correct any row that does not match. A common slip: Writing a product term for rows where the output is 0 instead of 1. Instead, selecting only the rows whose output is 1. Exam tip: Draw a column for every intermediate gate output so your working can be followed and checked.

    See it

    A top-down flowchart. It starts at a node labelled Truth table, which leads to Identify rows where output is 1. That leads to Write a product term for each such row, which branches into two nodes: Input is 1: include input directly, and Input is 0: invert with NOT gate. Both of these lead to Combine product terms with OR gates, which leads to Circuit. Circuit leads to Check circuit reproduces every row of the table, which leads to Correct any row that does not match.
    It shows the steps for constructing a logic circuit from a truth table, from selecting rows with output 1 to checking the finished circuit against every row.

    Key words

    Say what each word means before you turn the card.

    Product term

    Try answering aloud or in your head before turning the card.

    Verification

    Try answering aloud or in your head before turning the card.

    See every definition
    Product term
    A term that is true only for one row of a truth table, written using AND gates and NOT gates for inputs that are 0.
    Verification
    Checking that the finished circuit reproduces every row of the table and correcting any row that does not match.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. It starts at a node labelled Truth table, which leads to Identify rows where output is 1. That leads to Write a product term for each such row, which branches into two nodes: Input is 1: include input directly, and Input is 0: invert with NOT gate. Both of these lead to Combine product terms with OR gates, which leads to Circuit. Circuit leads to Check circuit reproduces every row of the table, which leads to Correct any row that does not match.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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