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Boolean Logic and Logic Gates

FoundationHigherAQA

Understand Boolean Logic and Logic Gates for GCSE Computer Science with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers. The logic gates NOT, AND, OR and XOR process binary inputs to produce a binary 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

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Boolean logic underlies how a processor makes decisions, and it is implemented physically using logic gates.

Three gates are required. An AND gate outputs 1 only when both inputs are 1. An OR gate outputs 1 when at least one input is 1. A NOT gate has a single input and inverts it, outputting 1 for an input of 0 and 0 for an input of 1.

Each gate has a standard symbol used in circuit diagrams, and a Boolean expression. AND is written with a dot or as A·B, OR with a plus as A+B, and NOT with a bar over the variable. The NOT gate is the only one of the three with a single input, which is worth remembering when reading a circuit.

Revision notes

The three gates

AND: outputs 1 only when both inputs are 1.

OR: outputs 1 when at least one input is 1, including both. NOT: a single input, inverting it — 0 becomes 1 and 1 becomes 0.

Boolean expressions

AND is written A·B or simply AB.

OR is written A+B. NOT is written with a bar over the variable. These allow a circuit to be described in writing rather than as a diagram.

Reading circuit diagrams

Each gate has a distinct standard symbol.

The NOT gate is the only one with a single input, which makes it easy to identify. Trace signals from the inputs on the left through to the output on the right.

Key points

  • An AND gate outputs 1 only when both inputs are 1.
  • An OR gate outputs 1 when at least one input is 1.
  • A NOT gate inverts its single input.
  • NOT is the only gate with one input.
  • AND is written A·B.
  • OR is written A+B.

Worked examples

Example 1

State the output of an AND gate when its inputs are 1 and 0. [2 marks]

Working

An AND gate outputs 1 only when both inputs are 1state the rule
Here one input is 0, so the output is 0apply it to the inputs

Example 2

State the output of an OR gate when its inputs are 1 and 0. [2 marks]

Working

An OR gate outputs 1 when at least one input is 1state the rule
Here one input is 1, so the output is 1apply it to the inputs

Example 3

Explain how a NOT gate differs from AND and OR gates. [2 marks]

Working

A NOT gate has only one input, whereas AND and OR each have twostate the structural difference
and it inverts that input rather than combining two valuesstate the functional difference

Common mistakes

  • Thinking OR excludes the both-1 case.

    OR outputs 1 when at least one input is 1, including both.

  • Giving a NOT gate two inputs.

    It has exactly one.

  • Confusing the AND and OR symbols in expressions.

    AND is a dot; OR is a plus.

  • Reading a circuit right to left.

    Signals flow from inputs on the left to output on the right.

Exam tips

  • Learn each gate's rule precisely.
  • Remember NOT has a single input.
  • Use a dot for AND and a plus for OR.
  • Trace circuits left to right.

Key terms

Logic gate
A component implementing a Boolean operation.
AND gate
Outputs 1 only when both inputs are 1.
OR gate
Outputs 1 when at least one input is 1.
NOT gate
Inverts its single input.

Related topics

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