OCR · GCSE · Computer Science
Course version: J277 · Version from Sept 2022
Boolean logic: Simple logic diagrams using the operators AND, OR and NOT
Logic diagrams show how Boolean operators combine binary inputs to produce an output.
Checked against the OCR J277 specification on .
- Point 1 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Logic diagrams show how Boolean operators combine binary inputs to produce an output. AND outputs 1 only when all inputs are 1; OR outputs 1 when at least one input is 1; NOT inverts a single input. Each gate has a distinctive symbol: AND has a flat back and curved front; OR has a curved input side and a pointed output side; NOT is a triangle with a small circle at its output. To evaluate a diagram, trace inputs through gates in order, writing the intermediate value on each connecting line. For example, with inputs A = 1 and B = 0, an AND gate gives 0, an OR gate gives 1, and a NOT gate after the AND gives 1. Diagrams may combine gates, so work left to right and substitute values carefully.
What earns the marks
- Identify the function of each gate symbol: AND requires all inputs to be 1, OR requires at least one input to be 1, and NOT inverts its single input.
- Trace signal values through a diagram from left to right, labelling each connecting line with its current binary value.
- Evaluate combined expressions correctly by applying the operator nearest the inputs first unless brackets or diagram layout indicate otherwise.
- Produce a correct output for any given combination of input values by substituting 0 or 1 systematically.
- Recognise that NOT gates have exactly one input and one output, while AND and OR gates may have two or more inputs.
- Distinguish the OR symbol (curved input side, pointed output side) from the AND symbol (flat back, curved front) when reading a diagram.
Common mistakes and how to put them right
Confusing the AND and OR gate symbols.
Put it right: AND has a flat back and curved front, while OR has a curved input side and a pointed output side.
Treating NOT as a two-input gate.
Put it right: NOT always has one input and inverts it, so 0 becomes 1 and 1 becomes 0.
Evaluating gates in the wrong order in a combined diagram.
Put it right: Trace from the inputs towards the output, not from the output backwards, unless you are deliberately working backwards to deduce an input.
Exam tips
- Write the value 0 or 1 on every line in the diagram before selecting the final answer; this reduces careless errors and shows your working.
- Check each gate against its truth table definition rather than relying on memory of the shape alone.
- If a diagram has more than two inputs to an AND or OR gate, apply the operator to all inputs together, not just the first two.
Try the lesson
The start of the Boolean logic: Simple logic diagrams using the operators AND, OR and NOT lesson, made from checked teaching notes for this specification point.
Have a go first
A logic diagram shows input A and input B connected to an OR gate. The output of this OR gate is then connected to a NOT gate. Which Boolean expression represents this logic circuit?
Listen
Logic diagrams show how Boolean operators combine binary inputs to produce an output. AND outputs 1 only when all inputs are 1; OR outputs 1 when at least one input is 1; NOT inverts a single input. Each gate has a distinctive symbol: AND has a flat back and curved front; OR has a curved input side and a pointed output side; NOT is a triangle with a small circle at its output. To evaluate a diagram, trace inputs through gates in order, writing the intermediate value on each connecting line. For example, with inputs A = 1 and B = 0, an AND gate gives 0, an OR gate gives 1, and a NOT gate after the AND gives 1. Diagrams may combine gates, so work left to right and substitute values carefully. A strong answer earns marks for these points. Identify the function of each gate symbol: AND requires all inputs to be 1, OR requires at least one input to be 1, and NOT inverts its single input. Trace signal values through a diagram from left to right, labelling each connecting line with its current binary value. Evaluate combined expressions correctly by applying the operator nearest the inputs first unless brackets or diagram layout indicate otherwise. Produce a correct output for any given combination of input values by substituting 0 or 1 systematically. Exam tip: Write the value 0 or 1 on every line in the diagram before selecting the final answer; this reduces careless errors and shows your working.
Key words
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Boolean operators AND, OR and NOT
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Binary inputs and outputs
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Logic gate symbols and functions
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Evaluating combined logic circuits
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See every definition
- Boolean operators AND, OR and NOT
- Operators that combine binary inputs to produce an output in a logic diagram.
- Binary inputs and outputs
- Values of 0 or 1 that enter a gate and the value it produces.
- Logic gate symbols and functions
- Each gate has a distinctive symbol, and AND requires all inputs to be 1, OR requires at least one input to be 1, and NOT inverts its single input.
- Evaluating combined logic circuits
- Tracing inputs through gates in order, working left to right and writing the intermediate value on each connecting line.
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