Write an expression from a circuit
Follow gate connections backward from the output to describe the circuit as a Boolean expression.
Exam scope and assessment notes
This original learning sequence follows Topic 10 of Cambridge IGCSE Computer Science 0478, 2026–2028 syllabus Version 6. It covers standard symbols and functions for NOT, AND, OR, NAND, NOR and XOR/EOR, and translation among statements, expressions, circuits and truth tables. NOT has one input; other gates have at most two. Circuit practice is limited to three inputs and one output and keeps the requested design without simplification. Lessons and checks support learning but do not award an official Cambridge grade. Full timed-paper practice, practical programming in an executable workspace and human subject-teacher review remain outstanding; the separate 2029–2031 syllabus is not mapped here.
Before you begin
- Be able to read binary 0 and 1 as the two possible logic values. Each lesson introduces the gate or translation skill it uses.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
When writing an expression from a circuit, where is a reliable place to start?
What you will learn
- Identify the final gate
- Represent intermediate outputs with brackets
- Preserve inversion and signal names
Core idea
A circuit can be read as a nested expression. Start with the gate nearest the output and substitute the expression produced by each earlier gate. A NOT bubble applies to the output of its own gate.
In a logic circuit, 1 represents TRUE and 0 represents FALSE. A gate applies a defined rule to its input value or values and produces one binary output.
A reliable method
Name each intermediate wire if useful. Write the inputs and operator for the first gate, then use that result as one input of the next gate. Add brackets to show grouping and avoid a changed meaning.
Keep the given statement, expression, diagram or table in view while working. Check each row or connection against the rule, and preserve the stated circuit structure; the syllabus does not ask you to simplify it.
Pause and explain
If the output gate is AND and its inputs are C and an OR result from A,B, how should that OR result be grouped?
Worked example
A and B feed OR; that result and C feed AND to output Y. Write Y.
Show the worked solution
- The final gate is AND.
- One AND input is the OR output A OR B; the other is C.
- Use brackets around the intermediate result.
Answer Y=(A OR B) AND C.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A and B feed AND, producing Y. Write the expression.
Give me a hint
There is one gate.
Compare my reasoning
- Read both gate inputs.
- Use AND between them.
- Label the output.
Y=A AND B.
Look for these in your work
- Inputs
- Operator
- Output
A and B feed XOR. The output and C then feed OR. Write Z.
Give me a hint
Write the first gate result in brackets.
Compare my reasoning
- The first result is A XOR B.
- The final gate combines that with C using OR.
- Use brackets to preserve the intermediate signal.
Z=(A XOR B) OR C.
Look for these in your work
- XOR result
- Final OR
- Grouping
A circuit sends A through NOT; B and that result feed NAND. Write the output expression and explain where inversion applies.
Give me a hint
NAND inverts the result of its two-input AND operation.
Compare my reasoning
- The NOT branch is NOT A.
- The NAND inputs are B and NOT A.
- NAND applies a further inversion to their AND result.
Y=NOT (B AND NOT A). The first NOT applies only to A; NAND inverts the combined AND output.
Look for these in your work
- Branch inversion
- NAND inversion
- Grouping clear
Common mistakes
- Writing a wire as a new independent input
- Losing the order of two gates
- Omitting a bracket that changes the grouping
What can you explain now?
A and B enter OR, then its output enters NOT. What is the expression?
Compare with the explanation
NOT (A OR B)
The NOT applies to the complete OR output.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What do brackets show when you write an expression from a circuit?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.