Build a logic circuit from an expression
Translate each operation in an expression into a connected gate without simplifying it.
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
Which shape represents an operation in an expression?
What you will learn
- Match each operator to a gate
- Connect intermediate results in order
- Preserve the expression's grouping
Core idea
A Boolean expression can be drawn as a sequence of gates. Inputs enter the first operation; its output becomes an input to the next gate. Keep NOT as its own one-input gate and preserve brackets by building their operations first.
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
Start at the innermost brackets, draw the required gate, then connect its output to the next gate. Label inputs and the single output. Keep the requested construction even if a different circuit could be simplified or rearranged.
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
For Y=(A OR B) AND C, which gate should produce the first intermediate result?
Worked example
Describe the circuit for Y=A AND NOT B.
Show the worked solution
- Send B through a NOT gate.
- Connect A and the NOT B output to an AND gate.
- Label the AND output Y.
Answer B enters NOT; A and NOT B enter AND; the output is Y.
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.
Describe the circuit for Y=A OR B.
Give me a hint
There is one operation and two inputs.
Compare my reasoning
- Connect A and B to an OR gate.
- Label the gate output Y.
A and B enter OR; its output is Y.
Look for these in your work
- Correct gate
- Both inputs
- Output label
Describe the circuit for Y=(A OR B) AND C.
Give me a hint
Make the bracketed result first.
Compare my reasoning
- Connect A and B to OR.
- Connect the OR output and C to AND.
- Label the final output Y.
A and B enter OR; its output and C enter AND; output Y.
Look for these in your work
- Bracket order
- Intermediate connection
- Final output
A siren sounds when a test T succeeds and either sensor A or B is active. Write the expression, then describe the gates and connections.
Give me a hint
The sensor alternatives form an intermediate result.
Compare my reasoning
- First combine A and B with OR.
- Combine that output with T using AND.
- Label the final output S.
S=(A OR B) AND T: A and B feed OR; that output and T feed AND.
Look for these in your work
- Statement represented
- Gate order
- Connections described
Common mistakes
- Connecting B directly to AND instead of NOT
- Dropping parentheses or operation order
- Simplifying away a required gate
What can you explain now?
For Y=A AND NOT B, which input enters the NOT gate?
Compare with the explanation
B
The expression negates B, not A.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
When an expression contains parentheses, which operation do you draw first?
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.