Respect Boolean circuit limits
Keep Topic 10 circuits within three inputs, one output and the stated gate-input limits.
Section 10 · Boolean logic
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
How many external inputs can a circuit use at most?
What you will learn
- Apply the syllabus circuit limits
- Keep NOT single-input and other gates two-input
- Draw the requested function without simplification
Core idea
For this syllabus, NOT is a single-input gate and every other listed gate is limited to two inputs. Circuits have at most three inputs and one output. When asked to draw a circuit from a given statement, expression or table, keep its requested construction without simplification.
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
Count the external input variables and final outputs. Check each gate's input count separately. Keep intermediate outputs connected to later gates, and do not replace the given design with an algebraically shorter equivalent unless the question asks for that.
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
A circuit has three input variables and one output, using two-input gates. Is that within the stated circuit limits?
Worked example
A proposed circuit sends A, B and C directly into one three-input AND gate. Does it meet the stated gate limit?
Show the worked solution
- The circuit has three external inputs, which is allowed.
- However, the AND gate itself has three inputs.
- Other than NOT, gates are limited to two inputs.
Answer No. Use two two-input AND gates if the required function is A AND B AND C, keeping one output.
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 circuit has four external variables and one output. Does it meet the Topic 10 input limit?
Give me a hint
Count the distinct external variables.
Compare my reasoning
- The maximum is three inputs.
- Four exceeds the limit.
No; it uses more than three external inputs.
Look for these in your work
- Limit stated
- Count compared
A NOT gate is drawn with two input wires. Identify the issue.
Give me a hint
Recall the exception among gate input counts.
Compare my reasoning
- NOT has one input only.
- Remove the extra input wire; do not change the operation.
The NOT symbol is being used incorrectly because it is single-input.
Look for these in your work
- NOT limit
- Correction
A question asks for a circuit for Y=(A OR B) AND C. A learner replaces it with a different equivalent design. Explain what the syllabus expects.
Give me a hint
Read the instruction about construction from the given expression.
Compare my reasoning
- Draw the stated OR operation on A and B.
- Connect its result and C to a two-input AND.
- Keep this requested arrangement rather than simplifying or substituting another form.
Use A,B into OR, then that output and C into AND, with one output Y; do not simplify the given circuit.
Look for these in your work
- Two gates
- Correct connections
- No simplification
Common mistakes
- Confusing the circuit's maximum variables with a gate's maximum input count
- Drawing multiple final outputs when one is required
- Simplifying when the question asks to preserve the stated circuit
What can you explain now?
Can an OR gate have three inputs in this syllabus?
Compare with the explanation
No; it is limited to two inputs
The overall circuit may have three variables, but each non-NOT gate has at most two inputs.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Which limit is per gate, and which applies to the whole 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.