Derive a circuit from a truth table
Use table patterns to select gates and assemble a circuit that matches all listed rows.
Section 10 · Boolean logic
Exam scope and assessment notes
This original learning sequence follows Topic 10 of Cambridge IGCSE Computer Science 0984, 2026–2028 syllabus Version 4. 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. Cambridge states that 0984 has the same 2026–2028 subject content as 0478, with 9–1 grading. In June and November, Cambridge lists 0984 in Administrative zone 3 and for centres in Oman and the UAE. Confirm availability for your centre and exam series with Cambridge International. The separately published 2029–2031 syllabus changes to Python 3 only and removes pseudocode; this 2026–2028 route does not cover those changes.
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 rows should you compare for two-input gate identification?
What you will learn
- Compare a truth table with gate patterns
- Build the circuit from identified operations
- Test the resulting circuit against the table
Core idea
A truth table can be used to design a circuit. When its outputs match a standard gate, draw that gate and label the inputs. When it is a combination, identify intermediate relationships and preserve them with connected gates.
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
Inspect all rows, identify a candidate gate or expression, draw the circuit, then recalculate its outputs across every row. If the task specifies a required design, draw that design without simplifying it.
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 table is true for 01 and 10 only. Which gate should you draw?
Worked example
A table is true only when both A and B are 1. Describe the circuit.
Show the worked solution
- The true row is 11 only.
- That matches AND.
- Connect A and B to an AND gate.
Answer A and B feed AND; the output matches the table.
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 table has output 1 only on 11. State the circuit.
Give me a hint
Match the standard pattern.
Compare my reasoning
- Identify the AND rule.
- Connect A and B to AND.
- Use its output as Y.
A,B → AND → Y.
Look for these in your work
- Gate selected
- Wiring stated
A table has outputs 1,1,1,0 for 00,01,10,11. State the circuit and a check row.
Give me a hint
This is the inverse of the AND pattern.
Compare my reasoning
- Choose NAND.
- Connect A and B to NAND.
- Check 11 gives 0.
A,B → NAND → Y; on 11, Y=0.
Look for these in your work
- NAND selected
- Input check
For rows 00,01,10,11 a table gives 0,1,1,1. Describe a circuit and verify its outputs against the table.
Give me a hint
The output is false only when neither input is 1.
Compare my reasoning
- This is the OR pattern.
- Connect A and B to OR.
- OR gives 0 on 00 and 1 on the other three rows.
A and B feed OR; its outputs 0,1,1,1 match all rows.
Look for these in your work
- Gate choice
- All-row verification
Common mistakes
- Using a gate that matches only some rows
- Confusing AND and NAND
- Omitting input labels
What can you explain now?
A table is false only for 00. What gate and circuit fit?
Compare with the explanation
OR with inputs A and B
OR is 0 only when both inputs are 0.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Why must a proposed circuit be checked against the entire table?
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.