Write an expression from a truth table
Infer a gate relationship from the rows where the output is 1 and verify every case.
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 gate is true for exactly one true input?
What you will learn
- Inspect true and false output rows
- Recognise standard gate patterns
- Verify a proposed expression against all rows
Core idea
A truth table specifies the output for every possible input combination. Standard two-input patterns are distinctive: AND is true only for 11; OR is false only for 00; XOR is true for 01 and 10; NAND and NOR invert their base 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
Compare the table to familiar gate patterns. If it appears to be a known gate, check all four rows before naming it. For a composite table, use intermediate columns or compare the rows where the output is true with a candidate expression.
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 outputs 0 only for row 00. Which gate matches?
Worked example
A two-input table has outputs 0,1,1,0 for rows 00,01,10,11. Give an expression.
Show the worked solution
- The output is 1 exactly when the two inputs differ.
- That is the XOR/EOR rule.
- Check 00 and 11 are both false.
Answer Y=A XOR B.
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.
Rows 00,01,10,11 have outputs 0,0,0,1. Identify a gate expression.
Give me a hint
Look for the only row where both inputs are 1.
Compare my reasoning
- The output is true only on 11.
- That is the AND condition.
Y=A AND B.
Look for these in your work
- True row identified
- Expression
Rows 00,01,10,11 have outputs 1,0,0,0. Identify the gate and justify it.
Give me a hint
Compare the table to the inverse of AND.
Compare my reasoning
- AND is true only on 11.
- The given table reverses every AND output.
- Therefore the pattern is NAND.
Y=A NAND B.
Look for these in your work
- Base pattern
- Inversion
A two-input output is 1 for rows 01 and 11, and 0 for 00 and 10. Identify and verify a simple expression.
Give me a hint
Compare the output with the value of one input column.
Compare my reasoning
- The output equals B in all four rows.
- A gate expression that produces B is not a two-input gate from the specified set by itself.
- If only standard gates are permitted, B could pass directly as a wire; do not claim a listed gate reproduces it without checking.
The table is Y=B (a direct connection). It does not match a two-input gate truth table from the six standard gates.
Look for these in your work
- Column comparison
- Scope of gate patterns
Common mistakes
- Identifying a gate from only one row
- Confusing inclusive OR with XOR
- Assuming a table with three inputs is a single gate
What can you explain now?
Outputs 1,1,1,0 for rows 00,01,10,11 match which gate?
Compare with the explanation
NAND
NAND is the inverse of AND, whose only true row is 11.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What is a safe check before identifying an expression from a truth 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.