Complete a truth table from an expression
Generate each output row from a named Boolean expression, including expressions with three inputs.
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
What is the first step before completing a three-input expression table?
What you will learn
- Choose the full set of input rows
- Calculate terms systematically
- Record the final output for every row
Core idea
An expression determines one output for each possible input combination. For expressions with intermediate terms, add a column for each term before combining them into the final output.
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
Set up all rows first. Evaluate brackets or NOT terms, then the final operation, one row at a time. For three inputs use all eight combinations; a correct rule applied to an incomplete table is still an incomplete answer.
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 A=1, B=0, C=1, evaluate (A OR B) AND C.
Worked example
Complete Y=(A OR B) AND C for row A=0, B=1, C=1.
Show the worked solution
- A OR B is 0 OR 1, so it is 1.
- Combine that result with C=1 using AND.
- The output is 1.
Answer Y=1.
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.
For Y=A AND NOT B, calculate the output for 00,01,10,11.
Give me a hint
Create a NOT B intermediate value.
Compare my reasoning
- NOT B values are 1,0,1,0.
- AND each with A values 0,0,1,1.
- The outputs are 0,0,1,0.
Y: 0, 0, 1, 0.
Look for these in your work
- Intermediate NOT
- Final outputs
Complete (A XOR B) OR C for row A=1, B=1, C=0.
Give me a hint
Evaluate XOR before OR.
Compare my reasoning
- 1 XOR 1=0.
- 0 OR 0=0.
0.
Look for these in your work
- XOR evaluated
- OR evaluated
A system outputs Y=(A AND B) OR (NOT C). Find Y for A,B,C=1,0,0 and explain each intermediate value.
Give me a hint
Compute AND and NOT C separately before OR.
Compare my reasoning
- A AND B=1 AND 0=0.
- NOT C=NOT 0=1.
- 0 OR 1=1.
Y=1; the AND term is 0 and NOT C is 1, so the final OR is 1.
Look for these in your work
- AND term
- NOT term
- Final OR
Common mistakes
- Using only two rows for three inputs
- Skipping a bracketed term
- Copying a previous row's output
What can you explain now?
For A=0, B=0, C=1, find (A OR B) AND C.
Compare with the explanation
0
A OR B is 0; 0 AND 1 is 0.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
When an expression has several operations, why are intermediate columns useful?
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.