Translate a problem statement into a Boolean expression
Convert words such as both, either, exactly one and not into gate expressions.
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
Which word most strongly indicates AND?
What you will learn
- Identify conditions and their input names
- Select the gate matching each connective
- Write a grouped expression from a statement
Core idea
Words describe the required logical relationship. “Both” usually signals AND; “at least one” signals OR; “exactly one” signals XOR; and “not” signals inversion. Define what each input means before writing the expression.
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
Name each condition, translate the connective, and add brackets if two operations are combined. Then test one example that should make the output true and one that should make it false.
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 light is on if at least one of A or B is 1. Which expression fits?
Worked example
A pump runs when level L is high and switch S is on. Write the expression.
Show the worked solution
- The inputs represent the two required conditions.
- Both must be true, so combine with AND.
- Use the output name P.
Answer P = L AND S.
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 door unlocks only when card C is valid and code K is correct. Write an expression for U.
Give me a hint
Both conditions are necessary.
Compare my reasoning
- Name the inputs C and K.
- Join with AND.
- Use U for the output.
U=C AND K.
Look for these in your work
- Inputs identified
- AND selected
A notification is sent when either sensor A or sensor B is triggered, or both. Write an expression.
Give me a hint
The words include both-true as an acceptable case.
Compare my reasoning
- “Either or both” means at least one input is 1.
- Use OR, not XOR.
- Name the output N.
N=A OR B.
Look for these in your work
- Inclusive OR recognised
- Expression complete
A backup starts when the main supply M is absent and the battery B is available. Define input meanings and write the expression.
Give me a hint
Absence of M needs inversion; availability is used directly.
Compare my reasoning
- Let M=1 mean main supply present and B=1 mean battery available.
- Main supply absent is NOT M.
- Both absence and battery availability are required.
Backup = (NOT M) AND B, where M=1 means the main supply is present and B=1 means the battery is available.
Look for these in your work
- Meaning stated
- NOT term
- AND relationship
Common mistakes
- Using OR for a requirement that says both
- Using OR for exactly one
- Leaving input meanings undefined
What can you explain now?
Which gate matches “exactly one of A or B”?
Compare with the explanation
XOR
XOR is true only when exactly one input is 1.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Which statement wording distinguishes OR from XOR?
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.