CIE IGCSE | TOPIC 10 ASSESSMENT
BOOLEAN LOGIC: END OF TOPIC REVIEW
Assess gate symbols and functions, circuit outputs, Boolean expressions and truth tables through recall, applied problems and written explanations. Work independently before revealing feedback.
BEFORE YOU BEGIN
Suggested time: 50–70 minutes, or split into two sessions. Complete sections A and B without notes. Write section C answers in your exercise book before revealing the marking guidance.
Sections A and B provide an automatic score out of 24, one point for each fully correct item. Section C has 34 suggested written marks, assessed separately. These are original practice questions, not an official Cambridge paper or grade boundary.
Draw standard gate symbols and label intermediate signals. Complete truth tables and explanations in your exercise book. State assumptions and show working where a question requires it. Your answers remain only while this page is open.
C | EXAM-STYLE WRITING
Write in your exercise book before revealing the guidance. Section C assesses subject knowledge and gives you practice expressing it clearly. The first table reproduces the command-word meanings supplied from the Cambridge syllabus. The second gives practical writing guidance for this review.
| CIE command word | Meaning from the specification |
|---|---|
| Calculate | work out from given facts, figures or information |
| Compare | identify/comment on similarities and/or differences |
| Define | give precise meaning |
| Demonstrate | show how or give an example |
| Describe | state the points of a topic / give characteristics and main features |
| Evaluate | judge or calculate the quality, importance, amount, or value of something |
| Explain | set out purposes or reasons / make the relationships between things clear / say why and/or how and support with relevant evidence |
| Give | produce an answer from a given source or recall/memory |
| Identify | name/select/recognise |
| Outline | set out the main points |
| Show (that) | provide structured evidence that leads to a given result |
| State | express in clear terms |
| Suggest | apply knowledge and understanding to situations where there are a range of valid responses in order to make proposals / put forward considerations |
The command applies to the subject context. A brief identification does not need an essay; an explanation needs accurate links. Use the guidance below for the commands in this written review.
| Command word | What your answer should do | Useful writing pattern |
|---|---|---|
| Describe | State the main features or relevant points; for a process, make the sequence clear. | First… Next… Finally… |
| Explain | Give reasons, purposes or clear relationships, supported by relevant subject knowledge. | …because…; therefore…; resulting in…; leading to… |
| Compare | Identify similarities and/or differences, addressing both things on the same basis. | Both…; whereas…; unlike… |
| Evaluate | Make a reasoned judgement about suitability or value in the given context. | A benefit is…; however…; therefore, for this purpose… |
| Calculate | Work out a result using the supplied data. | Show the relevant values and arithmetic. |
| Show (that) | Provide structured evidence leading to the stated result. | Trace intermediate states, then link them to the result. |
| Suggest | Apply knowledge to propose a valid solution or test. | State a proposal and relate it to the requirement. |
BUILD A CLEAR EXPLANATION
Point → reason or mechanism → consequence. Connectives help show the relationship, but the technical link must be accurate. Adding “because” to an unsupported claim does not make it a good explanation.
Thin answer: “The count changes.”
Developed answer: “The count increases by one only after an input is accepted because rejected attempts must not represent extra accepted scores, therefore invalid retries do not inflate the final count.”
Use because or because of to introduce a cause; therefore, resulting in or leading to to show a consequence. For comparison, use both and whereas. For evaluation, use however and finish with a justified judgement.
Write enough relevant detail for the marks available. Clear, concise sentences are better than padding. These are writing supports, not compulsory phrases or separate official language marks.
25 | FUNCTIONS AND SYMBOLS
[4 suggested marks]
describe the AND and NAND functions. Then demonstrate their standard symbols, labelling inputs A and B and output X.
AND outputs 1 only for two true inputs. NAND reverses AND, giving 0 only for two true inputs. Both use an AND-shaped body with a flat input side and rounded output; NAND adds the output inversion circle.
- AND function correct: one mark.
- NAND function correct: one mark.
- Correct labelled AND symbol: one mark.
- Correct labelled NAND symbol: one mark.
Writing focus: Describe the rule precisely, then draw the requested symbols rather than only writing their names.
26 | OR AND XOR
[4 suggested marks]
compare OR and XOR. Use input combinations 01 and 11 to support the comparison.
Both return 1 for 01 because one input is true. For 11, OR returns 1 because it accepts at least one including both, whereas XOR returns 0 because it requires exactly one. Both gates have two inputs.
- Shared two-input role or common exactly-one cases: one mark.
- Correct results for 01: one mark.
- Correct differing results for 11: one mark.
- Reason linking inclusive OR and exclusive XOR: one mark.
Writing focus: Address both gates on the same comparison point. Use whereas or because to explain the difference.
27 | TRACE WITH REASONS
[4 suggested marks]
For X = (A AND B) OR (NOT C), explain the output for ABC = 101 and ABC = 000, using intermediate signals P and Q.
For 101, P = 0 because AND requires both inputs true; Q = 0 because NOT reverses C = 1. Therefore X = 0 OR 0 = 0. For 000, P = 0 and Q = 1, therefore X = 1 because OR needs at least one true input.
- Correct P and Q for 101 with gate reasoning: one mark.
- Correct X for 101 with OR reasoning: one mark.
- Correct P and Q for 000 with gate reasoning: one mark.
- Correct X for 000 with OR reasoning: one mark.
Writing focus: Link input values to each gate rule. An unexplained final digit does not answer explain fully.
28 | COMPLETE THE TRUTH TABLE
[4 suggested marks]
demonstrate a complete truth table for X = (A AND B) OR (NOT C), including intermediate columns P and Q.
List every external combination. Calculate P and Q independently for each row before applying the final OR.
| A | B | C | P = A AND B | Q = NOT C | X |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
- All eight external combinations once: one mark.
- Correct complete P column: one mark.
- Correct complete Q column: one mark.
- Correct complete X column: one mark.
Writing focus: Use a structured table with clearly labelled columns. Keep each row as a separate case.
29 | GROUPING AND COUNTEREXAMPLE
[4 suggested marks]
compare X = (A AND B) OR (NOT C) with Y = A AND (B OR (NOT C)). show that they can give different outputs using ABC = 000.
X ends with OR between A AND B and NOT C. Y ends with AND between A and B OR NOT C. For 000, X = 0 OR 1 = 1, while Y = 0 AND (0 OR 1) = 0. This single differing case shows the expressions are not equivalent.
- Correct grouping or final gate for X: one mark.
- Correct grouping or final gate for Y: one mark.
- Structured calculation of X = 1: one mark.
- Structured calculation of Y = 0 and explicit differing-output conclusion: one mark.
Writing focus: Show the intermediate calculation and conclusion; do not merely claim that parentheses matter.
30 | BUILD A RULE FROM A TABLE
[4 suggested marks]
A two-input truth table has output 1 only for 01 and 10. identify a single suitable gate, and demonstrate an expression using NOT, AND and OR that gives the same outputs. explain the two true cases.
The single gate is XOR (EOR). An expanded expression is X = ((NOT A) AND B) OR (A AND (NOT B)). The first term represents 01; the second represents 10. OR combines the two acceptable cases. If asked to draw this expanded expression, retain its stated gate structure.
- XOR identified: one mark.
- Correct expanded expression: one mark.
- First true case explained as NOT A AND B: one mark.
- Second true case explained as A AND NOT B: one mark.
Writing focus: State the identification concisely, then link each expression term to its input row.
31 | CHECK AN ALTERNATIVE DESIGN
[4 suggested marks]
A student changes the rule “alarm when smoke or heat is detected” from OR to XOR. Inputs are A = SmokeDetected and B = HeatDetected. evaluate whether the change preserves the required behaviour.
XOR agrees with OR when neither signal is true or exactly one is true. It differs when both are true: OR outputs 1, while XOR outputs 0. Both detections satisfy the stated alarm requirement, therefore XOR does not preserve it. OR is appropriate for either or both detections.
- Relevant agreement cases: one mark.
- Correct both-true counterexample: one mark.
- Link to required alarm behaviour: one mark.
- Justified rejection and suitable OR choice: one mark.
Writing focus: Make a judgement supported by a concrete input case and its consequence. Avoid unsupported claims about every possible real alarm system.
32 | A COMPLETE GREENHOUSE SOLUTION
[6 suggested marks]
A fan runs when it is hot and the window is not open, or when manual override is selected. A = Hot, B = WindowOpen, C = ManualOverride, X = FanOn. demonstrate the expression, a labelled circuit and a complete truth table. Then explain why inverting B is necessary.
X = (A AND (NOT B)) OR C. Feed B through NOT to produce P; feed A and P into AND to produce Q; feed Q and C into OR to produce X. B means the window is open, but the required condition is closed, so inversion represents that opposite proposition.
| A | B | C | P = NOT B | Q = A AND P | X = Q OR C |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 0 | 1 |
- Correct expression including grouping: one mark.
- NOT B feeding AND with A: one mark.
- AND output feeding OR with C and labelled X: one mark.
- All eight combinations: one mark.
- Correct intermediate and final truth-table values: one mark.
- Input-definition reason for NOT B: one mark.
Writing focus: Provide all requested representations. For explain, use because to connect the input definition to the inversion.
CHECK YOUR WRITTEN COMMUNICATION
- Did I answer the command word, rather than just name facts?
- For explain, did I show an accurate reason or cause-and-effect link?
- For compare, did I address both things on the same point?
- For evaluate, did I weigh relevant factors and justify my judgement?
- Did I use precise terms and connectives naturally, without repeating or padding?
Self-assess using the suggested content marks, keeping the written total separate from your automatic score. Use the writing checklist to improve an answer rather than adding unofficial language marks.
YOUR NEXT REVISION STEP
Submit sections A and B for targeted lesson links.
Keep your automatic and written marks separate. Pick two weak areas, revisit their lessons and attempt a fresh circuit or explanation. Use the Topic 10 revision page for complete coverage, worked examples and a selectable flashcard list. These original practice scores are not official grade predictions.