← IGCSE Computer Science Paper 2

Writing exam answers about Boolean logic

A full-mark answer uses capital gate names, labelled inputs A, B, C and output X, correct brackets and a complete truth table with every row filled.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 41

Understanding Writing exam answers about Boolean logic in IGCSE Computer Science Paper 2

What it does: The output is named X, the inputs are A and B, and the brackets show NOT applies to the whole of A OR B. Three inputs give 2 x 2 x 2 = 8 input combinations, so a full-mark table lists all 8 rows from 000 to 111. Marks are given for labelling every input and the output, so none should be left out. Working columns let you check each gate and can earn method marks even if the final column has a slip. Choose the route that matches the question: statement to expression to circuit keeps each gate matched to the words.

Common mistakes: The brackets are missing. A full-mark expression must show the grouping, so line 1 should be X = (A AND B) OR C. Gate names must be written in capital letters. The expression should be X = NOT (A OR B).

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This module's key terms are also in a printable crossword (Modules 562–580) and word search (Modules 539–580).

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Learning
Duo
Which logic expression is written the way a full-mark exam answer should be?
x = a and b or cX = (A AND B) OR C
Matches
X = A and B or C
↓
Gate names are not in capitals and there are no brackets, so the order of the gates is unclear.
Applying
Meanings
Term
X = (A AND B) OR C
Meaning
A full-mark answer uses capital gate names, labelled inputs A, B, C and output X, correct brackets and a complete truth table with every row filled.
Practice
X = (A AND B) OR C
Testing
Gaps
X = (A AND B) C
Check Answer
Spots
1X = A AND B OR C
2A B C | A AND B | X

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Quick Questions

1. Which logic expression is written the way a full-mark exam answer should be?
A. X = (A AND B) OR C ✓
B. x = a and b or c
Use capital gate names, label the output X and the inputs A, B, C, and add brackets so the order is clear.
2. A question gives a circuit with inputs A, B, C and one output. How should you label it in your answer?
A. Label every input A, B, C and the output X ✓
B. Label only the output and leave the inputs blank
Marks are given for labelling every input and the output, so none should be left out.
3. A truth table for three inputs is asked for. How many rows must you complete?
A. All 8 rows ✓
B. Only the rows where X is 1
Three inputs give 2 x 2 x 2 = 8 combinations. Every row must be filled in, including those where X is 0.
4. The circuit has a gate whose output feeds another gate. What helps you show your working in the truth table?
A. Skip the middle step and only write the final X column
B. Add an extra working column for the middle gate's output ✓
Working columns let you check each gate and can earn method marks even if the final column has a slip.
5. The exam gives you a problem statement and asks for a logic circuit. Which route is best?
A. Guess the gates and draw them without any expression
B. Write the expression from the statement, then draw the gates from it ✓
Choose the route that matches the question: statement to expression to circuit keeps each gate matched to the words.

Match the Pairs

X = (A AND B) OR C → A full-mark expression: output X is labelled, gate names are in capitals and brackets show that A AND B is worked out first.
A B C | A AND B | X → A truth table header with a working column, so the intermediate result is shown before the final output X.
Label every input and the output so the examiner can follow your answer. → X = NOT (A OR B)
A three-input truth table must be complete, with every one of the 8 rows filled in. → 2 x 2 x 2 = 8 rows
X = A and B or C → Gate names are not in capitals and there are no brackets, so the order of the gates is unclear.
A B | X (only 3 of the 4 rows shown) → The truth table is incomplete because a row is missing. Two inputs need all 4 rows.

Key Term

X = (A AND B) OR C
A full-mark answer uses capital gate names, labelled inputs A, B, C and output X, correct brackets and a complete truth table with every row filled.

Fill in the Blanks

1. X = (A AND B) OR C
Hint: Type the capital-letter gate name that joins the bracketed part to input C.
2. X = (A AND B) OR C
Hint: Type the single capital letter used to label the output.
3. 3 inputs: 2 x 2 x 2 = 8 rows
Hint: Type how many rows a full three-input truth table needs.
4. A B C | A AND B | X 0 1 1 | 0 | 1
Hint: Type the value of the working column for this row, where A is 0 and B is 1.
5. Problem: X is 1 only if A and B are both 1 X = A AND B
Hint: Type the capital-letter gate name that matches the wording of the problem statement.

Spot the Error

Question 1
A X = A AND B OR C
B A B C | A AND B | X
C 0 0 0 | 0 | 0
D 0 0 1 | 0 | 1
Line A — The brackets are missing. A full-mark expression must show the grouping, so line 1 should be X = (A AND B) OR C.
Question 2
A Inputs: A, B
B Output: X
C X = not (A OR B)
Line C — Gate names must be written in capital letters. The expression should be X = NOT (A OR B).
Question 3
A A B | X = A AND B
B 0 0 | 0
C 0 1 | 1
D 1 0 | 0
E 1 1 | 1
Line C — AND only outputs 1 when both inputs are 1. With A = 0 and B = 1 the output X must be 0, so the row should be 0 1 | 0.
Question 4
A Inputs: P, Q, R
B Output: X
C X = (A OR B) AND C
Line A — Exam questions use the input labels A, B and C. The expression uses A, B and C, so line 1 should be Inputs: A, B, C.
Question 5
A X = (A OR B) AND C
B A B C | A OR B | X
C 0 0 1 | 0 | 0
D 1 0 1 | 0 | 1
E 1 1 0 | 1 | 0
Line D — The working column is wrong. When A = 1 and B = 0, A OR B is 1, not 0. The row should be 1 0 1 | 1 | 1.

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