Question Simulator

IGCSE Computer Science (0478)

Boolean logic Banker

11 questions · about 6% of the marks we indexed · examined in 9 of 9 sessions.

Questions by year

2026

  • 2026 May/June · Paper 22 · Q8 (a, b)9 marksLogic circuits, expressions and problem statements

2025

  • 2025 Oct/Nov · Paper 22 · Q6 (a, b)8 marksLogic circuits, expressions and problem statements
  • 2025 May/June · Paper 22 · Q8 (a, b(i), b(ii))8 marksLogic circuits, expressions and problem statements · Logic gate symbols and truth tables

2024

  • 2024 Oct/Nov · Paper 22 · Q9 (a, b)8 marksLogic circuits, expressions and problem statements
  • 2024 May/June · Paper 22 · Q24 marksLogic gate symbols and truth tables
  • 2024 May/June · Paper 22 · Q8 (a, b)7 marksLogic circuits, expressions and problem statements

2023

  • 2023 Oct/Nov · Paper 22 · Q9 (a, b)8 marksLogic circuits, expressions and problem statements
  • 2023 May/June · Paper 22 · Q24 marksLogic gate symbols and truth tables
  • 2023 May/June · Paper 22 · Q84 marksLogic circuits, expressions and problem statements

2022

  • 2022 Oct/Nov · Paper 12 · Q7 (a, b)6 marksLogic gate symbols and truth tables
  • 2022 May/June · Paper 12 · Q5 (a, b)9 marksLogic circuits, expressions and problem statements · Logic gate symbols and truth tables

References only, not question text. Open Official paper ↗ where Cambridge publishes the paper, or see the official Cambridge past-papers page; for other papers, ask your school. “Paper 42” means Paper 4, variant 2.

Practice questions

Original questions written by HomiLabs in the style of the exam, with answers and mark schemes. They are not Cambridge past paper questions and have not been reviewed by Cambridge. Try each one before opening the answer.

Q1Logic circuits, expressions and problem statements · Core · Paper 2 style · 4 marks

X = (A AND B) OR (NOT C)

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) A B C | X0 0 0 | 10 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 01 1 0 | 11 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q2Logic circuits, expressions and problem statements · Core · Paper 2 style · 6 marks
  1. (a) A logic circuit is described as follows. Inputs A and B go into an OR gate. Input C goes into a NOT gate. The outputs of the OR gate and the NOT gate are the inputs to an AND gate, whose output is X. Write the logic expression for this circuit. [2]
  2. (b) Complete the truth table for X for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) X = (A OR B) AND (NOT C)
    1 mark for (A OR B), 1 mark for AND NOT C correctly combined.
  2. (b) A B C | X0 0 0 | 00 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 01 1 0 | 11 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
Q3Logic circuits, expressions and problem statements · Core · Paper 2 style · 7 marks
  1. (a) A garden sprinkler S is switched on (S = 1) when the soil is dry (D = 1) and it is not raining (R = 0), or when the manual switch is on (M = 1). Write a logic expression for S. [3]
  2. (b) Complete the truth table for S for all combinations of inputs D, R, M. [4]
Show answer
  1. (a) S = (D AND NOT R) OR M
    1 mark for D AND …, 1 mark for NOT R, 1 mark for OR M correctly placed.
  2. (b) D R M | S0 0 0 | 00 0 1 | 10 1 0 | 00 1 1 | 11 0 0 | 11 0 1 | 11 1 0 | 01 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q4Logic circuits, expressions and problem statements · Core · Paper 2 style · 5 marks

X = (A XOR B) AND C

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
  2. (b) State how many rows of the truth table give X = 1. [1]
Show answer
  1. (a) A B C | X0 0 0 | 00 0 1 | 00 1 0 | 00 1 1 | 11 0 0 | 01 0 1 | 11 1 0 | 01 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
  2. (b) 2
    1 mark.
Q5Logic circuits, expressions and problem statements · Core · Paper 2 style · 4 marks
  1. (a) Complete the truth table for both expressions.X = (A OR B) AND (NOT (A AND B))Y = A XOR B [3]
  2. (b) State what the truth table shows about the two expressions. [1]
Show answer
  1. (a) A B | X Y0 0 | 0 00 1 | 1 11 0 | 1 11 1 | 0 0
    X column correct: 1 mark. Y column correct: 1 mark. Both columns fully correct: 1 further mark.
  2. (b) They are equivalent: they give the same output for every combination of inputs.
    1 mark.
Q6Logic circuits, expressions and problem statements · Core · Paper 2 style · 4 marks
  1. (a) A circuit has two inputs, P and Q. P goes into a NOT gate. The output of the NOT gate and Q are the inputs to an AND gate, whose output is X. Write the logic expression for X. [1]
  2. (b) Complete the truth table for X for all combinations of inputs P, Q. [2]
  3. (c) State the values of P and Q that make X = 1. [1]
Show answer
  1. (a) X = (NOT P) AND Q
    1 mark.
  2. (b) P Q | X0 0 | 00 1 | 11 0 | 01 1 | 0
    1 mark for each two correct rows.
  3. (c) P = 0 and Q = 1
    1 mark.
Q7Logic circuits, expressions and problem statements · Core · Paper 2 style · 7 marks
  1. (a) A car's interior light L is on (L = 1) when a door is open (D = 1), or when the light switch is on (S = 1) and the engine is not running (E = 0). Write a logic expression for L. [3]
  2. (b) Complete the truth table for L for all combinations of inputs D, S, E. [4]
Show answer
  1. (a) L = D OR (S AND NOT E)
    1 mark for D OR …, 1 mark for S AND …, 1 mark for NOT E.
  2. (b) D S E | L0 0 0 | 00 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 11 1 0 | 11 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q8Logic circuits, expressions and problem statements · Standard · Paper 2 style · 5 marks

X = (A NAND B) XOR C

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
  2. (b) State the number of logic gates needed to draw this circuit, if each gate has at most two inputs. [1]
Show answer
  1. (a) A B C | X0 0 0 | 10 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 01 1 0 | 01 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
  2. (b) 2 (one NAND gate and one XOR gate)
    1 mark.
Q9Logic circuits, expressions and problem statements · Standard · Paper 2 style · 4 marks

X = NOT (A XOR B) OR (B AND C)

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) A B C | X0 0 0 | 10 0 1 | 10 1 0 | 00 1 1 | 11 0 0 | 01 0 1 | 01 1 0 | 11 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q10Logic circuits, expressions and problem statements · Standard · Paper 2 style · 6 marks
  1. (a) A water tank has two level sensors, A and B, which should always give the same reading. A warning light W comes on (W = 1) when the sensors disagree, but only while the monitoring system is switched on (S = 1). Write a logic expression for W. [2]
  2. (b) Complete the truth table for W for all combinations of inputs A, B, S. [4]
Show answer
  1. (a) W = (A XOR B) AND S
    1 mark for A XOR B, 1 mark for AND S.
  2. (b) A B S | W0 0 0 | 00 0 1 | 00 1 0 | 00 1 1 | 11 0 0 | 01 0 1 | 11 1 0 | 01 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
Q11Logic circuits, expressions and problem statements · Standard · Paper 2 style · 6 marks
  1. (a) A logic circuit is described as follows. Inputs A and B go into a NOR gate. Inputs B and C go into a NAND gate. The outputs of the NOR gate and the NAND gate are the inputs to an OR gate, whose output is X. Write the logic expression for this circuit. [2]
  2. (b) Complete the truth table for X for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) X = (A NOR B) OR (B NAND C)
    1 mark for (A NOR B) and (B NAND C), 1 mark for joining them with OR.
  2. (b) A B C | X0 0 0 | 10 0 1 | 10 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 11 1 0 | 11 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
Q12Logic circuits, expressions and problem statements · Standard · Paper 2 style · 4 marks
  1. (a) The truth table shows the output X of a logic circuit.A B C | X0 0 0 | 00 0 1 | 10 1 0 | 00 1 1 | 11 0 0 | 11 0 1 | 11 1 0 | 01 1 1 | 1Write a logic expression that gives this output. [3]
  2. (b) State the only input combination with C = 0 that gives X = 1. [1]
Show answer
  1. (a) X = C OR (A AND NOT B) (or any equivalent expression)
    1 mark for C OR …, 1 mark for A AND …, 1 mark for NOT B. Accept any expression that gives the same truth table.
  2. (b) A = 1, B = 0, C = 0
    1 mark.
Q13Logic circuits, expressions and problem statements · Standard · Paper 2 style · 7 marks
  1. (a) The doors of a metro train open (O = 1) only when the train has stopped (S = 1) and either the driver presses the release button (R = 1) or a passenger pulls the emergency handle (E = 1). Write a logic expression for O. [3]
  2. (b) Complete the truth table for O for all combinations of inputs S, R, E. [4]
Show answer
  1. (a) O = S AND (R OR E)
    1 mark for S AND, 1 mark for (R OR E), 1 mark for correct brackets/structure.
  2. (b) S R E | O0 0 0 | 00 0 1 | 00 1 0 | 00 1 1 | 01 0 0 | 01 0 1 | 11 1 0 | 11 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q14Logic circuits, expressions and problem statements · Standard · Paper 2 style · 4 marks
  1. (a) Complete the truth table for X = NOT (A AND B) and for Y = (NOT A) OR (NOT B). [3]
  2. (b) Name the single logic gate that is equivalent to both expressions. [1]
Show answer
  1. (a) A B | X Y0 0 | 1 10 1 | 1 11 0 | 1 11 1 | 0 0
    1 mark for X column, 1 mark for Y column, 1 mark for both fully correct.
  2. (b) NAND
    1 mark.
Q15Logic circuits, expressions and problem statements · Standard · Paper 2 style · 5 marks

X = (A OR B) NAND (B XOR C)

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
  2. (b) List the input combinations (A, B, C) for which X = 0. [1]
Show answer
  1. (a) A B C | X0 0 0 | 10 0 1 | 10 1 0 | 00 1 1 | 11 0 0 | 11 0 1 | 01 1 0 | 01 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
  2. (b) (0, 1, 0), (1, 0, 1), (1, 1, 0)
    1 mark for all three and no others.
Q16Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 8 marks
  1. (a) A crane on a building site in Dubai is allowed to lift (L = 1) only when the load sensor shows the load is within the safe limit (W = 1) and either the wind speed is not high (H = 0) or the site engineer has turned an override key (E = 1). Write a logic expression for L. [3]
  2. (b) Complete the truth table for L for all combinations of inputs W, H, E. [4]
  3. (c) Explain why the override key cannot make the crane lift an unsafe load. [1]
Show answer
  1. (a) L = W AND (NOT H OR E)
    1 mark for W AND …, 1 mark for NOT H, 1 mark for OR E inside the bracket.
  2. (b) W H E | L0 0 0 | 00 0 1 | 00 1 0 | 00 1 1 | 01 0 0 | 11 0 1 | 11 1 0 | 01 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
  3. (c) W is ANDed with the rest of the expression, so if W = 0 then L = 0 whatever E is.
    1 mark.
Q17Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 8 marks
  1. (a) A bank vault unlocks (V = 1) when at least two of its three managers, A, B and C, have inserted their keys (1 = key inserted). Write a logic expression for V using only gates with at most two inputs. [4]
  2. (b) Complete the truth table for V for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) V = (A AND B) OR (C AND (A XOR B)) — or equivalent, e.g. (A AND B) OR (A AND C) OR (B AND C)
    1 mark for A AND B; 1 mark for a term covering C with A; 1 mark for a term covering C with B; 1 mark for correct OR combination with no extra combinations. Accept any equivalent expression.
  2. (b) A B C | V0 0 0 | 00 0 1 | 00 1 0 | 00 1 1 | 11 0 0 | 01 0 1 | 11 1 0 | 11 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
Q18Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 8 marks
  1. (a) A greenhouse heater H is switched on (H = 1) when the temperature is low (T = 0) and it is night-time (N = 1), unless a window is open (W = 1), in which case the heater stays off. Write a logic expression for H. [3]
  2. (b) Complete the truth table for H for all combinations of inputs T, N, W. [4]
  3. (c) State how many NOT gates are needed to draw the circuit directly from your expression in (a), using only AND, OR and NOT gates. [1]
Show answer
  1. (a) H = (NOT T AND N) AND NOT W
    1 mark for NOT T, 1 mark for AND N, 1 mark for AND NOT W.
  2. (b) T N W | H0 0 0 | 00 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 01 0 1 | 01 1 0 | 01 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
  3. (c) 2
    1 mark. (One NOT gate for T and one for W.)
Q19Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 7 marks
  1. (a) A logic circuit is described as follows.- Gate 1 is a NAND gate with inputs A and B.- Gate 2 is a NOR gate with inputs B and C.- Gate 3 is an XOR gate whose inputs are the outputs of gates 1 and 2.- Gate 4 is a NOT gate whose input is C.- Gate 5 is an AND gate whose inputs are the outputs of gates 3 and 4; its output is X.Write the logic expression for X. [3]
  2. (b) Complete the truth table for X for all combinations of inputs A, B, C. [4]
Show answer
  1. (a) X = ((A NAND B) XOR (B NOR C)) AND NOT C
    1 mark for (A NAND B) XOR (B NOR C); 1 mark for NOT C; 1 mark for AND combining them correctly.
  2. (b) A B C | X0 0 0 | 00 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 01 0 1 | 01 1 0 | 01 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
Q20Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 6 marks

A student claims that the circuit X = (A XOR B) XOR C outputs 1 whenever an odd number of its inputs are 1.

  1. (a) Complete the truth table for X for all combinations of inputs A, B, C. [4]
  2. (b) Use your truth table to state whether the student is correct. [1]
  3. (c) Suggest a use for this circuit in data transmission. [1]
Show answer
  1. (a) A B C | X0 0 0 | 00 0 1 | 10 1 0 | 10 1 1 | 01 0 0 | 11 0 1 | 01 1 0 | 01 1 1 | 1
    1 mark for each two correct rows (8 rows = 4 marks).
  2. (b) Correct: X = 1 for exactly the rows with one or three inputs equal to 1.
    1 mark.
  3. (c) Generating/checking a parity bit (it gives the parity of the bits).
    1 mark.
Q21Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 5 marks
  1. (a) The truth table shows the output X of a logic circuit.A B C | X0 0 0 | 00 0 1 | 00 1 0 | 10 1 1 | 01 0 0 | 01 0 1 | 01 1 0 | 11 1 1 | 1Write a logic expression for X using no more than three gates. [4]
  2. (b) Explain why X is always 0 when B = 0. [1]
Show answer
  1. (a) X = B AND (A OR NOT C) (or an equivalent expression)
    1 mark for B AND …; 1 mark for A OR …; 1 mark for NOT C; 1 mark for correct structure using no more than three gates. Accept equivalents, e.g. (B AND NOT C) OR (A AND B).
  2. (b) B is ANDed with the rest of the expression, so B = 0 forces the AND gate output to 0.
    1 mark.
Q22Logic circuits, expressions and problem statements · Challenge · Paper 2 style · 8 marks
  1. (a) A conveyor belt in a rice mill runs (R = 1) only when its motor is not overheating (M = 0) and exactly one of these is true: the hopper is full (F = 1), or the operator presses the manual start button (S = 1). Write a logic expression for R. [3]
  2. (b) Complete the truth table for R for all combinations of inputs M, F, S. [4]
  3. (c) Explain why an XOR gate is used rather than an OR gate. [1]
Show answer
  1. (a) R = NOT M AND (F XOR S)
    1 mark for NOT M, 1 mark for F XOR S, 1 mark for AND joining them.
  2. (b) M F S | R0 0 0 | 00 0 1 | 10 1 0 | 10 1 1 | 01 0 0 | 01 0 1 | 01 1 0 | 01 1 1 | 0
    1 mark for each two correct rows (8 rows = 4 marks).
  3. (c) XOR gives 1 only when exactly one input is 1; OR would also give 1 when both F and S are 1.
    1 mark.
Q23Logic gate symbols and truth tables · Core · Paper 2 style · 3 marks
  1. (a) Name the logic gate described by each symbol.(i) A triangle with a small circle at its output.(ii) A D-shaped symbol (flat input side, curved output side) with no circle.(iii) A shield-shaped symbol (curved input side, pointed output) with no circle.(iv) A D-shaped symbol with a small circle at its output.(v) A shield-shaped symbol with a small circle at its output.(vi) A shield-shaped symbol with an extra curved line across its input side. [3]
Show answer
  1. (a) (i) NOT (ii) AND (iii) OR (iv) NAND (v) NOR (vi) XOR
    1 mark for each two correct.
Q24Logic gate symbols and truth tables · Core · Paper 2 style · 2 marks
  1. (a) Complete a truth table for a two-input NAND gate and a two-input NOR gate, with inputs A and B. [2]
Show answer
  1. (a) A B | NAND NOR0 0 | 1 10 1 | 1 01 0 | 1 01 1 | 0 0
    1 mark for the NAND column, 1 mark for the NOR column.
Q25Logic gate symbols and truth tables · Core · Paper 2 style · 4 marks
  1. (a) Identify the two-input logic gate described by each statement.(i) The output is 1 only when both inputs are 0.(ii) The output is 1 only when the inputs are different.(iii) The output is 1 only when both inputs are 1.(iv) The output is 0 only when both inputs are 1. [4]
Show answer
  1. (a) (i) NOR (ii) XOR (iii) AND (iv) NAND
    1 mark for each.
Q26Logic gate symbols and truth tables · Standard · Paper 2 style · 4 marks
  1. (a) Each column shows the output of a different two-input gate for the inputs (A, B) = (0, 0), (0, 1), (1, 0), (1, 1) in that order. Identify each gate.(i) 0, 1, 1, 1(ii) 1, 0, 0, 0(iii) 0, 1, 1, 0(iv) 1, 1, 1, 0 [4]
Show answer
  1. (a) (i) OR (ii) NOR (iii) XOR (iv) NAND
    1 mark for each.
Q27Logic gate symbols and truth tables · Standard · Paper 2 style · 3 marks
  1. (a) The output of an XOR gate with inputs P and Q is connected to the input of a NOT gate, whose output is Z. Complete the truth table for Z. [2]
  2. (b) Describe in words when Z = 1. [1]
Show answer
  1. (a) P Q | Z0 0 | 10 1 | 01 0 | 01 1 | 1
    1 mark for each two correct rows.
  2. (b) When both inputs are the same (both 0 or both 1).
    1 mark.
Q28Logic gate symbols and truth tables · Standard · Paper 2 style · 4 marks
  1. (a) A student draws four logic gates. For each one, write the name of the gate and give its output when input A = 1 and input B = 0.(i) Shield-shaped symbol with an extra curved line at the input side.(ii) D-shaped symbol with a small circle at its output.(iii) Shield-shaped symbol with a small circle at its output.(iv) D-shaped symbol with no circle. [4]
Show answer
  1. (a) (i) XOR, 1 (ii) NAND, 1 (iii) NOR, 0 (iv) AND, 0
    1 mark for each row with both name and output correct.
Q29Logic gate symbols and truth tables · Challenge · Paper 2 style · 5 marks
  1. (a) Both inputs of a NAND gate are connected to the same signal A. Complete the truth table for the output and name the single gate this arrangement behaves like. [2]
  2. (b) The output of a NAND gate with inputs A and B is connected to both inputs of a second NAND gate, whose output is X. Complete the truth table for X and name the single gate this arrangement behaves like. [3]
Show answer
  1. (a) A | output0 | 11 | 0It behaves like a NOT gate.
    1 mark for the truth table, 1 mark for NOT.
  2. (b) A B | X0 0 | 00 1 | 01 0 | 01 1 | 1It behaves like an AND gate.
    2 marks for the truth table (1 mark for each two correct rows), 1 mark for AND.
Q30Logic gate symbols and truth tables · Challenge · Paper 2 style · 4 marks
  1. (a) Inputs A and B go into NOR gate 1. The output of NOR gate 1 is connected to both inputs of NOR gate 2, whose output is X. Complete a truth table showing the output of NOR gate 1 (P) and the output X. [3]
  2. (b) Name the single gate that is equivalent to this arrangement. [1]
Show answer
  1. (a) A B | P X0 0 | 1 00 1 | 0 11 0 | 0 11 1 | 0 1
    1 mark for the P column, 2 marks for the X column (1 mark for each two correct rows).
  2. (b) OR
    1 mark.

Similar questions

Questions that test the same subtopic in different years, grouped so you can work on one skill at a time.

References only: find each question in its paper (official link where available, otherwise through your school).

Logic circuits, expressions and problem statements Banker8 questions · 8/9 sessions
Logic gate symbols and truth tables 5 questions · 5/9 sessions

Subtopics

Our analysis of how often each subtopic was examined and how many marks it carried, 2022 to May/June 2026.

SubtopicMarks indexedSessions
Logic circuits, expressions and problem statements Banker558/9
Logic gate symbols and truth tables 205/9

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