MskProdComputing
Back to the topic

The mark scheme starts on a new page, so you can print pages one and two for a student and keep the last page yourself. Everything prints in black on white whichever theme you are using.

AQA GCSE CS · 3.4.2

Boolean Logic

Section A: 10 multiple choice questions, 10 marks. Section B: 4 written questions, 12 marks. Total 22 marks.

Name

Class

Date

Mark  / 22

Section A

Circle the letter of the correct answer. One mark each.

  1. 1What is the output of an AND gate when its inputs are 1 and 0?1
    1. A1
    2. BIt depends on the circuit
    3. CBoth 0 and 1
    4. D0
  2. 2Which gate gives an output of 1 only when its two inputs are different?1
    1. AXOR
    2. BOR
    3. CAND
    4. DNOT
  3. 3How many rows does a truth table need for a circuit with 4 inputs?1
    1. A4
    2. B8
    3. C12
    4. D16
  4. 4What is the output of NOT (A OR B) when A is 0 and B is 1?1
    1. A2
    2. BIt cannot be determined
    3. C0
    4. D1
  5. 5In how many rows of a two input truth table do OR and XOR give different outputs?1
    1. A0
    2. B1
    3. C2
    4. D3
  6. 6For the expression (A AND B) OR C, what is the output when A is 1, B is 0 and C is 1?1
    1. AIt depends on the order of the gates
    2. B1
    3. C0
    4. DUndefined
  7. 7Why should you add a column for each intermediate gate output when completing a truth table?1
    1. AIt reduces errors and earns method marks
    2. BIt makes the table shorter
    3. CIntermediate outputs are the final answer
    4. DIt is required by the specification
  8. 8Which expression matches a circuit where A and B feed an OR gate, whose output and C feed an AND gate?1
    1. A(A AND B) OR C
    2. BA AND B AND C
    3. C(A OR B) AND C
    4. DA OR (B AND C)
  9. 9What is the output of A XOR B when both inputs are 1?1
    1. AIt alternates
    2. B0
    3. CUndefined
    4. D1
  10. 10Two circuits are shown to be equivalent. What does this mean?1
    1. AThey contain the same number of gates
    2. BThey have the same number of inputs
    3. CThey use the same type of gate
    4. DThey produce the same output for every possible combination of inputs

Section B

Answer in the space provided. The number of marks tells you how many separate points to make.

  1. 1CompleteComplete a truth table for the Boolean expression Q = NOT A AND B.4
  2. 2ExplainExplain the difference between an OR gate and an XOR gate.2
  3. 3WriteA logic circuit has three inputs A, B and C. A and B feed an AND gate. The output of the AND gate and input C feed an XOR gate, whose output is Q. Write the Boolean expression for Q and state how many rows its truth table would have.3
  4. 4ExplainExplain why it is good practice to include a column for each intermediate gate output when completing a truth table for a combined circuit.3

Mark scheme

Section A

1D2A3D4C5B6B7A8C9B10D

Section B

1 Complete a truth table for the Boolean expression Q = NOT A AND B. 4

One mark for each of the following, to a maximum of 4.

  • Uses four rows covering all combinations of A and B
  • Includes a column for NOT A
  • Gives Q as 1 only when A is 0 and B is 1
  • Gives Q as 0 in the other three rows

Model answer. With A and B as inputs the table has four rows. Adding a column for NOT A gives 1, 1, 0, 0 as A runs 0, 0, 1, 1. Q is that column ANDed with B, so Q is 0 when A is 0 and B is 0, Q is 1 when A is 0 and B is 1, Q is 0 when A is 1 and B is 0, and Q is 0 when A is 1 and B is 1. The output is therefore 1 in exactly one row, the one where A is 0 and B is 1.

2 Explain the difference between an OR gate and an XOR gate. 2

One mark for each of the following, to a maximum of 2.

  • An OR gate outputs 1 when at least one input is 1
  • An XOR gate outputs 1 only when the inputs are different, so 0 when both are 1

Model answer. An OR gate gives an output of 1 whenever at least one of its inputs is 1, including when both are. An XOR gate gives an output of 1 only when its two inputs are different, so when both inputs are 1 its output is 0. The two gates therefore agree on three of the four rows of the truth table and differ only on the last.

3 A logic circuit has three inputs A, B and C. A and B feed an AND gate. The output of the AND gate and input C feed an XOR gate, whose output is Q. Write the Boolean expression for Q and state how many rows its truth table would have. 3

One mark for each of the following, to a maximum of 3.

  • Writes the AND operation in brackets
  • Applies XOR with C to that output
  • States 8 rows

Model answer. The AND gate acts first on A and B, so its output is written as A AND B and must be bracketed because it becomes a single input to the next gate. That output is then combined with C by the XOR gate, giving Q equals (A AND B) XOR C. With three inputs there are 2 to the power 3 combinations, so the truth table would have 8 rows.

4 Explain why it is good practice to include a column for each intermediate gate output when completing a truth table for a combined circuit. 3

One mark for each of the following, to a maximum of 3.

  • Each column applies one simple rule rather than several at once
  • This makes errors far less likely
  • The working is creditworthy, so method marks can be awarded even if the final column is wrong

Model answer. Adding a column for each gate turns the problem into a series of single steps, so at each column you are applying one gate's rule repeatedly rather than holding two or three rules in your head while working across a row. That is both faster and considerably less error prone. It also matters for marks: the intermediate columns are the visible working, so an examiner can award method marks for a correct approach even if a slip appears in the final output column. Working that has been rubbed out cannot earn anything.