A-LevelComputer ScienceHardware9618/31 · May/June 2024 · Q610 Marks
The diagram shows a logic circuit. [Figure 6.1]
- (a)Complete the truth table for the given logic circuit. Show your working. Working space A B C P Q R S Z 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1[3]
- (b)Write the Boolean expression that corresponds to the logic circuit as a sum-of-products. Z =[2]
- (c)(i)Complete the Karnaugh map (K-map) for the Boolean expression: A.B.C + A.B.C + A.B.C + A.B.C + A.B.C + A.B.C BC 00 01 11 10 A 0 1[2]
- (c)(ii)Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.[2]
- (c)(iii)Write the Boolean expression from your answer to part (c)(ii) as a simplified sum-of-products.[1]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [3] 6(a) One mark for working, all four columns P, Q, R and S
- 6(a) One mark for first four rows of column Z
- 6(a) One mark for second four rows of column Z
- 6(a) A B C | P | Q | R | S | Z
- 6(a) 0 0 0 | 1 | 0 | 0 | 1 | 1
- 6(a) 0 0 1 | 1 | 0 | 0 | 1 | 1
- 6(a) 0 1 0 | 0 | 0 | 0 | 0 | 0
- 6(a) 0 1 1 | 0 | 0 | 0 | 0 | 0
- 6(a) 1 0 0 | 1 | 1 | 1 | 1 | 1
- 6(a) 1 0 1 | 1 | 1 | 1 | 1 | 1
- 6(a) 1 1 0 | 0 | 1 | 0 | 0 | 1
- 6(a) 1 1 1 | 0 | 1 | 0 | 1 | 1
- [2] 6(b) Two marks for all five correct terms and no extras
- 6(b) One mark for any three correct terms
- 6(b) (Z =) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
- [2] 6(c)(i) Two marks if all correct
- 6(c)(i) One mark if one error present
- 6(c)(i) A=0, BC=00: 1
- 6(c)(i) A=0, BC=01: 1
- 6(c)(i) A=0, BC=11: 0
- 6(c)(i) A=0, BC=10: 0
- 6(c)(i) A=1, BC=00: 1
- 6(c)(i) A=1, BC=01: 1
- 6(c)(i) A=1, BC=11: 1
- 6(c)(i) A=1, BC=10: 1
- [2] 6(c)(ii) One mark for each correct loop (Max 2)
- 6(c)(ii) Loop 1: A=0, BC=00,01
- 6(c)(ii) Loop 2: A=1, all cells
- [1] 6(c)(iii) A + B
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