A-LevelComputer ScienceHardware9618/31 · May/June 2023 · Q77 Marks

Complete the Karnaugh map (K-map) for the following Boolean expression. Z = A.B.C.D + A.B.C.D + A.Β.C.D + Α.Β.C.D + A.B.C.D + A.B.C.D AB CD 00 01 11 10 00 01 11 10

(a)Complete the Karnaugh map (K-map) for the following Boolean expression. Z = A.B.C.D + A.B.C.D + A.Β.C.D + Α.Β.C.D + A.B.C.D + A.B.C.D AB CD 00 01 11 10 00 01 11 10[2]
(b)Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.[2]
(c)Write the Boolean logic expression from your answer to part (b) as a simplified sum-of-products. Z =[2]
(d)Use Boolean algebra to give your answer to part (c) in its simplest form. Z =[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[2] (a) Two marks if no errors present One mark if one error present AB CD 00 01 11 10 00 1 1 1 0 01 1 1 1 0 11 0 0 0 0 10 0 0 0 0
[2] (b) One mark for each correct loop (Max 2) Two groups of 4: one covering cells (00,00), (01,00), (00,01), (01,01) and another covering (01,00), (11,00), (01,01), (11,01).
[2] (c) One mark for each mark point (Max 2) • Any correct Boolean term • Boolean terms and operator correct and no other terms present (Z =) AC + BC
[1] (d) One mark for simplest form (Max 1) (Z =) C (A + B)

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