A-LevelComputer ScienceHardware9618/32 · Oct/Nov 2021 · Q710 Marks

Write the Boolean expression that corresponds to the given truth table as a sum-of-products. INPUT OUTPUT A B C D Z 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 Z =

(a)Write the Boolean expression that corresponds to the given truth table as a sum-of-products. INPUT OUTPUT A B C D Z 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 Z =[3]
(b)(i)Complete the Karnaugh map (K-map) for the given truth table. AB CD 00 01 11 10 00 01 11 10[2]
(b)(ii)Draw loop(s) around appropriate group(s) of 1s in the K-map to produce an optimal sum-of-products.[2]
(b)(iii)Write the Boolean expression from your answer to part b(ii) as a simplified sum-of-products. Z =[2]
(b)(iv)Write the simplified Boolean expression for your answer to part b(iii). Z =[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[3] (Z =) A B C D +ABCD+ABCD+ABCD + ABCD+ABCD
[2] (K-map values for Z) AB CD 00 01 11 10 00 0 0 1 0 01 0 0 1 1 11 0 0 1 1 10 0 0 1 0
[2] (Diagram of loops, one vertical group of 4 in AB=11 column, one 2x2 group from (01,01), (11,01), (01,11), (11,11))
[1] A B // A D
[1] + A D // + AB
[1] (Z =) A (B + D) // A (D + B)

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