A-LevelComputer ScienceHardware9618/32 · Oct/Nov 2024 · Q69 Marks

The truth table for a logic circuit is shown.

(a)Write the Boolean logic expression that corresponds to the given truth table as the sum-of-products. X =[3]
(b)Complete the Karnaugh map (K-map) for the given truth table.[2]
(c)Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.[2]
(d)Write the Boolean logic expression from your answer to part (c) as the simplified sum-of-products. X =[2]

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 (Oct/Nov 2024). The mark or mark type is shown in brackets.

[3] Three marks for all eight correct products and no additional products
[3] Two marks for five, six or seven correct products
[3] One mark for three or four correct products
[3] (X =) A'B'C'D + A'B'CD' + A'BC'D + A'BCD' + AB'C'D + AB'CD' + ABC'D + ABCD'
[2] Two marks if no errors present
[2] One mark if one error present
[2] AB CD 00 01 11 10 00 0 0 0 0 01 1 1 1 1 11 0 0 0 0 10 1 1 1 1
[2] One mark for each correct loop (Max 2)
[2] AB CD 00 01 11 10 00 0 0 0 0 01 (1 1 1 1) <- Group 1 11 0 0 0 0 10 (1 1 1 1) <- Group 2
[2] One mark for each mark point (Max 2)
[2] MP1 Any correct relevant Boolean term
[2] MP2 Boolean terms with correct operator + and no other terms present
[2] (X =) C'D + CD'

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