A-LevelComputer ScienceHardware9618/31 · Oct/Nov 2024 · Q710 Marks

The truth table for a logic circuit is shown. [Figure X.X - truth table]

(a)Write the Boolean logic expression that corresponds to the given truth table as the sum-of-products. T =[3]
(b)Complete the Karnaugh map (K-map) for the given truth table. [Figure X.X - K-map template][2]
(c)Draw loop(s) around appropriate group(s) in the K-map to produce an optimal sum-of-products.[2]
(d)(i)Write the Boolean logic expression from your answer to part (c) as the simplified sum-of-products. T =[2]
(d)(ii)Use Boolean algebra to write your answer to part (d)(i) in its simplest form. T =[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

7(a) One mark for every two correct products (Max 3)
7(a) (T =) Ā. B'. C'. D + Ā. B'. C. D + Ā. B. C. D + A. B'. C'. D + A. B'. C. D + A. B. C'. D + A. B. C. D
7(b) Two marks if no errors present One mark if one error present
7(b) K-map table: AB\CD | 00 | 01 | 11 | 10 -----|----|----|----|---- 00 | 0 | 1 | 1 | 0 01 | 0 | 0 | 0 | 0 11 | 0 | 1 | 1 | 0 10 | 0 | 1 | 1 | 0
7(c) One mark for each correct loop (Max 2)
7(c) [K-map with loops]: Two loops of four cells each. One loop encompassing (AB=00,CD=01), (AB=10,CD=01), (AB=00,CD=11), (AB=10,CD=11). Another loop encompassing (AB=00,CD=11), (AB=01,CD=11), (AB=11,CD=11), (AB=10,CD=11).
7(d)(i) One mark for each mark point (Max 2) • Any correct Boolean term • Boolean terms and operator correct and no other terms present
7(d)(i) (T =) A. D + B. D // B. D. + A. D
7(d)(ii) One mark for simplest form (Max 1)
7(d)(ii) D. (A. B)

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