A-LevelComputer ScienceHardware9618/31 · May/June 2025 · Q58 Marks

This truth table represents a logic circuit. INPUT OUTPUT A B C D Z 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1

(a)Write the Boolean logic expression that corresponds to the given truth table as the sum-of-products. Z =[2]
(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) in the K-map to produce an optimal sum-of-products.[2]
(b)(iii)Write the Boolean logic expression from your answer to part (b)(ii) as the simplified sum-of-products. Z =[2]

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Mark scheme

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[2] All six correct terms: Z = A.B.C.D + Ā.B.C̄.D + Ā.B.C.D + A.B̄.C̄.D̄ + A.B.C̄.D + A.B.C.D
[2] Correct K-map completion
[1] Loop covering cells (AB=01, CD=01), (AB=01, CD=11), (AB=11, CD=01), (AB=11, CD=11)
[1] Loop covering cells (AB=00, CD=00) and (AB=10, CD=00) (wrap-around)
[1] One correct Boolean term (e.g. B.D)
[1] Boolean terms and operator correct and no other terms present: z = B.D + B̄C̄D̄

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