O-LevelComputer ScienceBoolean logic2210/11 · May/June 2015 · Q310 Marks

Complete the truth table for the following logic circuit: [Figure showing logic circuit with inputs A, B, C and output X, and a truth table with columns A, B, C, Workspace, X. The Workspace column is empty, and the X column is empty except for the first row. Input values are provided for A, B, C rows 000 to 111.]

(a)Complete the truth table for the following logic circuit: [Figure showing logic circuit with inputs A, B, C and output X, and a truth table with columns A, B, C, Workspace, X. The Workspace column is empty, and the X column is empty except for the first row. Input values are provided for A, B, C rows 000 to 111.][4]
(b)Draw a logic circuit which corresponds to the following logic statement: X = 1 if ((A is NOT 1 OR B is 1) AND C is 1) OR (B is NOT 1 AND C is 1) A B C X[3]
(c)Write a logic statement which corresponds to the following logic circuit: [Figure showing another logic circuit with inputs A, B, C and output X.][3]

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 (May/June 2015). The mark or mark type is shown in brackets.

[(a)] X column values: 1, 0, 0, 0, 1, 1, 1, 1
[(a)] [1 mark] for X=1, 0 (rows 0, 1)
[(a)] [1 mark] for X=0, 0 (rows 2, 3)
[(a)] [1 mark] for X=1, 1 (rows 4, 5)
[(a)] [1 mark] for X=1, 1 (rows 6, 7)
[(b)] [1 mark] per dotted section (refers to the three main logical blocks of the circuit required for the statement)
[(c)] [1 mark] (A is 1 OR B is 1)
[(c)] [1 mark] AND
[(c)] [1 mark] (B is 1 OR C is NOT 1)
[(c)] [1 mark] accept equivalent ways of writing this: e.g. (A OR B = 1) AND (B OR NOT C = 1)
[(c)] [1 mark] e.g. (A OR B) AND (B OR NOT C)
[(c)] [1 mark] e.g. (A + B) (B + C)

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