O-LevelComputer ScienceBoolean logic2210/12 · Oct/Nov 2020 · Q48 Marks

Consider the logic statement: X = (((A NAND B) NOR (B AND C)) OR C)

(a)Draw a logic circuit to match the given logic statement. All logic gates must have a maximum of two inputs. Do not attempt to simplify the logic statement.[4]
(b)Complete the truth table for the given logic statement. A B C Working space X 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[4] One mark for each correct logic gate with correct input: The circuit diagram should show: 1. A NAND gate with inputs A and B. 2. An AND gate with inputs B and C. 3. A NOR gate with inputs from the output of (A NAND B) and the output of (B AND C). 4. An OR gate with inputs from the output of the NOR gate and C.
[4] Four marks for 8 correct outputs; Three marks for 6/7 correct outputs; Two marks for 4/5 correct outputs; One mark for 2/3 correct outputs A | B | C | X 0 | 0 | 0 | 0 0 | 0 | 1 | 1 0 | 1 | 0 | 0 0 | 1 | 1 | 1 1 | 0 | 0 | 0 1 | 0 | 1 | 1 1 | 1 | 0 | 1 1 | 1 | 1 | 1

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