O-LevelComputer ScienceBoolean logic2210/12 · May/June 2019 · Q810 Marks
Consider the logic statement: X = 1 if ((A is 1 NOR C is 1) AND (B is NOT 1 NOR C is 1)) OR (A is 1 AND B is 1)
- (a)Draw a logic circuit to match the given logic statement. Each logic gate used must have a maximum of two inputs. Do not attempt to simplify the logic statement.[6]
- (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 (May/June 2019). The mark or mark type is shown in brackets.
- [6] 1 mark per each correct logic gate, with correct input(s) [Diagram: A logic circuit consisting of two NOR gates, one NOT gate, two AND gates, and one OR gate. The inputs A, B, C should connect to form: (A NOR C), (NOT B), ((NOT B) NOR C), ((A NOR C) AND ((NOT B) NOR C)), (A AND B), and finally (((A NOR C) AND ((NOT B) NOR C)) OR (A AND B)) to output X. The provided image in the mark scheme shows this structure precisely.]
- [4] 4 marks for 8 correct outputs 3 marks for 6/7 correct outputs 2 marks for 4/5 correct outputs 1 mark for 2/3 correct outputs A | B | C | X 0 | 0 | 0 | 0 0 | 0 | 1 | 0 0 | 1 | 0 | 1 0 | 1 | 1 | 0 1 | 0 | 0 | 0 1 | 0 | 1 | 0 1 | 1 | 0 | 1 1 | 1 | 1 | 1
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