A gas fire has a safety circuit made up of logic gates. It generates an alarm (X = 1) in response to certain conditions. Input Description Binary value Conditions G gas pressure 1 gas pressure is correct 0 gas pressure is too high C carbon monoxide level 1 carbon monoxide level is correct 0 carbon monoxide level is too high L gas leak detection 1 no gas leak is detected 0 gas leak is detected The output X = 1 is generated under the following conditions: gas pressure is correct AND carbon monoxide level is too high OR carbon monoxide level is correct AND gas leak is detected

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

1. [5] (a) 1 mark per correct logic gate, correctly connected [Logic circuit diagram with G AND NOT C, OR C AND NOT L, all leading to X. Specific gates: NOT C, NOT L, two AND gates, one OR gate.]
2. [4] (b) G C L Workspace X 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 1 1 1 0 [1 mark for each row where X is correct, corresponding to the conditions: G=1, C=0 is true for X=1, and C=1, L=0 is true for X=1. Rows where X=1: 010 (G=0, C=1, L=0); 100 (G=1, C=0, L=0); 101 (G=1, C=0, L=1); 000 (G=0, C=0, L=0). Wait, MS X values are: 0,0,1,0,1,1,1,0. Let's re-evaluate based on the conditions. Condition 1: gas pressure is correct (G=1) AND carbon monoxide level is too high (C=0). Output X=1. Condition 2: carbon monoxide level is correct (C=1) AND gas leak is detected (L=0). Output X=1. So X = (G AND NOT C) OR (C AND NOT L) G C L | NOT C | NOT L | (G AND NOT C) | (C AND NOT L) | X 0 0 0 | 1 | 1 | 0 | 0 | 0 0 0 1 | 1 | 0 | 0 | 0 | 0 0 1 0 | 0 | 1 | 0 | 1 | 1 <-- X=1 0 1 1 | 0 | 0 | 0 | 0 | 0 1 0 0 | 1 | 1 | 1 | 0 | 1 <-- X=1 1 0 1 | 1 | 0 | 1 | 0 | 1 <-- X=1 1 1 0 | 0 | 1 | 0 | 1 | 1 <-- X=1 1 1 1 | 0 | 0 | 0 | 0 | 0 The MS gives X values: 0,0,1,0,1,1,1,0. Let me check the rows. Row 1 (000): X=0. Correct. Row 2 (001): X=0. Correct. Row 3 (010): X=1. Correct. Row 4 (011): X=0. Correct. Row 5 (100): X=1. Correct. Row 6 (101): X=1. Correct. Row 7 (110): X=1. Correct. Row 8 (111): X=0. Correct. It seems the MS has a typo in its own interpretation of which rows map to 1 mark. The full X column is needed. I'll take the full X column from the MS: X = 0,0,1,0,1,1,1,0. The mark scheme says '1 mark for each number in the correct order', then four square brackets next to different rows, each saying '1 mark'. This implies partial credit. I'll just state the full column is required for full marks, as is typical for truth tables. Total 4 marks for the entire table. The MS shows 4 rows receiving a mark, this usually means 1 mark for every 2 correct rows, or 1 mark for a specific block of rows. Given the [4] for the entire sub-question, and [1 mark] next to four different sections, it implies 1 mark for 2 correct rows. So 8 rows, 4 marks, 2 rows for 1 mark. This means 1 mark for each pair of rows correctly filled. I will list all values in the model answer. The MS is consistent with my derived truth table. ],
3. [1] (c) 1 mark for correctly completed truth table A B C 0 0 0 0 1 1 1 0 1 1 1 0