The diagram shows three logic gates.
Name each gate. [3]
- Gate 1: AND(1)
- Gate 2: OR(1)
- Gate 3: NOT(1)
- Answer: AND, OR, NOT
- Examiner tip: The NOT gate is the triangle with a small circle on its output.
Complete the truth table for Q = NOT (A AND B).
| A | B | Q |
|---|---|---|
| 0 | 0 | |
| 0 | 1 | |
| 1 | 0 | |
| 1 | 1 |
[2]
- Rows A=0, B=0 and A=0, B=1 both give Q = 1 (accept T/F for 1/0 throughout)(1)
- Row A=1, B=0 gives Q = 1 and row A=1, B=1 gives Q = 0(1)
- Answer: Q = 1, 1, 1, 0
- Examiner tip: Work out A AND B first, then flip it. Q is 0 only when both inputs are 1.
Look at the logic circuit.
(a) Write the Boolean expression for output P. [2]
(b) State the value of P when A = 1, B = 0, C = 0. [1]
(c) State the value of P when A = 0, B = 1, C = 1. [1]
- (a) A AND B (as one part). Allow A ∧ B, B AND A.(1)
- (a) NOT C joined to the AND part with OR: P = (A AND B) OR NOT C. Allow (A ∧ B) ∨ ¬C (a letter V is acceptable for OR), the two parts in either order (e.g. NOT C OR (A AND B)), and no brackets (A AND B OR NOT C), since AND is done before OR. Do not award if NOT covers more than C, e.g. NOT (C OR …).(1)
- (b) 1 (accept True / T)(1)
- (c) 0 (accept False / F)(1)
- Answer: (a) P = (A AND B) OR NOT C; (b) 1; (c) 0
- Examiner tip: Use brackets to show that the AND happens before the OR.
Complete the truth table for Q = (A OR B) AND NOT C.
| A | B | C | A OR B | NOT C | Q |
|---|---|---|---|---|---|
| 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]
- A OR B column correct: 0, 0, 1, 1, 1, 1, 1, 1(1)
- NOT C column correct: 1, 0, 1, 0, 1, 0, 1, 0(1)
- Q correct for the first four rows: 0, 0, 1, 0(1)
- Q correct for the last four rows: 1, 0, 1, 0. Accept T/F for 1/0 throughout.(1)
- Answer: Q = 0, 0, 1, 0, 1, 0, 1, 0
- Examiner tip: Fill in the working columns first, then AND them together row by row. Don't try to do Q in your head.
Describe how a logic circuit for X = (NOT (A OR B)) AND C would be drawn. You should name each gate and its inputs. [3]
- An OR gate with inputs A and B(1)
- A NOT gate whose input is the output of the OR gate(1)
- An AND gate whose inputs are the output of the NOT gate and C, giving output X. Allow a correctly drawn and labelled circuit instead of a written description for all 3 marks.(1)
- Answer: OR(A, B) → NOT → AND with C → X
- Examiner tip: The NOT applies to the whole bracket, so it goes on the output of the OR gate. Putting a NOT on A and on B and keeping the OR gate gives a different circuit.
An alarm (S) sounds if the door is open (D) and the system is armed (A), or if the panic button (P) is pressed.
(a) Write a Boolean expression for S. [3]
(b) State whether the alarm sounds when D = 1, A = 0, P = 0. [1]
(c) There are 8 possible combinations of D, A and P. State how many of these make the alarm sound. [1]
- (a) D AND A joined as one group (allow D ∧ A, A AND D). Not awarded if A is grouped with P instead, e.g. D AND (A OR P).(1)
- (a) P joined to the D AND A part with OR (allow ∨ or a letter V for OR, and P OR … at the start).(1)
- (a) Correct overall, with the AND done first: S = (D AND A) OR P. Allow P OR (D AND A), and D AND A OR P without brackets (AND is done before OR). Do not award for D AND (A OR P).(1)
- (b) No / S = 0 / False(1)
- (c) 5(1)
- Answer: (a) S = (D AND A) OR P; (b) no (0); (c) 5
- Examiner tip: In (c) go through the full truth table. Students often count the 4 rows where P = 1 and forget D = 1, A = 1, P = 0.
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