A building alarm has three binary inputs. A is 1 when a door sensor detects an open door. B is 1 when a window sensor detects an open window. C is 1 when th...
Question 1 Report
A building alarm has three binary inputs. A is 1 when a door sensor detects an open door. B is 1 when a window sensor detects an open window. C is 1 when the alarm system is armed. The output X is connected to the alarm sounder. A logic 1 at X causes the sounder to operate.
The table contains selected input combinations for this circuit.
| A | B | C | P | X |
|---|---|---|---|---|
| 0 | 0 | 0 | ||
| 0 | 1 | 1 | ||
| 1 | 0 | 1 | ||
| 1 | 1 | 1 |
(a) State what a logic 1 at X represents. [1]
(b) Complete the P column of the table. [4]
(c) Complete the X column of the table. [4]
(d) Identify the type of gate that produces P. [1]
(e) Give a Boolean expression for X. [2]
(f) Explain why X is always 0 when C is 0. [2]
(g) State the value of X when A = 0, B = 0 and C = 1. [1]
Answer Details
(a) A logic 1 at X means the alarm sounder operates [1].
(b) P is the OR result of A and B. (c) X is P AND C.
| A | B | C | P | X |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
All P values and all X values are required [4] [4].
(d) P is produced by an OR gate [1].
(e) \(X=(A\text{ OR }B)\text{ AND }C\) [2].
(f) C is an input to the final AND gate. An AND gate outputs 0 whenever either input is 0, so \(C=0\) forces \(X=0\) [2].
(g) When A = 0, B = 0 and C = 1, P is 0 and therefore X is 0 [1].
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