Engineers use a small logic circuit in a solar-powered rescue beacon on a sailing boat. Fig. 1 shows the circuit. Input N is 1 when the navigation computer ...
Question 1 Report
Engineers use a small logic circuit in a solar-powered rescue beacon on a sailing boat. Fig. 1 shows the circuit. Input N is 1 when the navigation computer reports a distress position. Input R is 1 when the crew presses the radio switch. Input B is 1 when the backup battery has enough charge. The transmitter output X must be 1 only when the battery is available and either N or R is 1. Each test is saved as binary data in a log file so that engineers can identify a fault after a voyage.
Table 1 contains output data from six checks of the circuit.
| Check | N | R | B | Recorded X |
|---|---|---|---|---|
| 1 | 0 | 0 | 0 | 0 |
| 2 | 0 | 1 | 0 | 0 |
| 3 | 1 | 0 | 1 | 1 |
| 4 | 1 | 1 | 1 | 1 |
| 5 | 0 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 0 |
(a) Identify the two gates used in Fig. 1. [2]
(b) State the checks in Table 1 for which the recorded output is correct. [3]
(c) Give the correct output X for check 5 and state why. [4]
(d) Complete the two missing input combinations needed for a full truth table, and give X for each combination. [4]
(e) Write a Boolean expression for X. [4]
Answer Details
(a) The circuit uses an OR gate [1] followed by an AND gate [1]. [2]
(b) The recorded outputs are correct for checks 1, 2, 3, 4 and 6. [3] Check 5 is wrong: the battery is available, but neither N nor R requests transmission.
(c) For check 5, X = 0 [2]. Neither N nor R is 1, so the OR gate output is 0 [2]; an AND gate cannot output 1 when one of its inputs is 0. [4]
(d) The two missing combinations are:
| N | R | B | X |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
In the first row the OR output and B are both 1. In the second, B is 0, so the final AND output is 0. Each row gains [2]. [4]
(e) The Boolean expression is:
\[X = (N \text{ OR } R) \text{ AND } B\]
[4]
Download The App On Google Playstore
Everything you need to excel in your exams
