Boolean Logic and Logic Gates: Question 2
Syllabus 10.1, 10.2, 10.3
A workshop uses a benchtop 3D printer fitted with a safety enclosure. To protect the print head, the printer's control board only sends the start-print signal G when both of the following are true at the same time:
- the enclosure door sensor confirms the door is closed (input D = 1 if the door is closed, 0 if it is open)
- the filament sensor confirms filament is loaded in the feed tube (input F = 1 if filament is present, 0 if the feed tube is empty)
(a) State the name of the single logic gate that combines inputs D and F to produce this behaviour. [1]
(b) Complete the truth table for the start-print signal G. [2]
| D | F | G |
|---|---|---|
| 0 | 0 | |
| 0 | 1 | |
| 1 | 0 | |
| 1 | 1 |
(c) A technician closes the enclosure door but does not notice that the filament spool has run out, leaving the feed tube empty. Using your completed truth table, explain whether the printer starts the print job, and state what the technician should do instead. [2]
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Worked solution
Part (a): Naming the gate
The start-print signal G must be true only when both conditions hold at once: the enclosure door is closed (D = 1) and filament is loaded (F = 1). A gate whose output is 1 only when both of its inputs are 1 is an AND gate, so G = D AND F.
Part (b): Completing the truth table
An AND gate outputs 1 only for the single row where both inputs are 1, and 0 for every other combination:
| D | F | G |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
- (0, 0): neither condition holds, so G = 0.
- (0, 1): filament is loaded, but the door is open, so G = 0.
- (1, 0): the door is closed, but the feed tube is empty, so G = 0.
- (1, 1): both conditions hold, so G = 1.
Part (c): Applying the truth table to a real case
The technician’s situation is D = 1 (door closed) and F = 0 (filament spool empty, so not present). Looking up row (D = 1, F = 0) in the completed truth table gives G = 0.
So the printer does not start the print job. A closed door on its own is not enough, because the AND condition also needs F = 1. Since the failing condition is the filament, the technician should reload the filament spool before the printer will start, rather than simply checking the door again.
Final answers
- (a) AND gate, so G = D AND F
- (b) G values in row order: 0, 0, 0, 1
- (c) The printer does not start (G = 0), because F = 0 fails the AND condition; the technician should reload the filament spool.