Question 16
The ceiling fans in a meeting room operate on demand. When staff access the room using a swipe card and the temperature in the room is above 25º C, the fans turn on, activating a one-hour timer. The fans then turn off after one hour of operation, unless a movement sensor is activated, resetting the timer to keep the fans on for another hour.
Analyse this information to create a logic circuit that meets the requirements for ceiling fan operation. Clearly identify all inputs and outputs.
[10 marks]The fans need two conditions at once, and movement keeps the second one alive
This is one afternoon in the meeting room, drawn as a signal for each input and the fans. A raised line is 1 and a flat line is 0. Watch what keeps the fans running.
Condition 1 is the swipe card and the temperature together. Condition 2 is the timer still running or movement in the room. The fans run only while both hold.
Build QCAA’s circuit one gate at a time and watch the marks tick
The wiring is laid out as QCAA drew it. Press each box to label it, choose a gate for each empty slot, then press the 0 and 1 badges to test your circuit. Each marking-guide dot point ticks as soon as you earn it.
Orange wires carry 1 and grey wires carry 0. A dashed wire has no signal yet because a gate before it is missing. On a phone, scroll the circuit sideways.
Work through the solution one mark at a time
Try each step yourself before you reveal it. Five marks are for labels and five are for gate paths.
List the inputs and the output before you draw a gate. Each one needs its name and what 1 and 0 mean for it, exactly as QCAA labelled them.
Yes = 1
No = 0
Yes = 1
No = 0
Yes = 1
No = 0
Yes = 1
No = 0
Yes = 1
No = 0
The timer is an input to your circuit. Its 1 means the hour is still running. The temperature label must carry the “> 25”, because that requirement is written into its mark.
Marker: provides a correctly applied logic circuit including clearly identified swipe card input · clearly identified temperature input with temperature requirement >25 · clearly identified one-hour timer input · clearly identified movement sensor input · clearly identified ceiling fan operation output. “For marks to be awarded for input sensors and the output, the yes and no conditions for operation should be clearly included.”
“When staff access the room using a swipe card and the temperature in the room is above 25º C” needs both inputs at 1. Feed them into AND1. Its output is condition 1.
$$\text{condition 1}=S\cdot T$$
Marker: swipe card and temp sensor => AND1. “Condition 1 includes swipe card and temp sensor.” “Allow FT error for incorrect: temperature sensor => AND1 or AND2 providing it is linked to the swipe card”
Work back from the output. The fans run only while condition 1 and condition 2 both hold, so a final AND2 feeds the ceiling fan operation output.
$$\text{fans}=\text{condition 1}\cdot\text{condition 2}$$
The guide also lets the outputs of AND1 and AND3 link back to the timer, to show what starts and resets it. You do not need that link for full marks.
Marker: condition 1 and condition 2 => AND2 => ceiling fan operation. “Condition 2 includes one hour timer and movement sensor.” “The output from AND1 and AND3 may also link to the one-hour timer, although this is not required for full marks to be awarded.”
Condition 2 starts with the timer. While the hour is running, its 1 goes straight into an XOR gate, and the XOR output goes to AND2.
Marker: one-hour timer => XOR => AND2 => ceiling fan operation. “Allow FT error for incorrect: AND2 when determining the timer and movement sensor logic paths”
“Unless a movement sensor is activated” only matters once the hour is up. QCAA branches the timer through a NOT gate into AND3, so AND3 can only fire while the timer reads 0.
$$\text{AND3}=\overline{H}\cdot M$$
Marker: one-hour timer => NOT => AND3 => XOR => AND2 => ceiling fan operation. “Allow FT error for incorrect: XOR gate when determining the timer and movement sensor => NOT gate logic paths”
The movement sensor is the second input to AND3. AND3 feeds the XOR, which feeds AND2. Now check what the timer section does.
| Timer | Movement | NOT | AND3 | XOR |
|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 1 | 0 | 0 | 1 |
The XOR column is 1 whenever the timer or the movement sensor is 1. QCAA’s three gates do the job of a single OR gate. The marks are written for QCAA’s XOR, NOT and AND3 paths, and the guide does not say how a single OR was marked, so learn the paths it names.
$$\begin{aligned}\text{fans}&=(S\cdot T)\cdot\\&\big(H\oplus(\overline{H}\cdot M)\big)\end{aligned}$$
QCAA’s sample response, 2022 marking guide.
Marker: movement sensor => AND3 => XOR => AND2 => ceiling fan operation. “Allow FT error for incorrect: movement sensor => AND3 providing it is linked to the timer”
Each phrase of the question gave you something
The 2022 subject report does not discuss this question by number. Its advice for teachers asks for work on the “interpretation of specific conditions to create logic gate circuits that include clearly annotated inputs and outputs, e.g. on and off conditions”, and this was the only circuit you had to create on the 2022 paper. A near-identical line appears in the 2023 and 2025 reports.
The shape is the familiar one, conditions gathered by a final AND, but you have to pull two conditions and a timer reset out of a paragraph before any gate goes down, across ten marks. QCAA did not publish a band for this question. It reads as complex familiar because the gates themselves are routine, while finding the two conditions in the paragraph takes real analysis.
If I had to guess where you might lose marks, it would be the labels. Half the question is five boxes with a name and “Yes = 1, No = 0” in each, and a box that says only “timer” or “temperature” earns nothing. Write “> 25” on the temperature input. Then do not sink ten minutes into the timer section. Draw the labels and AND1 and AND2 first, because those are seven of the ten marks.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording, any figures and marking-guide steps are from the 2022 QCAA Engineering external assessment, © State of Queensland (QCAA) 2022, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.
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