Game plan 6 · Unit 4 Topic 2
Logic and control
Logic gates and truth tables, and how to build a circuit from a paragraph of conditions.
There is a logic circuit, a truth table, or a paragraph of conditions that describes when a machine should switch on.
Logic is the largest non-calculation topic in the past papers, with 52 marks of circuit and table questions from 2020 to 2025 (43 in Section 2 up to 2024, and 9 in Section 3 in 2025). Every paper has a written logic question, and every year except 2022 also has a logic multiple choice question.
Check which section you are in first. Logic sat in Section 2 every year from 2020 to 2024, then moved to Section 3 in 2025 as Question 21. The answer shape is the same in both sections. Your time budget is different.
Part 1
The three shapes a logic question takes
Every logic question from 2020 to 2025 is one of three shapes. Read the task line and work out which way it runs before you write anything.
Ask this first
“Is the circuit printed, or do you have to draw it?”
The circuit is printed
Shape A. You complete a truth table. Go to Game plan 6.1.
Written: 2020 Question 14 and 2023 Question 13a. Multiple choice: 2021 Q2, 2023 Q3 and 2024 Q5.
You draw the circuit
Shape B. The conditions come as a paragraph, or as a supplied truth table. Go to Game plan 6.2.
2021 Question 15, 2022 Question 16, 2024 Question 15 (from a supplied table) and 2025 Question 21. In 2022 and 2025 it was the biggest question on the paper.
There is one gate
Shape C. You name the gate or describe what it does. Go to Game plan 6.3.
2020 Q8 and 2025 Q4 (multiple choice), and 2022 Question 13.
One question can ask for two shapes. 2025 Question 21 asked you to build the circuit and then complete its truth table, so you run Game plan 6.2 first and Game plan 6.1 second.
Find the task line and decide the direction before you draw: circuit to table, or words to circuit.
Part 2
The six gates and their rules
The formula book gives you the six gate symbols. It gives you no truth tables and does not say what any gate does. Every rule below is recall, and so is the order you write the rows in.
| Gate | Output is 1 when | As a rule (inputs A, B) |
|---|---|---|
| AND | every input is 1 | $X = 1$ for $AB = 11$ only |
| OR | at least one input is 1 | $X = 0$ for $AB = 00$ only |
| XOR | the inputs are different | $X = 1$ for $AB = 01$ and $AB = 10$ |
| NAND | at least one input is 0 | $X = 0$ for $AB = 11$ only |
| NOR | every input is 0 | $X = 1$ for $AB = 00$ only |
| NOT | its single input is 0 | $X = 1$ for $A = 0$ |
The syllabus also names four truth table terms. Logical true and logical false are the 1 and 0 states. Logical identity means the output copies its input. Logical negation means the output reverses it.
Telling NAND and NOR apart
Both look like an ordinary gate with a bubble on the end, so learn them by counting rows.
- •NAND is AND inverted. AND is 1 in one row out of four, so NAND is 0 in one row out of four: the row where both inputs are 1.
- •NOR is OR inverted. OR is 0 in one row out of four, so NOR is 1 in one row out of four: the row where both inputs are 0.
The 2022 mark guide gave one mark for each of two NAND statements: “output is 0 when all inputs are 1” and “output is 1 when all inputs are not 1”. Use the same two-sentence pattern for any gate you describe.
In the Topic Guides
Part 3
The four game plans
Game plans 6.1 to 6.3 match the three shapes. Game plan 6.4 is the check you run on every circuit you draw.
Completing a truth table from a printed circuit
Shape A. The circuit is printed and the table is empty, or the options are truth tables.
- 1Count the inputs and check the row count. Two inputs give 4 rows, three give 8 and four give 16. A sixteen-row table means four inputs.
- 2Write the rows in binary counting order. Start with all zeros. The right-hand input alternates fastest and the left-hand input changes once, halfway down. QCAA printed its tables in this order in 2023, 2024 and 2025, and the 2022 report asks for “inputs in logical order”.
- 3Name the intermediate signals. Papers usually letter them for you (D, E, F). Each one is the output of a single gate.
- 4Fill one column at a time, top to bottom. Take the gate that feeds the column, apply its rule to the columns feeding that gate, and finish the column before you start the next. Working across the rows is where scattered errors come from.
- 5Do the output column last, from the intermediate columns rather than the original inputs.
Follow-through applies. The 2025 mark guide allowed the mark for column X based on whatever the student wrote in column E, even when column E was wrong. Finish every table, even when you doubt an earlier column.
Building a circuit from a written scenario
Shape B. A paragraph of conditions, or a supplied truth table, and an empty box to draw in.
- 1List the inputs and their 1 conditions before you draw a gate, for example proximity sensor (package detected = 1). Write the output and its 1 condition too.
- 2Start from the output. Name what the machine does, such as “conveyor 2 receives power”, and ask what must be true for that to happen.
- 3Gather the conditions with a final AND. Usually several conditions must all hold, so a final AND gate feeds the output.
- 4Build each condition as a small sub-circuit. Use the word table below as a first guess, then check it against what must be true.
- 5Count the rows that switch the output on. A safety interlock should let very few rows through. If half your rows give 1, read the scenario again.
Naming or describing a single gate
Shape C. One gate symbol, one truth table, or “Describe the function of …”.
- 1Match the symbol against the formula book if a symbol is given. A bubble on the output means the gate is inverted.
- 2Count the 1s in the output column if a table is given. One 1 is AND (at 11) or NOR (at 00). Three 1s is OR (0 only at 00) or NAND (0 only at 11). Two 1s, at 01 and 10, is XOR.
- 3Describe the rule in two sentences, one for when the output is 1 and one for when it is 0. The 2022 mark guide gave a mark for each.
- 4Add a truth table with the input columns in binary order. In 2022 each correct column earned a mark.
Checking a logic circuit before you move on
Every circuit you draw, in either section.
- 1Every input has a line, a letter and a plain-English label, with its 1 condition stated.
- 2The output line says what the machine does, with its 1 condition.
- 3Every gate is one of the six standard symbols. Copy them from the formula book if you are unsure. A box with “AND” written inside it does not count as the symbol.
- 4Every inversion has its bubble drawn on the output side of the gate.
- 5Every gate input connects to something, with no floating lines.
- 6Intermediate signals are lettered so your truth table columns have names, and repeated gates are numbered (AND1, AND2) so the marker can follow each path.
The marks here are for separate features. A half-finished circuit with every line labelled still earns the label marks, and a neat circuit with no labels loses them.
Translating the words in Game plan 6.2
2025 Question 21 has two conditions. Both power supplies must be on (an AND), and neither the proximity sensor nor the emergency stop can be triggered (a NOR). Those two feed a final AND. Exactly one of the sixteen rows switches conveyor 2 on, the row with both power inputs on and both stop conditions clear.
Words to gates: starting points
| Words in the question | Gate |
|---|---|
| “both … and”, “when … and also” | AND |
| “either … or”, “any of” | OR |
| “not”, “unless”, “must be off”, “when no … is detected” | An inversion: a NOT gate, or the bubble on NAND or NOR |
| “either one but not both” | XOR |
| “when neither … nor” | NOR |
Treat the table as a first guess. QCAA does not always follow it. Its 2021 key turned “either a component is detected or the shut-down switch is not activated” into an AND, and its 2022 key handled “unless a movement sensor is activated” as an OR with the timer. Decide what must be true for the output, then pick the gate.
Two circuits, both full marks
Wherever two inputs must both be off, you have two choices.
- •Method 1: one NOR gate taking both inputs.
- •Method 2: a NOT gate on each input, feeding an AND.
The two give the same output on every row (De Morgan’s law), and the 2025 mark guide accepted both. Use the NOR if you can see it, because it means fewer gates to draw and fewer lines to label. If you cannot see it, two NOT gates and an AND get you there.
Part 4
Where the marks are in a logic question
2022 Question 16 (ceiling fans with a swipe card, temperature, a timer and a movement sensor) is one of the four ten-mark questions on record, and the only one outside Section 3. Its marks split evenly.
5 marks for labels
Clearly identified inputs and output: swipe card, temperature above 25 °C, one-hour timer, movement sensor, and the fan operation output.
5 marks for gate paths
One mark for each correct path through the gates to the fan output.
Five of the ten dot points are for the four inputs and the output, each with its yes/no condition. Draw and label them first.
Label marks in every circuit-building question
| Question | Marks for labels | Total marks |
|---|---|---|
| 2021 Question 15 | 2 | 6 |
| 2022 Question 16 | 5 | 10 |
| 2024 Question 15 | 5 | 8 |
| 2025 Question 21 | 4 | 9 |
Say what each label means
The 2022 mark guide is explicit: “for marks to be awarded for input sensors and the output, the yes and no conditions for operation should be clearly included.”
The 2022, 2023 and 2025 subject reports all ask for logic gate circuits with “clearly annotated inputs and outputs, e.g. on and off conditions”.
Not: C
Yes: proximity sensor (package detected = 1)
The 2025 mark guide accepted bare letters A to X because the paper had already printed a key defining them. Naming the component and stating its 1 condition costs one line and satisfies every mark guide on record.
In the Topic Guides
Part 5
Common QCAA language: Logic and control
These are task lines QCAA has used for logic questions from 2020 to 2025, with the routine each one calls for.
| You see this | The move it demands |
|---|---|
| “Interpret the logic circuit to create the corresponding truth table” (2020) | Game plan 6.1. Count the inputs, check the row count, fill column by column and do the output last. |
| “Complete the corresponding truth table” (2023, 2025) | Game plan 6.1. In 2025 the circuit was the one you had just built, so finish the circuit first. |
| “Develop a logic gate circuit …” (2021) | Game plan 6.2. Work backwards from the output. Label every input with its 1 condition before you draw a gate. |
| “Analyse this information to create a logic circuit” (2022) | Game plan 6.2. Analyse signals a longer item, and 2022’s version was worth ten marks. Game plan 7 covers the verb. |
| “Construct a logic gate circuit, based on the truth table” (2024) | Game plan 6.2, with the table as your specification. The intermediate columns tell you what each gate does. |
| “Describe the function of a NAND gate” (2022) | Game plan 6.3. Two sentences, one for output 0 and one for output 1, then a truth table. |
| “Which logic gate corresponds to the table?” (2025) | Game plan 6.3. Count the 1s in the output column. |
| “Explain how the logic circuit determines …” (2023) | Complete the table first, then describe each input condition in sentences. Say which gate passes which signal. |
| A sixteen-row table printed | Four inputs. Do not add a fifth because the scenario names five things. Some of them are outputs or intermediate signals. |
Likely contexts
The syllabus names traffic lights, boom gates at a railway crossing, a thermostatically controlled incubator or cooking system or barbecue, sun-tracking systems for solar panels, and solar-powered devices such as battery chargers, model vehicles and lighting systems.
The past papers have used a punching machine, ceiling fans, a solar or wind powered motor, a forklift reversing system and a conveyor line. None of them was lifted directly from the syllabus list (the 2023 solar or wind motor is the closest), but every one has the same shape. Learn the six gate rules and the backwards-from-the-output method instead of memorising contexts.
Where to go next
Circuits with volts, amps and ohms are a different topic, covered in Game plan 3.5. This game plan is control logic only: gates and truth table rows, with no numbers or formulas.
For the response shape, use Template T5, Logic creation, in Game plan 7. The worked exam questions are in Topic guide 7.
Wording quoted from past QCAA Engineering external assessments is © State of Queensland (QCAA), licensed under CC BY 4.0. Tangent Tuition is not affiliated with the QCAA.
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