Engineering · Past QCAA questions All past questions
2022 · Section 2 · Short response

Question 13

[5 marks] Simple familiar
Topic guidesPremiumTopic guide 7 · The six gates and their rulesTopic guide 7 · Worked example: 2022 Question 13
Game planPremium6.3 Naming or describing a single gate
The question

Describe the function of a NAND gate. Include a truth table to support your response.

[5 marks]
Watch the situation first

A NAND gate is an AND gate with its output inverted, so only 1 and 1 give 0

The gate steps through all four input pairs in binary order. Watch what the AND part gives, what the bubble does to it, and how the table fills.

A = 0, B = 0. AND gives 0, so the bubble makes Q = 1 A = 0, B = 1. AND gives 0, so the bubble makes Q = 1 A = 1, B = 0. AND gives 0, so the bubble makes Q = 1 A = 1, B = 1. AND gives 1, so the bubble makes Q = 0 The output is 0 only when all inputs are 1 NAND the AND part gives 0 the AND part gives 1 the bubble inverts it Input AInput B Output Q 01 01 01 ABQ 001 011 101 110 one 0, in the 1 1 row 1, on0, off

AND is 1 in one row of four. The bubble flips every row, so NAND is 0 in one row of four, the row where every input is 1.

Now for the engineering

Switch the inputs and watch every wire

Press an input, or a row of the truth table. Then open the gate up as an AND gate followed by a NOT gate and check that nothing changes.

NAND AND NOT Orange wires carry 1 (on). Grey wires carry 0 (off).
Inputs
Draw the gate as
Truth table (press a row)
Input AInput BOutput Q

Build an answer and see which marks it earns

Pick the sentences you would write, then fill in the truth table by pressing each cell. The five dot points from the marking guide tick as you earn them.

Sentences
Your truth table
InputInputOutput

QCAA marking guide · 5 marks

Work through the solution one mark at a time

Try each step yourself before you reveal it.

Step 11 mark

Start with the one row that makes NAND different. Say when the output is 0.

“A NAND gate output is 0 when and only when all its inputs are at 1.”

Write “all its inputs”, which covers a gate with more than two inputs, instead of “both inputs”.

Marker: appropriately describes NAND gate function using wording that indicates the output is 0 when all inputs are 1

Step 21 mark

Then say what happens in every other row. This is a separate dot point, so it needs its own sentence.

“Otherwise the output is 1.”

The guide also accepts describing the gate as an inverted AND gate. If you use that wording, still state both output rules, because those are what the marker ticks.

Marker: appropriately describes NAND gate function using wording that indicates the output is 1 when all inputs are not 1. “Accept an explanation that includes use of the term inverter AND gate to describe NAND gate function.”

Step 32 marks

Draw the table and fill the two input columns first, in binary counting order. Two inputs give four rows. The right-hand input alternates fastest.

InputInputOutput
00
01
10
11

Each column is a mark on its own, so the inputs are two easy marks before you think about the gate at all.

Marker: provides a truth table with one column correct · a second column correct

Step 41 mark

Fill the output column from your two rules. Three 1s, then a single 0 in the row where both inputs are 1.

InputInputOutput
001
011
101
110

A NAND gate output is 0 when and only when all its inputs are at 1. Otherwise the output is 1.

Check the table against your sentences before you move on. If the words say one thing and the table another, the marker cannot tick both.

Marker: a third column correct

Putting it all together

Each phrase of the question gave you something

“Describe”
The glossary says describe means to give an account of a characteristic or feature. For a gate, the feature is what the output does for each input, so two plain rules answer it.
“the function of a NAND gate”
This is recall. The formula book gives you the symbol and nothing about what it does. You need the rule for 0 and the rule for 1, one mark each.
“Include a truth table”
Three columns, three marks. Two of them are the input columns, which you can write in binary order before you think about NAND at all.
“to support your response”
The table backs up the words. It does not replace them. A table on its own earns three of the five marks.
What makes this simple familiar

It is one gate, recalled and written out in the form every textbook uses. QCAA did not publish a band for this question. It reads as simple familiar because it asks for one gate that the formula book already draws for you, and the 2022 subject report says students responded well to simple familiar logic control questions.

If I had to guess where you might lose marks, it would be swapping NAND for NOR, which looks the same with a bubble on the end. NAND is 0 in one row and NOR is 1 in one row. The other trap is writing one sentence that only covers the 0 row. That is half the description, and it costs a mark that the second sentence, “Otherwise the output is 1”, would have earned.

Only mark this done when you could do it without help. Reading the solution does not count.

Back to the index

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.

Spot a mistake on this page? Report it