Question 4
The truth table for a logic gate is shown.
Which logic gate corresponds to the table?
Not quite. OR also has three 1s and one 0, which is why it looks close. Its 0 sits at AB = 00, where both inputs are 0. In this table the 0 is at AB = 11. In 2025, 2.2% of Queensland students chose (A).
Not quite. AND gives 0, 0, 0, 1, the exact opposite of this table in every row. A gate whose output is AND flipped is AND with a bubble on the end. In 2025, 1.7% of Queensland students chose (B).
Not quite. NOR is the inverted gate students swap with NAND. NOR gives 1 in one row only, at AB = 00. This table has a single 0, at AB = 11, so it matches NOR in the top and bottom rows and fails in the middle two. In 2025, 10.2% of Queensland students chose (C).
That is it. Step through the hints below to see why. In 2025, 85.6% of Queensland students chose (D).
Count the 1s in the output column. There are three, and one 0.
Only two of the six gates are 1 in three rows out of four: OR and NAND. That rules out (B) AND and (C) NOR, which are each 1 in a single row.
Now look at where the single 0 sits. It is in the bottom row, where both inputs are 1.
$$X=0\text{ only for }AB=11$$
OR puts its 0 in the top row, at AB = 00. So this is not OR.
A gate that is 0 only when every input is 1 is AND with its output inverted. That is NAND, not AND.
On the formula book symbol it is the AND shape with a bubble on the output. The 2022 marking guide described NAND in exactly these two halves: output 0 when all inputs are 1, otherwise 1.
$$\begin{aligned}X&= 1,\ 1,\ 1,\ 0\Rightarrow\quad X\\&=0\text{ only when }A=B=1\end{aligned}$$
Three 1s narrows it to OR or NAND. The single 0 at AB = 11 makes it NAND, which is AND with an inverted output.
The most common wrong answer was (C), NOR, from mixing up the two gates with a bubble. NAND is 0 in exactly one row and NOR is 1 in exactly one row. Count the 1s before you name either.
Only mark this done when you could do it without help. Reading the solution does not count.
Question wording and any figures are from the 2025 QCAA Engineering external assessment, © State of Queensland (QCAA) 2025, 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