Question 3
A logic circuit is shown.
Which truth table corresponds to the logic circuit?
That is it. Step through the hints below to see why. In 2023, 59.1% of Queensland students chose (A).
Not quite. 1, 1, 0 is the circuit with the NOT gate left out, so R goes straight into the XOR. Flipping one input of an XOR flips its output, which is why (B) is the correct column with every value flipped. In 2023, 13.6% of Queensland students chose (B).
Not quite. 0, 1, 0 is what you get if the last gate is an AND. In the middle row both inputs to the last gate are 1, and an XOR gives 0 when its inputs match. The second curved line at the back marks the XOR. In 2023, 16.4% of Queensland students chose (C).
Not quite. 1, 0, 1 is what you get if the first gate is an OR. In the top row P = 1 and Q = 0, which an AND turns into 0. The flat back and round front mark the AND. In 2023, 10.5% of Queensland students chose (D).
Fill the P AND Q column, then NOT R, then S. Click a cell to cycle it through ?, 0 and 1. Click the P, Q and R cells to send that row to the circuit.
Name the three gates against the formula book first. Flat back and round front is AND. The triangle with a bubble is NOT. The curved back with a second line behind it is XOR.
The options only list three of the eight rows, and every option uses the same three. You only need to work those.
Fill the two gates on the left before the XOR. Do a whole column at a time.
$$P\text{ AND }Q=0,\ 1,\ 1$$
$$\text{NOT }R=0,\ 1,\ 0$$
Only the top row has a 0 in P or Q, so only the top row makes the AND output 0.
XOR gives 1 only when its two inputs are different. Read across the two columns you just made.
$$S=0,\ 0,\ 1$$
The inputs match in the top two rows and differ in the bottom row. That is (A). Each wrong option is this circuit with one gate changed, and the toggles on the left show which.
Fill the AND column and the NOT column first, then apply the XOR rule to those two columns.
The most common wrong answer was (C), 16.4%, from treating the XOR as an AND. The middle row is the test: both inputs to the last gate are 1, and XOR gives 0 when its inputs match. Only 59.1% of students chose the key.
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 2023 QCAA Engineering external assessment, © State of Queensland (QCAA) 2023, 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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