Boolean Logic and Logic Gates: Question 8
Syllabus 10.1, 10.2, 10.3
PixelPlay Labs tests game controllers on a production line. Each controller has two analogue joystick modules that are calibrated separately: the left-stick calibration test produces input L (L = 1 if the left stick passes, 0 if it fails), and the right-stick calibration test produces input R (R = 1 if the right stick passes, 0 if it fails). A mismatch-warning LED, output M, must light (M = 1) only when the two calibration results disagree with each other, meaning one stick passes while the other fails, and must stay off (M = 0) whenever the two results agree, whether both pass or both fail.
Which single logic gate, combining inputs L and R, produces this behaviour for M?
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Worked solution
Step 1: Restate the requirement as a truth table
Translating the description into the four combinations of L and R:
| L | R | Agree or disagree? | M |
|---|---|---|---|
| 0 | 0 | agree (both fail) | 0 |
| 0 | 1 | disagree | 1 |
| 1 | 0 | disagree | 1 |
| 1 | 1 | agree (both pass) | 0 |
Step 2: Recall which gate matches this pattern
A gate whose output is 1 only when its two inputs differ, and 0 whenever they are the same, is by definition an XOR gate. Checking XOR’s rule row by row against the table above confirms an exact match.
Step 3: Rule out the other options
- AND gives (0,0)→0, (0,1)→0, (1,0)→0, (1,1)→1. The opposite pattern from what is needed on the two disagreement rows, where M should be 1, not 0.
- OR gives (0,0)→0, (0,1)→1, (1,0)→1, (1,1)→1. Correct on three rows, but wrong on (1,1), where both sticks pass (agreement) yet OR would still light the LED.
- NOR gives (0,0)→1, (0,1)→0, (1,0)→0, (1,1)→0. Wrong on the very first row, where both sticks fail (agreement, so M should be 0) but NOR gives 1.
Final answer
The gate is XOR, option D.