ExpertMedium1 markMultiple Choice
AQA GCSE · Question 03.3 · Computer systems
Another circuit in the game will output True if any two sensors are activated or if all three sensors are activated. This has been represented as the Boolean expression:
(W . D) + (D . L) . (W . L)
The expression contains an error.
Shade one lozenge that shows the expression with the error corrected.
Another circuit in the game will output True if any two sensors are activated or if all three sensors are activated. This has been represented as the Boolean expression:
(W . D) + (D . L) . (W . L)
The expression contains an error.
Shade one lozenge that shows the expression with the error corrected.
Answer options:
A.
(W . D) . (D . L) . (W . L)
B.
(W . D) . (D . L) + (W . L)
C.
(W . D) + (D . L) + (W . L)
D.
(W . D) + (D + L) . (W . L)
How to approach this question
1. Understand the logic: "any two sensors are activated or if all three sensors are activated". This means we need to check all combinations of at least two sensors being on.
2. The combinations of two sensors being on are: (W and D), (D and L), (W and L).
3. The condition "or" means we should use the OR operator (+) to connect these combinations.
4. The expression should therefore be (W AND D) OR (D AND L) OR (W AND L).
5. In Boolean algebra notation, this is (W . D) + (D . L) + (W . L).
6. Compare this to the options provided. The original expression has a `.` instead of a `+` between the second and third terms. Option C corrects this error.
Full Answer
C.(W . D) + (D . L) + (W . L)✓ Correct
The correct option is C. The expression should be (W . D) + (D . L) + (W . L).
The requirement is for the circuit to be True if *at least* two sensors are on. Let's break this down:
- Case 1: W and D are on. (W . D)
- Case 2: D and L are on. (D . L)
- Case 3: W and L are on. (W . L)
The circuit should be True if Case 1 OR Case 2 OR Case 3 is true. The OR operator in Boolean algebra is `+`.
Therefore, the correct expression is `(W . D) + (D . L) + (W . L)`.
This expression also correctly handles the case where all three (W, D, and L) are on. If all are on, then (W.D) is true, (D.L) is true, and (W.L) is true, making the whole expression true.
The original expression `(W . D) + (D . L) . (W . L)` has an error because of the final `.` (AND). This would mean "(W and D are on) OR ((D and L are on) AND (W and L are on))", which is not the required logic.
Common mistakes
✗ Misinterpreting the logical requirement "any two".
✗ Confusing the symbols for AND (`.`) and OR (`+`).
✗ Not carefully checking the difference between the original expression and the options.
Practice the full AQA GCSE Computer Science Paper 2
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