XNOR truth table completion: For a two-input XNOR gate with inputs (A,B) ordered as 00, 01, 10, 11, the corresponding outputs w, x, y, z are ____, ____, ____, and ____, respectively.
-
A1, 0, 0, 1
-
B0, 1, 0, 1
-
C1, 1, 1, 0
-
D1, 0, 0, 0
-
E0, 0, 1, 1
Answer
Correct Answer: 1, 0, 0, 1
Explanation
Introduction / Context:The exclusive-NOR (XNOR) function outputs HIGH when its inputs are equal and LOW when they differ. Completing a truth table tests conceptual understanding of equality detection in digital logic.
Given Data / Assumptions:
- Two-input XNOR gate.
- Row order: (A,B) = 00, 01, 10, 11.
- Positive logic convention.
Concept / Approach:XNOR is the complement of XOR. XOR is 1 when inputs differ; therefore XNOR is 1 when inputs are the same: 00 or 11. It is 0 for 01 and 10. This maps directly to the requested sequence w, x, y, z.
Step-by-Step Solution:
For 00: inputs equal → XNOR = 1 → w = 1.For 01: inputs differ → XNOR = 0 → x = 0.For 10: inputs differ → XNOR = 0 → y = 0.For 11: inputs equal → XNOR = 1 → z = 1.Verification / Alternative check:Boolean identity: XNOR = A′B′ + AB. Evaluate each row to confirm 1,0,0,1 in the specified order.
Why Other Options Are Wrong:
- 0,1,0,1 or 1,1,1,0 etc.: These patterns do not match the equality-only HIGH behavior; they either assert on differing inputs or on too many cases.
Common Pitfalls:Swapping XOR and XNOR; mixing row order; assuming a different input ordering, which would permute the output sequence.
Final Answer:1, 0, 0, 1