In the design of digital circuits, what is the result of cascading two XOR…
2025
In the design of digital circuits, what is the result of cascading two XOR gates such that the output of the first XOR gate is fed as one input to the second XOR gate, while the other input to each gate is fixed?
Let the inputs be:
First XOR gate: A ⊕ B
Second XOR gate: (A ⊕ B) ⊕ B
What is the final output?
- A.
A ⊕ B
- B.
A
- C.
B
- D.
0
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Show answer & explanation
Correct answer: B
The problem asks for the final output of a cascaded XOR gate circuit. The first gate computes A ⊕ B. This result is then fed into the second XOR gate along with input B. Therefore, the expression for the final output is (A ⊕ B) ⊕ B.
Using the associative property of XOR, we can regroup this as A ⊕ (B ⊕ B). In Boolean algebra, any variable XORed with itself results in 0 (i.e., B ⊕ B = 0). Substituting this back into the expression gives A ⊕ 0.
Since XORing any value with 0 leaves it unchanged (identity property), the final result simplifies to A. This corresponds to Option B.
Option A (A ⊕ B) is incorrect because it represents the output of only the first gate, ignoring the second stage. Option C (B) is incorrect as it suggests the output depends solely on B, which contradicts the derivation. Option D (0) is incorrect because it would require both A and B to cancel out completely, which does not happen here. Thus, the correct answer is A.