An EXCLUSIVE–NOR (XNOR) gate is logically equivalent to an EXCLUSIVE–OR (XOR) gate followed by an inverter (logical NOT). Select the correct equivalence.

Introduction / Context:
Composite logic design often relies on equivalences between gates. Understanding that XNOR is the complement of XOR simplifies synthesis and analysis of digital circuits, especially when implementing parity checks, equality comparators, and error-detecting logic.

Given Data / Assumptions:

• XOR outputs 1 when inputs differ and 0 when they are equal.
• XNOR outputs 1 when inputs are equal and 0 when they differ.
• An inverter flips a logic value: 0 becomes 1, 1 becomes 0.

Concept / Approach:
If Y = XOR(A, B), then XNOR(A, B) = NOT(Y). Therefore, cascading an XOR gate with a NOT gate yields XNOR behavior. This equivalence is used in hardware to build equality comparators by XNORing bits and then ANDing the results to confirm all bits are equal.

Step-by-Step Solution:
Define XOR truth: 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0.Apply inversion: NOT(0)=1, NOT(1)=0 to each case.Observe the result matches XNOR truth: 1 when inputs equal, 0 otherwise.Conclude that “XOR followed by inverter” implements XNOR.

Verification / Alternative check:
Boolean algebra: XNOR = A·B + A'·B' = (A ⊕ B)'; reading “double prime” as NOT of XOR, confirming the cascade equivalence.

Why Other Options Are Wrong:
OR: cannot produce equality detection by simple inversion.AND/NAND: do not match the “equal inputs are 1” truth table when inverted.None of the above: incorrect because XOR is the correct precursor to an inverter for XNOR.

Common Pitfalls:
Confusing XOR with OR; forgetting that XNOR is “equivalence” (outputs 1 when inputs are the same). In multi-bit comparisons, remember to combine XNOR results with AND to detect equality across all bits.

Final Answer:
XOR