Gate identity check — is XNOR simply OR followed by inversion? Consider the statement: “An exclusive-NOR (XNOR) gate is an OR gate followed by a NOT gate.” Decide if this description is valid for standard two-input logic.

Introduction / Context:
XNOR (exclusive-NOR) is the logical equality function: its output is 1 when the inputs are the same and 0 when they differ. Misidentifying XNOR as a simple OR followed by NOT is a common mistake that leads to incorrect truth tables and design errors in parity checking and comparator circuits.

Given Data / Assumptions:

• Two-input logic in positive logic convention.
• “OR followed by NOT” means output = NOT(OR(A,B)) = NOR(A,B).
• We compare NOR with XNOR behavior.

Concept / Approach:
Define functions explicitly: XNOR(A,B) = (A AND B) OR (A′ AND B′). NOR(A,B) = NOT(A OR B) = A′ AND B′. NOR is true only when both inputs are 0. XNOR is true when A=B, i.e., for pairs (0,0) and (1,1). Because XNOR also outputs 1 for (1,1), it cannot be realized by a single OR followed by NOT.

Step-by-Step Solution:

Verification / Alternative check:
Implement XNOR as NOT(XOR(A,B)) or as (A AND B) OR (A′ AND B′). Both implementations yield equality logic, not NOR.

Why Other Options Are Wrong:

• Correct / mutually exclusive inputs / wired-OR / De Morgan: None transform OR+NOT into XNOR for all input pairs.

Common Pitfalls:
Equating “NOR” and “XNOR” due to the “N” prefix; assuming any gate followed by NOT simply adds an “X.” Only XOR + NOT becomes XNOR.

Final Answer:
Incorrect