Question E7A09:
What logical operation is performed by a two-input exclusive NOR gate?  

Choices:  
A: It produces a 0 at its output only if all inputs are 0  
B: It produces a 1 at its output only if all inputs are 1  
C: It produces a 0 at its output if one and only one of its inputs is 1  
D: It produces a 1 at its output if one and only one input is 1    

Correct Answer is  C: It produces a 0 at its output if one and only one of its inputs is 1  

To understand a 2‑input exclusive NOR (XNOR):

- XNOR is the complement of XOR.
- It outputs 1 when the two inputs are the same, and 0 when they are different.

Useful formulas:
$$\text{XNOR}(A,B) = \overline{A \oplus B} = A B + \overline{A}\,\overline{B}$$
- Truth table summary:
  - 0,0 → 1
  - 0,1 → 0
  - 1,0 → 0
  - 1,1 → 1

Why the correct answer (C) is correct:
- “It produces a 0 at its output if one and only one of its inputs is 1” describes exactly the “inputs differ” case, which is when XNOR outputs 0 (since XOR would output 1 there and XNOR is its inverse).

Why the other choices are incorrect:
- A: “0 only if all inputs are 0” describes an OR gate, not XNOR.
- B: “1 only if all inputs are 1” describes an AND gate, not XNOR.
- D: “1 if one and only one input is 1” describes an XOR gate, not XNOR.

Rule of thumb:
- XOR = “odd parity” detector (1 when an odd number of 1s).
- XNOR = “equality” detector (1 when inputs are equal).