GATE CS 2011 Q.13 (CS Q.13): Combinational Circuits | GATE CS Mastery

Which one of the following circuits is NOT equivalent to a 2-input XNOR (exclusive NOR) gate?

A

Option A logic circuit with 2-input XOR gate followed by NOT gate

B

Option B logic circuit with NOT gates on both inputs, XOR gate, and NOT gate on output

C

Option C logic circuit with NOT gate on top input feeding a 2-input XOR gate

D

Circuit with inputs x (top) and y (middle): x feeds an AND gate and the bottom input of an OR gate; y is inverted and the inverted y feeds the other input of both the AND gate and the OR gate; the AND output is inverted and ANDed with the OR output, and that result is inverted to give the output.

Official answer and solution

Official answer: D
From: Official GATE 2011 answer key

Solution

Derive the Boolean transfer function for each circuit and compare it with the 2-input XNOR function.

The 2-input XNOR operation on inputs $A$ and $B$ produces output $A \odot B = \overline{A \oplus B} = A B + \overline{A}\,\overline{B}$ .

Option A: An XOR gate followed by an inverter produces $\overline{A \oplus B} = A \odot B$ (XNOR).

Option B: Inverting both inputs prior to an XOR gate followed by an output inverter gives:

\overline{\overline{A} \oplus \overline{B}} = \overline{A \oplus B} = A \odot B

Option C: Inverting a single input to an XOR gate gives $\overline{A} \oplus B = \overline{A}\,\overline{B} + \overline{\overline{A}}\,B = \overline{A}\,\overline{B} + A B = A \odot B$ (XNOR).

Option D: The top NAND gate produces $\overline{A \cdot \overline{B}} = \overline{A} + B$ . The bottom OR gate produces $A + \overline{B}$ . Feeding these into the final NAND gate gives:

\overline{(\overline{A} + B)(A + \overline{B})} = \overline{A B + \overline{A}\,\overline{B}} = A \oplus B

Circuit D produces the XOR function, not XNOR. Therefore, circuit D is NOT equivalent to an XNOR gate.

Final answer

D

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2011 Computer Science and Information Technology (CS)
Question: 13 of 65, printed as CS Q.13
Section: Computer Science and Information Technology

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