# Exclusive NOR Gate     Logic gates are the building blocks of any digital system. All the digital devices such as mobiles, computers store the data in the form of binary numbers 1 or 0. 1 is considered as the high input and 0 is the low input value. The logic gates are used to perform certain mathematical operations for binary digits.

Depending upon the type of operation required the logic gates are categorized as OR-gate for addition, AND-gate for multiplication, NOT gate for inversion.  Logic gates are further classified as basic gates(OR, AND, NOT), Universal gates(NAND, NOR), and the special gates Exclusive OR gate and Exclusive NOR gate.

## What is XNOR Gate?

• The Exclusive NOR gate is also known as the XNOR gate or Ex-NOR gate. It performs the operation same as XOR gate followed by NOT gate, thus it is abbreviated as XNOR gate.

• The exclusive NOR gate is the combination of the exclusive OR gate and the NOT gate. Thus, the operation of the XNOR gate is reciprocal of the XOR gate.

• The exclusive NOR gate gives the output as 1 when both inputs are identical. I.e., either both inputs are 1’s or 0’s.

• The output of the XNOR is high(.i.e., 1) for the input combinations like 11 or 00.

### XNOR Gate Expression:

XNOR Symbol:

• While studying logic gates the important part of understanding the function of any gate is to first recognize the logic expression (Or Boolean expression) and the logic symbol.

• The XNOR logic symbol is an Exclusive OR gate followed by an inversion bubble at the output indicating presence of NOT gate. Thus XNOR gate is a reciprocal or complementary form of the XOR gate.

• The logic symbol of the Exclusive NOR gate is:

XNOR Expression or Boolean Expression For XNOR Gate:

• The XNOR gate is a complementary form of the XOR gate, thus the boolean expression of the XNOR gate is given by:

$\Rightarrow Y= \overline{A\oplus B}$

• From the XNOR equation, it is understood that output will be 1 if and only if both A and B are either having high logic(1’s) or low logic(0’s).

### Exclusive NOR Gate Truth Table:

• For the 2-input XNOR gate, the logical expression is:

$\Rightarrow Y= \overline{A\oplus B}=AB+ \overline{AB}$

• Therefore, the Ex NOR gate truth table is:

 A B $Y= AB+ \overline{AB}$ 0 0 1 0 1 0 1 0 0 1 1 1

• Similarly, the XNOR equation of XNOR gate boolean equation for 3-input is given by:

$\Rightarrow Y=\overline{ABC}+\overline{A}BC+A\overline{B}C+AB\overline{C}$

• If any two inputs among 3 are high or if all 3 inputs are low then the output will be high.

• The truth table for the 3-input XNOR gate is given by:

 A B C $Y=\overline{ABC}+\overline{A}BC+A\overline{B}C+AB\overline{C}$ 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 0

### Uses of XNOR Gate:

• The XNOR gate is used as a parity checker.

• The exclusive nor gate is used in calculators, computers, etc..

• They are used for encryption and arithmetic circuits.

### Did You Know:

• From the boolean expression, we can understand that the XNOR gate can be constructed as a combination of OR gate, AND gate, and NOT gate.

• Thus, the equivalent circuit for the XNOR gate is:

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