# Exclusive NOR gate

Exclusive-NOR gate is formed by combining the Exclusive-OR gate (XOR gate) and the NOT gate. On analysing the truth table of Exclusive-NOR gate, we understand that the output is similar to the standard NOR gate except that the output of the Ex-NOR gate is high when both the inputs are high. The output of EX-NOR gate is 1 when both the inputs are 1 (high) and if both the inputs are 0 (low). If either one of the input is 1 (high) the output will be 0 (low). In other words, both the inputs should be in the same logic level for the output to be 1.

## Symbol and Boolean expression for NOR gate

The logic symbol of an Exclusive-NOR gate is an XOR gate (Exclusive-OR gate) with the “inversion bubble” or the circle in front. Therefore, the Exclusive-NOR gate is the complementary form of the Exclusive-OR gate. The Boolean expression for the Exclusive-NOR gate is given by

## Truth table for 2-input Ex-NOR gate

 A B Y 0 0 1 0 1 0 1 0 0 1 1 1

The same logic can be used to find the output of 3 input Ex-NOR gate. The Boolean expression for the same is given by
. The truth table for 3 input is given below

## Truth table for 3-input Ex-NOR gate

 A B C Y 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

## Exclusive-NOR gate equivalent circuit

The Ex-NOR gate can be constructed by combining the OR gate, AND gate and NOT gate.

One easier way of constructing the Ex-NOR gate is from using a single gate like the AND gate.

## Application of Exclusive-NOR gate

Some of the application of Ex-NOR gate is in

• Encryption and arithmetic circuits
• Error-detecting circuits to find odd parity and even parity in digital data transmission.