# XNOR Gate: Symbol and Truth Table

XNOR gate is a hybrid gate. It is a combination of the XOR gate and NOT gate. The XNOR gate outputs 1 when both of its inputs are either 0 or 1. The symbol of XNOR and XOR gates are the same, only the complement sign is added to XNOR.

In digital electronics, there are various types of logic gates available, such as AND Gate, OR Gate, NOT Gate, NAND Gate, NOR, Gate, Ex-OR Gate, and Ex-NOR Gate. In this article, we will cover the definition, truth table, Boolean function, and logic symbol of the Ex-NOR gate.

## What is an XNOR Gate?

The XNOR gate, also known as the Exclusive-NOR gate or Ex-NOR gate, is a type of derived logic gate which is constructed by combining two logic gates namely, the XOR gate and the NOT gate. It performs NOTed XOR operation.

The Ex-NOR gate is a two-input and one-output logic gate. It gives a HIGH (logic 1) output if both of its inputs are the same, i.e. 0 and 0 or 1 and 1, and it gives a LOW (logic 0) output if its inputs are different, i.e. 0 and 1 or 1 and 0.

The logic symbol of an XNOR gate is shown in the following figure.

It is important to note about the Ex-NOR gate that it is complementary to the Ex-OR gate. Therefore, it can be implemented by connecting an Ex-OR gate to a NOT gate as shown in the following figure.

In other words,

XNOR Gate = XOR Gate + NOT Gate

## XNOR Truth Table

The truth table of an XNOR gate provides the behavior of the Ex-NOR gate for different combinations of inputs. The truth table of an Ex-NOR gate is given below:

### 2-input Ex-NOR Gate

From the truth table of XNOR gate, it is clear that it has a HIGH (logic 1) output if both of its inputs are the same, and it has LOW (logic 0) output if both inputs are different.

## Boolean Expression of XNOR Gate

Boolean expression or function is a logical formula that provides a relationship between the inputs and output of an Ex-NOR gate. The Boolean function of an XNOR gate is given below:

This expression is equivalent to the following logical function,

## Operation of XNOR Gate

We can understand the operation of an Ex-NOR gate through its Boolean function for different input combinations as follows:

• When A = 0 and B = 0, the output Y = 0’.0’ + 0.0 = 1.1 + 0.0 = 1.
• When A = 0 and B = 1, the output Y = 0’.1’ + 0.1 = 1.0 + 0.1 = 0.
• When A = 1 and B = 0, the output Y = 1’.0’ + 1.0 = 0.1 + 1.0 = 0.
• When A = 1 and B = 1, the output Y = 1’.1’ + 1.1 = 0.0 + 1.1 = 1.

## Ex-NOR Gate using AND, OR, and NOT Gates

We can implement the Ex-NOR function by using only AND, OR, and NOT gates. The circuit diagram of XNOR gate using AND, OR, and NOT gates is shown in the following figure.

## Ex-NOR Gate ICs

The following are the commonly available XNOR gate ICs in TTL and CMOS logics:

• 74LS266 is a quad 2-input Ex-NOR gate IC in transistor-transistor logic.
• CD4077 is a quad 2-inout Ex-NOR gate IC in CMOS logic.

## Applications of Ex-NOR Gate

XNOR gate is widely used in the following applications:

• Ex-NOR gate is widely used in digital arithmetic circuits like adders and subtractors.
• Ex-NOR gate is also used in data-checking systems like parity checkers.
• Ex-NOR gate can also be used for comparing the magnitude of two binary numbers.
• It is also used in digital comparators.

Hence, this is all about the XNOR gate and its truth table. In conclusion, an Ex-NOR gate or Exclusive NOR gate is a combination of an XOR gate and a NOT gate. It gives a HIGH output only when both of its inputs are the same. It is widely used in various digital arithmetic circuits.