A **XNOR gate** is a gate that gives a true (1 or HIGH) output when all of its inputs are true or when all of its inputs are false (0 or LOW). An XNOR gate is also called **exclusive NOR gate** or **EXNOR gate**. In a two input XNOR gate, the output is high (logic 1 or true) when two inputs are same.

In Boolean expression, the term XNOR is represented by symbol (⊙) and the Boolean expression is represented as Y = A ⊙ B. It is read as “A xnor B”.

It can be denoted as also.

## XNOR gate symbol

Table of Contents

The logic symbol of XNOR gate is shown in figure 1.

## XNOR gate truth table

The **XNOR gate truth table** for figure 1 is shown below.

A |
B |
Y = A ⊙ B |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

From XNOR gate truth table, it can be concluded that the output will be true (logical 1 or high) when all of its inputs are true or when all of its inputs are false (0 or LOW).

Y = A ⊙ B =

Y =

Above algebraic expression represent the XNOR gate with inputs A and B.

### XNOR gate using OR, AND, and NOT gate

To produce XNOR gate using OR, AND, and NOT gate, the gates are joined together as shown in figure 2.

### XNOR gate using NOR gate

To produce XNOR gate using 4 NOR gates, the NOR gates are connected as shown in fig. 3.

To produce XNOR gate using 5 NOR gates, the NOR gates are connected as shown in fig. 4.

### XNOR gate using NAND gate

To produce XNOR gate using 5 NAND gates, the NAND gates are connected as shown in fig. 5 and fig. 6.