XNOR gate

XNOR gate truth table
Input		Output
A	B	A XNOR B
0	0	1
0	1	0
1	0	0
1	1	1

ANSI XNOR gate symbol

In digital electronics, a XNOR gate or Exclusive NOR gate is a logic gate which produces an output of true only when either all the inputs are false or true. A LOW (0) output results when any of the inputs are HIGH (1) both not all of them; if all the inputs are LOW, the result is also a HIGH output.

The XNOR gate (along with the XOR gate) is one of the only two logic gates that does not have an integrated circuit containing more than two inputs.

Logic

A two-input XNOR gate can be expressed in Boolean logic as $(A+{\overline {B}})\cdot ({\overline {A}}+B)$, $A\cdot B+{\overline {A}}\cdot {\overline {B}}$ or $A\odot B$.

Alternatives

If a specific type of gate is not available, a circuit that implements the same function can be constructed from other available gates. Through the use of the "universal" NAND gates and NOR gates, almost any other Boolean logic gate can be constructed.

A XNOR gate can be constructed using five NAND gates or four NOR gates in the following topologies:

An AND gate constructed from two NAND gates

Additionally, using a different topology, the same can be achieved as follows:

See also

• AND gate
• OR gate
• NAND gate
• NOR gate
• XOR gate
• Inverter (NOT gate)
• IMPLY gate
• NIMPLY gate