XNOR gate

Gate types
	NOT
AND	NAND
OR	NOR
XOR	XNOR

An XNOR gate ( X clusive N OT OR ) is a logic gate with a logical “1” at the output if “1” is applied to an even number of inputs and “0” to the remaining ones. In the case of two inputs, the output is “1” if “1” is present at both inputs or “0” is present at both inputs (in the second case “1” is present at zero inputs and 0 counts as an even number). The XNOR link is also referred to as equivalence , bi-implication or biconditional. Together with the XOR it forms a Boolean ring , like AND with OR and NAND with NOR.

Overview

function	Circuit symbol			Truth table	Relay logic
	IEC 60617-12	US ANSI 91-1984	DIN 40700 (before 1976)
${\displaystyle Y={\overline {A\,{\underline {\lor }}\,B}}}$ ${\displaystyle Y=A\,{\overline {\underline {\lor }}}\,B}$ ${\displaystyle Y={\overline {A\oplus B}}}$ ${\displaystyle Y=AB+{\overline {AB}}}$			or	A. B. Y = A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1

Logic synthesis

XNOR gates and their implementation:

shortcut	Means	implementation
x XNOR y
	NAND	(x NAND y) NAND ((x NAND x) NAND (y NAND y))
	NOR	(x NOR (x NOR y)) NOR (y NOR (x NOR y))

The XNOR gate can also be constructed using an exclusive-or gate with a downstream non-gate (inverter).

hardware

The component 4077 from the 4000 logic family and the 74x7266 from the 74 series contain four XNOR gates with two inputs each.

literature

• Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology . 12th edition. Springer, 2002, ISBN 3-540-42849-6 .
• Klaus Beuth: Digital technology . 10th edition. Vogel, 1998, ISBN 3-8023-1755-6 .
• Manfred Seifart, Helmut Beikirch: Digital circuits . 5th edition. Technology, 1998, ISBN 3-341-01198-6 .