XNOR gate: Difference between revisions
Created page with "{| class="wikitable floatright" style="text-align:center" |- ! colspan="3" | XNOR gate truth table |- bgcolor="#ddeeff" |colspan=2|'''Input''' || '''Output''' |- bgcolor="#ddeeff" | A || B || A XNOR B |- |{{no2|0}} || {{no2|0}} || {{yes2|1}} |- |{{no2|0}} || {{yes2|1}} || {{no2|0}} |- |{{yes2|1}} || {{no2|0}} || {{no2|0}} |- |{{yes2|1}} || {{yes2|1}} || {{yes2|1}} |} thumb|165x165px|ANSI XNOR gate symbol In digital electronics, a '''XNOR ga..." |
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! colspan="3" | XNOR gate [[truth table]] | ! colspan="3" | XNOR gate [[truth table]] | ||
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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. | 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. | ||
{{Clear}} | |||
= Logic = | = Logic = | ||
A two-input XNOR gate can be expressed in [[Boolean logic]] as <math>(A + \overline B) \cdot (\overline A + B)</math>, <math>A \cdot B + \overline A \cdot \overline B</math> or <math>A \odot B</math>. | A two-input XNOR gate can be expressed in [[Boolean logic]] as <math>(A + \overline B) \cdot (\overline A + B)</math>, <math>A \cdot B + \overline A \cdot \overline B</math> or <math>A \odot B</math>. | ||
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* [[NOR gate]] | * [[NOR gate]] | ||
* [[XOR gate]] | * [[XOR gate]] | ||
* [[Inverter|Inverter (NOT gate)]] | * [[Inverter (logic gate)|Inverter (NOT gate)]] | ||
* [[IMPLY gate]] | * [[IMPLY gate]] | ||
* [[NIMPLY gate]] | * [[NIMPLY gate]] | ||
Latest revision as of 16:09, 27 October 2024
| XNOR gate truth table | ||
|---|---|---|
| Input | Output | |
| A | B | A XNOR B |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
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 , or .
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:
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Additionally, using a different topology, the same can be achieved as follows:
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