XNOR gate

<table><tbody><tr><th colspan="3">XNOR gate <a href="/facts/Truth_table/4KsmArDW">truth table</a></th></tr><tr><td colspan="2">Input</td><td>Output</td></tr><tr><td>A</td><td>B</td><td>A XNOR B</td></tr><tr><td>0</td><td>0</td><td>1</td></tr><tr><td>0</td><td>1</td><td>0</td></tr><tr><td>1</td><td>0</td><td>0</td></tr><tr><td>1</td><td>1</td><td>1</td></tr></tbody></table>

<p>The XNOR gate (sometimes ENOR, EXNOR, XAND, or — the strictly correct — NXOR, and pronounced as Exclusive NOR) is a digital <a href="/facts/Logic_gate/RHLulvKI">logic gate</a> whose function is the <a href="/facts/Logical_complement/q5AQBvBj">logical complement</a> of the Exclusive OR gate (<a href="/facts/XOR_gate/WSfdqTcA">XOR gate</a>; hence, the common name can be confusing as it is not an "Exclusive variant" of a <a href="/facts/NOR_gate/3l3MqaMI">NOR gate</a>). It is equivalent to the logical connective (
  
    
      
        ↔
      
    
    {\displaystyle \leftrightarrow }
  
) from <a href="/facts/Mathematical_logic/SaI7Y3wN">mathematical logic</a>, also known as the material biconditional. The two-input version implements <a href="/facts/Logical_equality/MqQLxbzU">logical equality</a>, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.
</p><p>The <a href="/facts/Boolean_algebra/VkCToAmg">algebraic notation</a> used to represent the XNOR operation is 
  
    
      
        S
        =
        A
        ⊙
        B
      
    
    {\displaystyle S=A\odot B}
  
. The algebraic expressions 
  
    
      
        (
        A
        +
        
          
            B
            ¯
          
        
        )
        ⋅
        (
        
          
            A
            ¯
          
        
        +
        B
        )
      
    
    {\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)}
  
 and 
  
    
      
        A
        ⋅
        B
        +
        
          
            A
            ¯
          
        
        ⋅
        
          
            B
            ¯
          
        
      
    
    {\displaystyle A\cdot B+{\overline {A}}\cdot {\overline {B}}}
  
 both represent the XNOR gate with inputs <i>A</i> and <i>B</i>.
</p>

XNOR gate open-in-new

XNOR gate