Basically the “ExclusiveNOR” gate is a combination of the ExclusiveOR gate and the NOT gate but has a truth table similar to the standard NOR gate in that it has an output that is normally at logic level “1” and goes “LOW” to logic level “0” when ANY of its inputs are at logic level “1”.
However, an output “1” is only obtained if BOTH of its inputs are at the same logic level, either binary “1” or “0”. For example, “00” or “11”. This input combination would then give us the Boolean expression of: Q = (A ⊕ B) = A.B + A.B
Then the output of a digital logic ExclusiveNOR gate ONLY goes “HIGH” when its two input terminals, A and B are at the “SAME” logic level which can be either at a logic level “1” or at a logic level “0”. In other words, an even number of logic “1’s” on its inputs gives a logic “1” at the output, otherwise is at logic level “0”.
Then this type of gate gives and output “1” when its inputs are “logically equal” or “equivalent” to each other, which is why an ExclusiveNOR gate is sometimes called an Equivalence Gate.
The logic symbol for an ExclusiveNOR gate is simply an ExclusiveOR gate with a circle or “inversion bubble”, ( ο ) at its output to represent the NOT function. Then the Logic ExclusiveNOR Gate is the reverse or “Complementary” form of the ExclusiveOR gate, (A ⊕ B) we have seen previously.
ExNOR Gate Equivalent
The ExclusiveNOR Gate, also written as: “ExNOR” or “XNOR”, function is achieved by combining standard gates together to form more complex gate functions and an example of a 2input ExclusiveNOR gate is given below.
The Digital Logic “ExNOR” Gate
2input ExNOR Gate
Symbol  Truth Table  
2input ExNOR Gate

B  A  Q 
0  0  1  
0  1  0  
1  0  0  
1  1  1  
Boolean Expression Q = A ⊕ B  Read if A AND B the SAME gives Q 
Giving the Boolean expression of: Q = AB + AB
The logic function implemented by a 2input ExNOR gate is given as “when both A AND B are the SAME” will give an output at Q. In general, an ExclusiveNOR gate will give an output value of logic “1” ONLY when there are an EVEN number of 1’s on the inputs to the gate (the inverse of the ExOR gate) except when all its inputs are “LOW”.
Then an ExNOR function with more than two inputs is called an “even function” or modulo2sum (Mod2SUM), not an ExNOR. This description can be expanded to apply to any number of individual inputs as shown below for a 3input ExclusiveNOR gate.
3input ExNOR Gate
Symbol  Truth Table  
3input ExNOR Gate

C  B  A  Q 
0  0  0  1  
0  0  1  0  
0  1  0  0  
0  1  1  1  
1  0  0  0  
1  0  1  1  
1  1  0  1  
1  1  1  0  
Boolean Expression Q = A ⊕ B ⊕ C  Read as “any EVEN number of Inputs” gives Q 
Giving the Boolean expression of: Q = ABC + ABC + ABC + ABC
We said previously that the ExNOR function is a combination of different basic logic gates ExOR and a NOT gate, and by using the 2input truth table above, we can expand the ExNOR function to: Q = A ⊕ B = (A.B) + (A.B) which means we can realise this new expression using the following individual gates.
ExNOR Gate Equivalent Circuit
One of the main disadvantages of implementing the ExNOR function above is that it contains three different types logic gates the AND, NOT and finally an OR gate within its basic design. One easier way of producing the ExNOR function from a single gate type is to use NAND gates as shown below.
ExNOR Function Realisation using NAND gates
ExNOR gates are used mainly in electronic circuits that perform arithmetic operations and data checking such as Adders, Subtractors or Parity Checkers, etc. As the ExNOR gate gives an output of logic level “1” whenever its two inputs are equal it can be used to compare the magnitude of two binary digits or numbers and so ExNOR gates are used in Digital Comparator circuits.
Commonly available digital logic ExclusiveNOR gate IC’s include:
TTL Logic ExNOR Gates
 74LS266 Quad 2input
CMOS Logic ExNOR Gates
 CD4077 Quad 2input
74266 Quad 2input ExNOR Gate
In the next tutorial about Digital Logic Gates, we will look at the digital Tristate Buffer also called the noninverting buffer as used in both TTL and CMOS logic circuits as well as its Boolean Algebra definition and truth table.