Exclusive NOR Gate
 Muhammad Shahid
 m_shahid@live.co.uk

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ExclusiveNOR Gate
The ExclusiveNOR logic is the complement (reverse) form of the ExclusiveOR logic. It is the serial combination of ExclusiveOR and the NOT gates. The ExclusiveNOR gate gives an output given by the expression “Both A & B, not A or B”. It means that the output of the ExclusiveNOR gate is “HIGH” when both inputs “A” and “B” are at the same logic level i.e. both “HIGH” or “LOW”. In the case of, either “A” or “B” that is “01” or “10” the output of the ExclusiveNOR gate will be “LOW”. The ExclusiveNOR gate outputs logic “HIGH” only when both of its inputs are equal and, therefore, it is sometimes referred to as “Equivalence Gate”.
The ExclusiveNOR is also referred to by writing only ExNOR or XNOR. The ExNOR is a very useful logic and is mostly used in circuits involving arithmetic operations such as Parity Checkers, Adders and Subtractors, etc.
Similar to the ExOR gate, the construction of ExNOR logic is complex compared to other logic gates and is constructed using basic logic gates. Similarly, the ExNOR gate is also commercially available as a separate logic gate. Because of its construction from multiple basic logic gates, it is also called a “hybrid” logic gate. The truth table of the logic NOR gate is somewhat similar to the ExNOR gate in that its output remains at logic level “HIGH” and goes to “LOW” when any of its inputs goes “HIGH”. However, the ExNOR gate’s output goes “HIGH” again when both of its inputs go to logic level “HIGH”.
The Boolean algebraic equation of an ExNOR logic is given below:
The equivalent circuit of an ExclusiveNOR gate is:
Logic ExNOR Gate Symbol & Truth Tables
The representation of an ExNOR logic by a symbol is shown in the following figure.
The symbol of the ExNOR logic is similar to the ExOR logic except for an “Inversion Bubble” which is added at the output to denote the “NOT” function.
The truth table of a twoinput ExNOR logic is shown below:
It is clear from the truth table that when inputs are at the same levels i.e. either “00” or “11” state then the ExNOR logic output is “HIGH” and in case the inputs are at the different levels then output is “LOW”. In other words, the expression is “A” AND “B”, Same!
The truth table of a threeinput ExNOR logic is as follow and can be expanded to include any number of inputs:
As discussed in the previous article, the ExOR logic is an odd function and gives a logic “HIGH” output when there is an odd number of inputs having logic “HIGH” or “1”. Whereas, the ExNOR logic is an even function which is eminent from the truth tables given above. The ExNOR logic gives a “HIGH” output when inputs with the logic “HIGH” are in even numbers except for the case when all of the inputs are “OFF” or at logic “LOW”. This characteristic makes the ExNOR an even gate.
The symbol and expression of a 3input ExNOR logic are given below:
ExNOR (XNOR) Logic Circuit
Using the logic expression of a twoinput ExNOR logic, an equivalent circuit can be constructed which is shown in the following figure.
The above equivalent ExNOR logic comprises AND, OR, and NOT logic. However, it is not a good practice to include multiple logics for the construction of logic gates and a better ExNOR circuit can be constructed using only NAND logic gates.
The construction of the ExNOR gate using NAND gates only is shown below:
The ExclusiveNOR logic gates are helpful in performing arithmetic operations and computations. They are also used in data error detection circuits as Parity Bit Checkers.
Commercially Available ENOR (XNOR) Gates
The XNOR logic gates are available in both TTL and CMOS logic families. The most commonly used XNOR logic packages are:
CMOS based XNOR Gate IC Package
 CD4077 Quad 2input
TTL based XNOR Gate IC Package
 74LS266 Quad 2input
Example of XNOR Logic
In the following figure, an XNOR gate is used to drive a 12V relay to switch on the lamp using NI Multisim. The XNOR gate turns on the relay when all of the inputs are connected to VCC/ Ground. The relay thus turns on the lamp through an external circuit of 12V. When inputs are at different levels, XNOR logic goes “OFF” turning the relay and lamp to “OFF” state.
Conclusion
 The output of the ExNOR logic is “HIGH” when both of the inputs have the “SAME” logic states.
 The ExNOR gate outputs logic “LOW” when inputs have different logic states.
 The ExNOR gate checks for the equality of the inputs and as such also known as Equivalence Gate.
 It is an Even Parity Checker as it outputs a “HIGH” signal when there is an even number of signals at the input having logic “HIGH”.
 It is mostly used in arithmetic, computational and errordetection circuits.
 The ExNOR logic gates are commercially available in both TTL and CMOS packages.
 An external circuit can be controlled by ExNOR logic with the use of a magnetic relay.