XNOR Logic Gate
XNOR (Exclusive NOR) logic gate is a digital logic gate that gives the output 1 (HIGH) only when the two inputs are same. If the inputs are the differnet, the output is 0 (LOW). This is the defination for 2-input XNOR gate.
| Important: The XNOR operation is commonly represented using the ⊙ symbol, all notations are given below
A XNOR B = AB + A̅B̅ = AB + A′B′ = A ⊙ B = (A ⊕ B)’ |
XNOR is the opposite of XOR gate, when we apply NOT gate to the output of XOR gate, then we get XNOR gate.
XNOR Gate Boolean Expression
The Boolean expression of XNOR logic Gate is given below
where
A, B are the inputs, X is the output, and ⊕ is the operator for XOR gate, and bar over A and B represents XNOR.
XNOR Gate Symbols
Here are standard diagrams that show the symbol of XNOR logic gate. The number of inputs to a XNOR logic gate can be different according to the requirement
XNOR Gate Symbol for 2 Inputs
In the following XNOR gate diagram, A and B are the inputs, and A⊕B is the output
XNOR Gate Symbol for 3 Inputs – Using 3 XNOR
In the following XNOR gate diagram, A, B, and C are the inputs, and A⊕B⊕C with a bar is the output.
XNOR Gate Symbol for 4 Inputs – Using 3 XNOR
In the following XNOR gate diagram, A, B, C, and D are the inputs, and A⊕B⊕C⊕D with a bar is the output.
XNOR Gate Symbol for 5 Inputs – Using 3 XNOR
In the following XNOR gate diagram, A, B, C, D, and E are the inputs, and A⊕B⊕C⊕D⊕E with a bar is the output.
XNOR Gate Symbol for 6 Inputs – Using 3 XNOR
In the following XNOR gate diagram, A, B, C, D, E, and F are the inputs, and A⊕B⊕C⊕D⊕E⊕F with a bar is the output
XNOR Gate Symbol for 7 Inputs – Using 5 XNOR
In the following XNOR gate diagram, A, B, C, D, E, F, and G are the inputs, and A⊕B⊕C⊕D⊕E⊕F⊕G with a bar is the output
XNOR Gate Symbol for 7 Inputs – Using 1 XNOR
In the following XNOR gate diagram, A, B, C, D, E, F, and G are the inputs, and A⊕B⊕C⊕D⊕E⊕F⊕G with a bar is the output. In this process, we can use several XNOR gates, but it can be done through a single XNOR gate, as shown in the following diagram.
Important: In the above examples
both examples have the same output |
XNOR Logic Gate Truth Table
The truth table shows all possible input combinations and their corresponding outputs for a logic gate. XNOR Logic Gate truth tables for different numbers of inputs are given below
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The number of possible input combinations in a truth table is calculated using 2ⁿ, where n represents the number of inputs. For Example:
|
XNOR Logic Gate Truth Table for 2 inputs
A 2-input XNOR gate gives an output of 1 when the two inputs are the same (00 or 11). If the inputs are different (01 or 10), the output is 0. XNOR Logic Gate Truth Table for two inputs (A, B) is given below.
XNOR Logic Gate Truth Table for 3 inputs
A 3-input XNOR gate outputs 1 when an even number of inputs are 1 (0 or 2). If the number of 1s is odd (1 or 3), the output is 0. XNOR Logic Gate Truth Table for three inputs (A, B, C) is given below.
XNOR Logic Gate Truth Table for 4 inputs
A 4-input XNOR gate outputs 1 when an even number of inputs are 1 (0, 2, or 4). If the number of 1s is odd (1 or 3), the output is 0. XNOR Logic Gate Truth Table for four inputs (A, B, C, D) is given below.
