XNOR Gate: Truth Table, Symbol, Boolean Expression, Formula and Circuit Diagram

The XNOR gate is a digital logic gate that performs the exclusive-NOR operation. Its output becomes 1 when both inputs are the same, either both 0 or both 1, and becomes 0 when the inputs are different.

Because of this behavior, the XNOR gate is widely used as a similarity checker or equality detector in digital circuits. It is also known as the equivalence gate or material biconditional in logic.

One important way to understand the XNOR gate is through its relation to the XOR gate. An XNOR gate is simply the complement of an XOR gate. So, if an XOR gate tells us when inputs are different, the XNOR gate tells us when inputs are equal. In symbolic form:

XNOR Gate = XOR Gate + NOT Gate

The XNOR operation is sometimes represented by the symbol ⊙. The gate is also called the equivalence gate, because it checks whether two logic conditions are equivalent.

XNOR Gate Symbol

The xnor gate symbol looks similar to the XOR gate symbol, but with an additional small circle (inversion bubble) at the output. This bubble indicates logical negation. Since the XNOR gate is the inverse of the XOR gate, the symbol directly reflects that relationship.

In a standard symbol:

• there are two inputs, usually labelled A and B

• there is one output, usually labelled Y

• the output line ends with a small circle, showing inversion

So, when you see an XOR-shaped symbol with a bubble at the output, you can identify it as an XNOR gate.

XNOR Gate Circuit Diagram

An xnor gate circuit diagram can be made in several different ways. Since the XNOR gate is not always available as a direct primitive in all design situations, it is often constructed using other gates or transistors.

The file explains that XNOR can be implemented using:

• basic logic gates

• NAND gates only

• NOR gates only

• transistors

XNOR Gate Truth Table

The xnor gate truth table clearly explains how the gate behaves for all possible input combinations.

This xnor gate truth table shows one very important rule:

• output is 1 when inputs are the same

• output is 0 when inputs are different

This is exactly why the XNOR gate is called a similarity checker.

Operation of XNOR Gate

The operation of the XNOR gate is based on equality of inputs. It compares two input values and checks whether they match.

Case 1: Both Inputs are 0

If A = 0 and B = 0, then the output is 1.

Case 2: Inputs are Different

If one input is 0 and the other is 1, then the output becomes 0.

Case 3: Both Inputs are 1

If A = 1 and B = 1, then the output is 1.

So, the XNOR gate acts like a digital “same/not same” detector. If the inputs are equal, the output is HIGH. If they are unequal, the output is LOW.

XNOR Gate Boolean Expression

The xnor gate boolean expression is written as:

Y = A ⊙ B

This expression simply states that output Y is the XNOR of inputs A and B.

Another common and more expanded xnor gate boolean expression is:

Y = AB + A'B'

This means:

• the output is 1 when A and B are both 1

• or when A and B are both 0

This expression exactly matches the truth table.

XNOR Gate Formula and Equation

XNOR Gate Formula and Equation are often written in the following equivalent ways:

Standard XNOR Form

Y = A ⊙ B

H3 - Sum-of-Products Form

Y = AB + A'B'

Inverted XOR Form

Y = (A ⊕ B)'

All three forms mean the same thing. These are just different mathematical ways to represent the same XNOR logic.    

XNOR Gate Using Basic Logic Gates

One common xnor gate circuit diagram uses the basic gates:

• AND

• OR

• NOT

The required Boolean expression is:

Y = AB + A'B'

To implement this:

1. use two NOT gates to get A' and B'

2. use one AND gate to get AB

3. use another AND gate to get A'B'

4. combine both outputs using an OR gate

This gives the final XNOR output.

This method is conceptually simple and clearly shows how the XNOR gate equation is translated into hardware.

XNOR Gate Using NAND Gate

The XNOR gate can also be formed using NAND gates only. This is important because NAND is a universal gate, meaning any logic function can be built using NAND gates alone.

According to the file, we require five two-input NAND gates to construct an XNOR gate. The intermediate outputs first generate XOR behavior, and then that XOR output is inverted again using another NAND arrangement to obtain XNOR.

Important points:

• total 5 NAND gates are needed

• the circuit first behaves like XOR

• final inversion gives XNOR

This type of construction is common in digital design exercises.

XNOR Gate Using NOR Gate

An XNOR gate can also be implemented using NOR gates only, and again five NOR gates are required. NOR is also a universal gate, so it can be used to build any logical function.

The process involves:

• generating intermediate inverted terms

• combining them through NOR logic

• simplifying using De Morgan’s law

This method is useful in exam questions that ask students to implement gates using only NOR.

XNOR Gate Using Transistors

The file also describes the implementation of XNOR gate using transistors. It states that an efficient XNOR design can be made using five transistors, and this is preferred over less efficient designs using larger transistor counts.

In this arrangement:

• the initial transistor pair functions like a NAND gate

• a middle transistor acts as a switch

• the final transistors help produce OR-like behavior

Together, these parts create XNOR functionality. This is an important point for students learning transistor-level logic implementation.

XNOR Gate IC Number

The query xnor gate IC number is very common in electronics searches. In practice, XNOR functionality is commonly associated with standard IC families that implement exclusive-NOR logic. When discussing the xnor gate IC number, students usually refer to integrated circuits designed to perform XNOR operations directly or through equivalently labelled logic packages.

For board-style and concept learning, the most important point is not only memorising the IC number, but understanding:

• the logic operation

• the truth table

• the symbol

• the Boolean expression

• the circuit construction

That said, in practical electronics, XNOR gate IC packages are available in standard digital logic families.

Applications of XNOR Gate

The XNOR gate has many practical applications because it checks input equality.

1. Comparators

XNOR gates are used in comparators to compare binary values bit by bit. If all corresponding bits match, the output remains HIGH.

2. Binary Arithmetic

They help detect equal values in binary addition and subtraction circuits.

3. Parity Checking

XNOR gates are used in parity checking systems where equality of bit patterns is important.

4. Multiplexers

They assist in selecting channels or validating signal matching conditions in multiplexer circuits.

5. Latch and Flip-Flop Control

XNOR gates can enable or disable storage elements depending on input matching.

6. Decoders

They help activate outputs based on matching input code patterns.

7. Clock Synchronization

XNOR gates are used in synchronization circuits for comparing clock signals.

8. Data Storage

When combined with memory circuits such as SRAM structures, XNOR gates can improve reliability.

9. Control Logic

They are useful in digital control and sequencing operations.

10. Full Adders and ALUs

XNOR gates are important in arithmetic logic units and digital arithmetic design.

Advantages of XNOR Gate

The file lists several advantages of XNOR gate:

1. Simplicity

It is simple to understand and implement.

2. Dedicated Equality Testing

It is purpose-built for comparison or equality checking.

3. Complementary Outputs

It provides complementary logic behavior relative to XOR.

4. Ease of Integration

It simplifies the design of circuits that involve comparisons.

5. Data Reliability

Its use in memory and control systems improves data integrity and reliability.

Disadvantages of XNOR Gate

The file also notes some disadvantages of XNOR gate:

1. Limited Functionality

It is mainly useful for equality comparison and not for a wide range of logic operations.

2. Design Complexity in Large Circuits

Designing bigger circuits using only XNOR gates can be inefficient and difficult.

3. Input Dependency

It is more naturally suited to even-numbered equality comparisons and can be less flexible in some logic arrangements.

4. Unsuitable for Many Arithmetic Tasks

Compared with gates like AND and XOR, XNOR is not the first choice for many core arithmetic operations.