An XNOR Gate (Exclusive NOR Gate) is a digital logic gate that outputs a high (1) only when the number of high inputs is even. It is the inverse of the XOR (Exclusive OR) gate. The XNOR gate is sometimes referred to as an Equivalence gate because its output is high (1) when both of its inputs are equal.
Truth Table of XNOR Gate:
| Input A | Input B | Output (A XNOR B) |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Key Features of an XNOR Gate:
- Equality Output:
- The XNOR gate outputs a 1 when both inputs are equal (either both 0 or both 1). If the inputs are different, the output is 0.
- Logic Function:
- The XNOR gate performs the logical function of an Exclusive OR followed by a NOT operation, making it the inverse of the XOR gate.
- Symbol:
- The symbol for an XNOR gate is similar to the XOR gate but with an additional circle (representing NOT) at the output.
- Boolean Expression:
- The Boolean expression for an XNOR gate is: A XNOR B=(A⋅B)+(A‾⋅B‾)A \text{ XNOR } B = (A \cdot B) + (\overline{A} \cdot \overline{B})A XNOR B=(A⋅B)+(A⋅B) Or, it can also be expressed as: A XNOR B=(A⊕B)‾A \text{ XNOR } B = \overline{(A \oplus B)}A XNOR B=(A⊕B) Where AAA and BBB are the inputs, and ⊕\oplus⊕ denotes the XOR operation.
Applications of XNOR Gate:
- Equality Detection:
- The XNOR gate is commonly used for equality checking, where it can compare two binary values and determine if they are the same. This is useful in error detection systems, digital comparison, and in circuits like parity checkers.
- Error Detection and Correction:
- XNOR gates are used in parity generators and parity checkers, which are essential for error detection in data transmission systems. They help ensure that data sent over communication channels remains intact.
- Digital Comparators:
- Used in digital circuits to compare binary numbers, ensuring they match. The output will be 1 if the numbers are equal.
- Conditional Operations in Circuits:
- The XNOR gate can be used in more complex logic circuits, such as decision-making circuits where an action is taken if two conditions are met (inputs are equal).
Advantages of XNOR Gate:
- Simple Logic:
- XNOR gates are simple to implement and are often used to perform basic equality checks or parity operations in digital circuits.
- Versatile:
- The XNOR gate is versatile in various applications, such as error detection, comparators, and digital arithmetic.
- Low Power Consumption:
- It can be used in low-power circuits, especially where binary data comparison is required with minimal energy expenditure.
Disadvantages of XNOR Gate:
- More Complex than AND/OR:
- Although simpler than many other gates, the XNOR gate can be more complex than basic AND or OR gates when implemented in larger circuits.
- Requires More Logic Gates:
- To implement the XNOR operation using other basic gates like AND, OR, and NOT, more gates are typically required compared to XOR or AND operations alone.