# Exclusive OR Gate

## Definition of Exclusive OR Gate

An Exclusive OR Gate, also known as an XOR Gate, is a fundamental digital logic gate that implements an exclusive disjunction operation. It takes two input signals and produces one output signal, which is true (logic 1) only when the number of true inputs is odd. In simpler terms, the output is true if either one of the inputs is true, but not both.

### Phonetic

Exclusive OR Gate phonetics: /ÉªkËˆsklu sÉªv É”r É¡eÉªt/

## Key Takeaways

1. An Exclusive OR (XOR) Gate is a digital logic gate that outputs a high signal (1) only when an odd number of its inputs are high (1).
2. XOR Gates are widely used in binary addition, digital circuits, and error detection/correction algorithms due to their unique behavior of outputting a high signal when only one of their inputs is high.
3. Using multiple XOR Gates together can form more complex circuits such as half-adders, full-adders, and parity generators/checkers for error detection in data transmission.

## Importance of Exclusive OR Gate

The Exclusive OR (XOR) Gate is an essential digital logic gate that plays a crucial role in modern technology, particularly in digital electronics and computer systems.

It enables us to perform a vital binary operation on two input signals, resulting in a logical “true” output if the input values differ and a “false” output when they are equal.

This unique property makes XOR Gates critical in a variety of applications, such as arithmetic operations, error detection/correction, cryptography, and decision-making processes.

By only producing a true output when the inputs have different values, the XOR Gate provides a means for efficient data storage, processing, and transmission, which contributes significantly to the functionality and effectiveness of contemporary technology.

## Explanation

In digital circuits, the Exclusive OR (XOR) gate is a fundamental component which serves the purpose of comparing binary inputs and generating outputs based on their logical differences. XOR gates are prominently used for tasks including data manipulation, arithmetic operations, parity generation, and error checking. They exhibit a unique functionality as they produce a true (1) output when the input signals being compared differ from each other, and a false (0) output when they are the same.

This distinct property of XOR gates facilitates their application in various digital systems where the comparison of signals and the detection of dissimilarities is essential. One notable application of XOR gates is in arithmetic operations, particularly bitwise addition. They are used to build half adders and full adders, which are essential components of arithmetic logic units (ALU) in processors.

Through these adders, XOR gates help perform binary addition without carrying over the bits, thereby extending their utility to more complex operations such as subtraction, multiplication, and division. Furthermore, XOR gates play a crucial role in the generation of parity bits for data transmission, where error checking is necessary to maintain the integrity and reliability of data communication. By examining input bits and producing a parity bit based on their state, XOR gates pave the way to detect any discrepancies in the transmitted information, allowing for efficient error detection and subsequent corrective actions in digital systems.

## Examples of Exclusive OR Gate

Exclusive OR (XOR) gates are used in various real-world applications including error detection, encryption, and arithmetic operations. Here are three such examples:

Error Detection – XOR gates are widely used in error detection schemes such as parity checks. A simple example is a 9-bit even parity checker, where eight data bits are combined with a parity bit to ensure an even number of 1s in the overall transmitted data. When the data is received, the parity is checked using XOR gates to determine if there are any transmission errors. If an error is detected, the receiving device can request retransmission of the data.

Encryption – XOR gates are employed in various cryptographic techniques, such as stream ciphers. In a stream cipher, the plain text message and a secret key generated from a pseudo-random number generator are combined using XOR operations. The XOR operation ensures that the encrypted message (cipher text) is completely different from the original message, providing increased security. Decryption is performed using the same XOR operation with the same secret key, as the XOR operation is reversible.

Arithmetic Operations – XOR gates are crucial in binary addition. They are used in Half Adders and Full Adders, which are essential components of Arithmetic Logic Units (ALUs) in digital circuitry. Half Adders add two single-bit binary numbers, while Full Adders can add multiple bits, carry-over, and multi-digit binary numbers. The XOR gate is responsible for computing the “sum” output of the adder, while an AND gate helps compute the “carry” output for further addition operations.

## Exclusive OR Gate FAQ

### 1. What is an Exclusive OR gate?

An Exclusive OR gate, also known as XOR gate, is a digital logic gate that implements an exclusive or function. It has two or more inputs and one output, where the output is high (1) only when an odd number of inputs are high (1). In other words, the output is true when only one of the inputs is true, and false when either both inputs are true or both inputs are false.

### 2. What is the symbol for the Exclusive OR gate?

The symbol for the XOR gate is a combination of the OR gate symbol and an additional curved line at the input side. It looks like an OR gate symbol, but with a curved line on the left side which differentiates it from an OR gate.

### 3. What is an example of an Exclusive OR gate application?

The XOR gate is commonly used in binary addition, also called half-adder circuits, where two binary numbers are added together. The XOR operation will give the result of the sum, while an AND gate is used to produce the carry signal.

#### 4. What is the truth table for the Exclusive OR gate?

The truth table for a 2-input XOR gate is:

```  A  |  B  | Output
-------------------
0  |  0  |   0
0  |  1  |   1
1  |  0  |   1
1  |  1  |   0
```

Here, A and B are the inputs and the Output column shows the result of A XOR B.

### 5. Can an Exclusive OR gate be created with basic gates like AND, OR, and NOT gates?

Yes, an Exclusive OR gate can be created using a combination of AND, OR, and NOT gates. A two-input XOR gate can be created with the following gate combination: ((A AND (NOT B)) OR ((NOT A) AND B)).

## Related Technology Terms

• Binary operations
• Logic circuits
• Boolean algebra
• Truth table