# Exclusive OR Gate (XOR Gate)

Someone recently introduced the term “XOR gate” to you as you’re learning about logic gates and circuits. What the heck? Don’t worry—we’ve all been confused beginners. One of the coolest and most useful logic gates is the XOR gate. In this brief beginner’s guide, we’ll explain XOR gates, how they function, and their common uses. Stay with me for a few minutes and you’ll master XOR gates.

## What Is an XOR Gate?

Digital logic gates called XOR gates or exclusive OR gates output true (1) when either input is true but not both. It’s an essential circuit component.

#### A ⊕ B

The symbol ⊕ represents the XOR operator.

XOR gates have two inputs and one output. The output is true only if one input is true and the other false. The output is false if both inputs are false or true.

An XOR gate outputs “one or the other but not both”. It’s employed in applications that require an either/or choice, not both.

### Some uses of XOR gates:

•Parity bit checking detects single-bit data transmission faults using XOR gates.

•Stream ciphers encrypt data with XOR gates.

• Comparators—XOR gates can compare two bits and output 1 if they differ.

•SR flip-flops, a basic digital circuit memory storage element, use XOR gates.

• Multiplexers—XOR gates choose one input according to a select input.

To conclude, the XOR gate is a basic logic gate used in many digital circuits. Understanding complicated digital logic and computation requires mastering the XOR gate.

## How an XOR Gate Works

XOR gates are digital logic gates that execute exclusive or operations. Two inputs, one output. XOR gates only output true when one input is true. The output is false if both inputs are false or true.

To understand an XOR gate, look at its truth table:

1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 0

Only when one input is 0 and the other is 1 does the truth table output 1 (true). Other than that, output is 0.

Applications that need to determine if an input has changed utilize an XOR gate. Simple example: a light switch. Flipping the switch turns on the light. Flipping the switch again turns off the light. The switch is an XOR gate that receives the light’s current state and the switch flip.

### Other XOR gate uses:

Communication error detection. XOR detects single-bit data transfer problems.
Generate random numbers. XOR gates generate random bits in random number generators.
Encryption methods. The one-time pad cipher encrypts and decrypts data using XOR gates.
XOR gates are essential to digital devices and computers. Analyzing an XOR gate teaches Boolean logic and digital electronics.

## Real-World Applications of XOR Gates

XOR gates are useful in electronics and computing. They form the basis of more complicated circuits and systems.

One of the most common uses of XOR gates is error detection. XORing a data word with a parity bit reveals a single bit fault during transmission or storage. If there are odd 1s, the XOR outputs 1, otherwise 0 is returned. Errors occur when the parity bit and XOR output don’t match.

XOR gates are widely utilized in cryptography and computer security. Stream ciphers encode and decrypt with XOR gates. Simple logic gates conceal information well.

XOR gates are utilized in computer keyboards. The keyboard detects simultaneous key presses using XOR encoding. Each key press XORs its scan code. If 1 is returned, the keyboard understands two keys were hit simultaneously.

XOR gates are used in error-correcting codes like hamming. They detect and fix data storage and transmission bit mistakes. Add extra parity bits and use XOR logic to detect and rectify single bit problems.

Also uses XOR gates for random number creation. Basic hardware random number generators XOR two free-running oscillators. A random stream of 1s and 0s will be emitted. Most consider the pattern statistically random, even if it may reoccur.

The basic but versatile XOR gate has several real-world applications, including error detection, data encryption, and random number generation. They underpin computers and digital devices.

## XOR Gate Symbols and Circuits

The exclusive OR gate (XOR) is represented by the logic symbol ⊻. Digital circuits use the XOR gate with two or more inputs and one output. It uses the exclusive OR operation on its inputs, therefore the output is true only when one input is true. The output is false if both inputs are false or true.

XOR gates are used in parity checks, counters, and error-detecting codes. The ⊻ sign in a logic diagram indicates an XOR logic gate. The Boolean equation A ⊻ B represents the XOR gate, where ⊻ represents the exclusive OR operator.

A basic XOR gate circuit uses NAND or NOR gates. Two NAND gates form a basic XOR gate circuit:

``````NAND1   NAND2
A│B    A│B
│       │``````

Output
This is “NAND-NAND” setup. A third NAND gate receives outputs from the first two. Final output comes from third NAND gate. This circuit outputs high (1) only when A and B have different logic levels.

### Other XOR gate terms:

Exceptional prohibition
Inequality gate
Unequal gate
Non-equivalence gate
From simple logic circuits to large digital systems and microprocessors, the XOR gate is a key digital circuit building component. Understanding the XOR gate will solidify your digital logic knowledge.

## XOR Gate Truth Table and Logic Operations

Digital logic gates that conduct exclusive OR operations on their inputs are called XOR gates. An XOR operation returns true if just one input is true. The output is false if both inputs are false or true.

XOR gate truth tables show input and output logic states:

1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 0

The output is only 1 (true) when one input is 0 and the other is 1. Other than that, output is 0.

XOR gates are useful for error detection circuits since one input changes the output. They also do addition, subtraction, and bitwise exclusive OR in circuits.

#### The following examples demonstrate XOR logic:

•Two rooms have “on/off” light switches. Light should be on if one switch is on and off if both are. An XOR gate could manage this.

•In your security system, an alarm should sound if a motion detector or door/window contact is triggered, but not both. XOR gates function nicely here.

•Check if two binary numbers differ at any bit position. The XOR gate will return 1 if any bits differ and 0 if they are the same.

•A password should be accepted if a fingerprint or code match, not both. XOR gates can validate inputs this way.

Finally, the XOR gate is a simple but useful logic gate for situations where you want an output when one or the other input occurs but not both. XOR gates can be used in digital circuits if you grasp their truth table and logic operations.