The XOR function, short for "exclusive OR", is a logical operation that compares two binary inputs and returns a 1 if the inputs are different, and a 0 if they are the same.
In mathematical notation, the XOR function is represented with the symbol ⊕ or ⊻, and can also be written as x ⊕ y or x ⊻ y. It is often used in Boolean algebra and digital logic circuits.
The truth table for the XOR function is as follows:
| x | y | x ⊕ y |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
The XOR function is commonly used in coding to perform bitwise operations, such as flipping specific bits in a binary sequence or encrypting data. It is also used in error detection and correction algorithms.
The XOR function differs from the OR function in that it only returns a 1 when the inputs are different, whereas the OR function returns a 1 when at least one of the inputs is 1. In other words, the XOR function is only true when the inputs are exclusive, while the OR function is true when the inputs are inclusive.