Exclusive Disjunction Operator (XOR)
The exclusive disjunction operator, commonly referred to as XOR, is a logical operator that returns true if and only if the two input values are different
The exclusive disjunction operator, commonly referred to as XOR, is a logical operator that returns true if and only if the two input values are different. It is denoted by the symbol ⊕ or sometimes by the symbol XOR.
The XOR operator can be applied to two logical values, typically represented by either 0 or 1. When applied to two inputs, the following truth table illustrates the result:
| Input A | Input B | Output |
|:——-:|:——-:|:——:|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
As seen in the truth table, the XOR operator returns 0 when both inputs are the same (either both 0s or both 1s), but returns 1 when the inputs are different.
The XOR operator is often used in computer science and mathematics, as it has several practical applications. Here are a few examples:
1. Data Encryption: XOR is used in cryptographic algorithms to encrypt and decrypt data. Each bit in the data is XORed with a corresponding key bit, and the resulting encrypted data can only be decrypted back to the original message if the correct key is used.
2. Error Checking: XOR can be used to perform parity checks, where a checksum is generated from a set of binary values. By XORing all the values together, you can create a parity bit that can be used for error detection.
3. Switching Logic: XOR is used in electronic circuits as part of switching logic. It allows for the creation of circuits that toggle between two states depending on the input values.
It’s worth noting that XOR is associative and commutative, meaning that the order of the inputs does not affect the result, and grouping of inputs does not affect the final output.
In summary, the XOR operator returns true when the values of its inputs are different, and false when the values are the same. Its practical applications include data encryption, error checking, and switching logic.
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