Understanding XOR (Exclusive OR)
XOR (exclusive OR) is a fundamental bitwise operation in computer science and digital logic. It compares two bits and returns 1 if exactly one of the bits is 1, and 0 if both bits are the same. XOR is represented by the symbol ^ in most programming languages.
How XOR Works
Bitwise Operation
XOR operates on each pair of corresponding bits independently.
A ^ B (bit by bit)
Key Property: Self-Inverse
XOR-ing a value with itself always gives zero.
A ^ A = 0
Identity Element
XOR-ing with zero returns the original value.
A ^ 0 = A
Common Applications
- Cryptography: XOR is used as a building block in many encryption algorithms.
- Error Detection: Parity bits and checksums use XOR to detect transmission errors.
- Swapping Values: Two variables can be swapped without a temporary variable using XOR.
- Data Comparison: XOR highlights differences between two binary values.
- RAID Storage: XOR is used in RAID 5 for parity calculations and data recovery.
XOR Properties
- Commutative: A ^ B = B ^ A
- Associative: (A ^ B) ^ C = A ^ (B ^ C)
- Self-inverse: A ^ A = 0
- Identity: A ^ 0 = A