Bitwise XOR

The Bitwise XOR Calculator computes the bitwise exclusive OR (XOR) operation between two integers. For each bit position, the result is 1 if the corresponding bits of A and B differ, and 0 if they are the same. In boolean notation, this is expressed as A ⊕ B or A ^ B. The calculator displays results in both decimal and binary (0b prefix) formats for easy verification.

XOR is a fundamental operation in computer science and digital logic. It is used in cryptography (such as the XOR cipher and one-time pad), error detection (parity bits and checksums), graphics (bitmap masking and sprite rendering), and low-level programming for toggling specific bits. One well-known property is that XORing a value twice with the same key returns the original value, which makes it ideal for reversible encryption. XOR is also commonly used to swap two integer variables without using a temporary third variable, leveraging the property a ^= b; b ^= a; a ^= b; to exchange their values.

In digital electronics, the XOR gate is a fundamental building block used in adder circuits, comparators, and pseudo-random number generators (LFSRs). The operation is also called modulo-2 addition because the result bit is the sum of the input bits modulo 2. Understanding XOR is essential for students of computer science, electrical engineering, and anyone working with low-level data manipulation or encryption algorithms.