A Deep Dive into XOR: From Boolean Logic to Cryptography

This article delves into the seemingly simple XOR (exclusive OR) operator in computer science. Starting with XOR in Boolean logic, it progresses to bitwise operations on integers and explores XOR's applications in cryptography, pixel graphics, game theory, and finite fields. The author uses engaging storytelling and numerous examples to explain XOR's properties and uses, such as its role as a simple encryption method in cryptography, reversible drawing and erasing in pixel graphics, and determining optimal strategies in the game of Nim. Finally, the article connects XOR to mathematical concepts like the symmetric difference of sets, groups of exponent 2, Nim-sum, GF(2) finite field, and CRC checksums, revealing the deeper mathematical underpinnings and broad applications of the XOR operator.