XORverdi

XORverdi is a term used to describe the result of applying the exclusive OR (XOR) operation across a set of boolean inputs or bits. In this sense, XORverdi is closely related to the concept of parity, indicating whether an odd or even number of inputs are true (1).

Formally, if b1, b2, ..., bn are bits in {0,1}, then the XORverdi is b1 XOR b2 XOR ... XOR bn. For multi-bit values, the operation is performed bit by bit, so the XORverdi of two integers is obtained by applying XOR to each corresponding bit. The result behaves as an algebraic combination where the order of operands does not matter (commutative) and grouping does not affect the outcome (associative). The identity element is 0, and XORing a value with itself yields 0.

Applications of XORverdi appear in several areas. In digital circuits, parity bits use XOR verifications to detect errors. In data integrity and cryptography, XOR operations provide a simple reversible primitive for masking data. In programming, XORverdi is useful for toggling bits, computing parity across collections, or combining multiple values without introducing simple carry-overs as in addition.

Example: the XORverdi of the bits 1, 0, and 1 is 0, since 1 XOR 0 equals 1, and 1 XOR 1 equals 0. For bytes, the XORverdi of 0x5A and 0x3F is 0x65 (01011010 XOR 00111111 = 01100101).

Related topics include the XOR operation, parity, and bitwise manipulation.