0xcorresponds

0xcorresponds is a term used in computer science to describe the canonical mapping between nonnegative integers and their hexadecimal textual representations prefixed with 0x. In this usage, each integer n ≥ 0 corresponds to a unique hexadecimal literal h, typically formed from digits 0-9 and a-f and prefixed with 0x. The canonical form conventionally uses lowercase letters and omits unnecessary leading zeros, with the exception that zero is represented as 0x0. The 0xcorresponds relation consists of pairs (n, h) where h is the canonical hex form of n.

Properties and implications: The mapping from integers to hexadecimal strings is injective, meaning each integer has a single canonical hex representation. There is a straightforward inverse: parsing a hex string back to an integer, provided the parsing rules are clear (for example, ignoring case and leading zeros). This facilitates reliable round-trip conversions: a number can be converted to its canonical hex form and then parsed back to the original integer.

Variations: In practice, some contexts allow uppercase letters or leading zeros, which means representations are non-canonical. In such cases, the relation may not be strictly a function if multiple hex strings map to the same integer. Definitions of 0xcorresponds therefore depend on the chosen normalization rules for hex literals.

Applications: The concept underpins canonical number formatting in programming languages, debuggers, compilers, and data formats that use hexadecimal notation. It helps clarify expectations about how numbers are displayed, parsed, and validated across tools and environments.

Example: 0 corresponds to 0x0; 26 corresponds to 0x1a; 255 corresponds to 0xff. See also hexadecimals, numeric literals, and base conversion.