34base

34base is a positional numeral system with base 34, used to represent integers and, with a radix point, fractions as well. The digit set for 34base is 34 symbols: the ten decimal digits 0–9 and the uppercase letters A–X, where A stands for 10 and X for 33. Some presentations also treat lowercase letters as alternate representations, but the conventional form uses the stated set.

Example: decimal 1234 converts to 12A in 34base, because 34^2 = 1156, leaving a remainder of 78; 34^1 = 34 yields a 2, with a final remainder of 10, which is A. Reading from most significant to least significant gives 12A.

In calculations, digits are added with a base-34 carry: any sum equal to or greater than 34 carries 1 to the next higher place. Subtraction and multiplication follow the same positional rules, and conversions between 34base and decimal can be done via repeated division or multiplication by powers of 34. Fractions use the same digit set after the radix point.

Potential uses include compact encodings for identifiers or hashes, educational demonstrations of non-decimal bases, or any domain requiring alphanumeric digit sets. However, base-34 is not widely standardized, and its adoption is limited by readability, tooling support, and the availability of established bases like binary, octal, decimal, and hexadecimal.

34base is part of the broader family of base-N numeral systems, in which the number of distinct digits equals the base. It shares properties with other mixed-digit bases and illustrates how changing the base affects digit length and carry behavior.