base15

Base15 is a positional numeral system with a base of 15, meaning it uses 15 distinct digits to represent numbers. Unlike the more commonly used base 10 (decimal) or base 2 (binary), base15 offers a more compact representation for certain types of data, particularly in programming and computer science. Each digit in base15 ranges from 0 to F, where the letters A through F correspond to decimal values 10 through 14. For example, the base15 number "1A" translates to 1 * 15 + 10 = 25 in decimal.

One of the primary advantages of base15 is its efficiency in encoding hexadecimal values. Since hexadecimal (base16) uses digits 0-9 and letters A-F, base15 can represent the same information with one fewer digit. This can be particularly useful in low-level programming, where memory and storage efficiency are critical. For instance, a 16-bit hexadecimal value (0x0000 to 0xFFFF) can be represented as a single 15-bit base15 number, reducing redundancy.

Base15 is also used in certain esoteric programming languages and in the encoding of data formats that prioritize space optimization. While it is not as widely adopted as base10 or base16, its niche applications highlight its utility in specific computational contexts. Converting between base15 and other bases typically involves standard positional arithmetic, though specialized tools or libraries may simplify the process for developers.