Enneadecimal

Enneadecimal is a positional numeral system with base 19. The name derives from Greek roots for nine and ten, signifying nineteen as the base. In practice, a full set of 19 distinct digits is used: typically 0 through 9 for values 0–9 and the letters A through I for values 10–18. Other symbol sets are possible, but this is a common convention.

Numbers are written as sequences of base-19 digits. For example, the decimal number 18 is written as I, and 19 is written as 10 in base 19, since 1×19 + 0 = 19. The decimal 38 becomes 20 (2×19 + 0), and 123 becomes 69 (6×19 + 9).

Arithmetic in enneadecimal follows the same principles as other positional systems, with carries, borrows, and remainders calculated relative to the base. Addition and multiplication proceed digit by digit from right to left, applying carries when sums exceed 18. Conversions between base-19 and base-10 typically use division by 19 for decimal to enneadecimal, and multiplication and summation for the reverse, recording remainders to obtain digits in the correct order.

Enneadecimal has rarely been adopted beyond theoretical discussions, puzzles, and numeral-system research. It is not widely used in computing or standard mathematics, where base-2, base-10, base-16, and a few other bases predominate. See also lists of numeral systems and base conversions.