Base21

Base21 is a positional numeral system that uses twenty-one digits to represent numbers. In any base-b numeral system, the value of a digit depends on its position and is computed as digit multiplied by b raised to the power of its place. In base-21, each place value is a power of 21, and the digits range from zero to twenty.

A common convention for base-21 uses the digits 0–9 for values zero through nine, and the letters A through K for values ten through twenty (A=10, B=11, C=12, D=13, E=14, F=15, G=16, H=17, I=18, J=19, K=20). Numbers are written with the most significant digit on the left, just as in decimal.

For example, the decimal number 442 equals 1×21^2 + 0×21 + 1, so 442 in base-21 is 101_21. The decimal 1234 equals 2×21^2 + 16×21 + 16, which is represented as 2GG_21, since 16 maps to G.

Arithmetic in base-21 follows the same rules as other bases. Addition, subtraction, multiplication, and division use carries or borrows when a digit reaches or exceeds 21. Zero is written as 0.

Base-21 is not widely used for everyday computation; it is primarily of theoretical interest and appears in educational contexts, recreational puzzles, or encoding schemes that require 21 distinct symbols.

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