Senary base-6 converter

A senary converter rewrites a non-negative whole number between everyday base-10 and base-6, the radix-six system also called senary or heximal. The six digit symbols are simply zero through five—no letter digits—so every place value is a power of six, matching six-sided dice faces, some traditional counting schemes, and recreational number-system lessons. You choose a direction—decimal to senary or senary back to decimal—enter the value, and receive a deterministic result with the cleaned decimal integer, the base-6 string, the digit count, and the fixed alphabet. Any character outside 0–5 fails with a clear invalid-input error instead of a silent wrong answer.

How senary (base-6) encoding and decoding work

Senary is positional notation with radix six. Each place is a power of six, just as decimal places are powers of ten: the units place is six to the zero, the next place is six, then thirty-six, then two hundred sixteen, then one thousand two hundred ninety-six, and so on. The six digit symbols used here are zero through five for values zero through five—there are no letter digits, because base six never needs a symbol past five.

That pure digit alphabet matches dice-face notation, elementary place-value drills, and programming exercises that treat six as a clean teaching radix before hex or base sixty-two. To encode a non-negative decimal integer, divide repeatedly by six and record each remainder as the next least-significant digit; reverse those remainders to obtain the usual left-to-right string without leading zeros except for the number zero itself. To decode, walk the string from left to right, multiply the running total by six, and add the digit value of the next character—the classic Horner scheme.

An invalid character such as a space, plus sign, the digit six, seven, eight, nine, a letter, or punctuation aborts with invalid input naming the bad character and its position. Values must stay inside JavaScript’s safe integer range so every digit remains exact when the result is serialized. Negative inputs are rejected on purpose; the senary alphabet has no sign digit, and signed base-6 is a separate convention.

If you need arbitrary bases from two through thirty-six with letter digits A through Z, that is a different search intent served by a general radix converter rather than this senary-specific landing.

Where senary converters show up in real work

Mathematics education and history-of-numeration courses introduce base six because it sits between binary and decimal, has only six symbols, and maps naturally onto a standard six-sided die whose faces already show one through six in decimal labels but can be remapped to place-value exercises in radix six. Tabletop game designers, RPG tool authors, and probability teachers who work with d6 dice often need a shared oracle that converts pile totals and inventory counts into pure 0–5 digit strings for homebrew number systems, alien calendars, or dice-coded puzzles.

Recreational mathematicians and puzzle authors publish tables that stay inside digits zero through five and need deterministic conversion for answer keys. Treat general multi-base radix tables that stop at thirty-six with A through Z, pure hexadecimal dumps, binary-only converters, octal converters, duodecimal with dek and el, and Base64 byte encoding as separate search intents with their own landings rather than stretching this integer senary converter past its honest scope.