Quaternary (base-4) converter

A quaternary converter rewrites a non-negative whole number between everyday base-10 and base-4, the four-digit positional system whose alphabet is simply zero, one, two, and three. Each base-4 digit packs exactly two bits, which makes quaternary a natural bridge for DNA-style four-letter alphabets, two-bit pixel channels, and compact state machines that only need four symbols. You choose a direction—decimal to quaternary or quaternary back to decimal—paste the value, and receive a deterministic result with the cleaned decimal integer, the base-4 digit string, the digit count, and the fixed alphabet. Any character outside zero through three fails with a clear invalid-input error instead of a silent wrong answer.

How quaternary (base-4) encoding and decoding work

Quaternary is positional notation with radix four. Each place is a power of four, just as decimal places are powers of ten: the units place is four to the zero, the next place is four, then sixteen, then sixty-four, two hundred fifty-six, and so on. The four digit symbols are zero, one, two, and three—nothing else.

That tiny alphabet is exactly what you need when a value lives in two bits: binary 00 maps to 0, 01 to 1, 10 to 2, and 11 to 3, so a long bit string can be regrouped into quaternary digits without padding games beyond an optional leading zero on an odd-length bit run.

To encode a non-negative decimal integer, divide repeatedly by four 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 four, and add the next digit—the classic Horner scheme. An optional 0q or 0Q prefix is stripped the same way binary tools accept 0b, so scripts can tag base-4 literals clearly.

An invalid character such as a space, plus sign, digit four or higher, letter, or punctuation mark 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 quaternary alphabet has no sign digit, and signed base-4 is a separate convention.

If you need arbitrary bases from two through thirty-six, that is a different search intent served by a general radix converter rather than this base-4-specific landing.

Where quaternary converters show up in real work

Bioinformatics tutorials and coding-theory courses introduce base four because DNA’s four nucleotides map cleanly onto two-bit codes and therefore onto quaternary digits: one common teaching map is A equals zero, C equals one, G equals two, and T equals three, so a short oligo becomes a compact base-4 string students can convert to decimal for hashing demos or puzzle keys.

Computer graphics and embedded firmware sometimes pack two-bit-per-channel data—palette indices, dither flags, or state machines with four modes—and engineers need a deterministic oracle that turns those digit strings into integers for tests without hand-rolling divmod in every language. Game designers invent four-state runes, inventory stacks, or alien numbering systems and need deterministic conversion for lore tools and save formats.

Treat general multi-base radix tables that stop at thirty-six, pure binary or hexadecimal dumps, and Base64 byte encoding as separate search intents with their own landings rather than stretching this integer quaternary converter past its honest scope.