Number Base Converter — Binary, Octal, Decimal & Hex

A number base (or radix) is just the count of distinct digits a numeral system uses. Decimal is base 10 (digits 0–9); binary is base 2 (0–1); hexadecimal is base 16 (0–9 then A–F). The quantity never changes — only how it is written. This converter moves a value between any two bases from 2 to 36 using two standard, verifiable steps.

Step 1 — source to decimal (positional expansion). Every numeral is a sum of its digits times powers of the base. For an n-digit number with digits d₍n−1₎ … d₁ d₀ in base b:

N = Σ value(dᵢ) · bⁱ, for i = 0 … n−1

where value maps 0–9 to 0–9 and A–Z to 10–35. That digit alphabet is not arbitrary: it is the mapping fixed by the ECMAScript specification (ECMA-262) for parseInt and Number.prototype.toString(radix), which is also why the radix tops out at 36 — base 36 already exhausts all ten digits and all 26 letters.

Step 2 — decimal to target (repeated division). To write that quantity in the target base, divide repeatedly by the base and collect remainders:

while N > 0: r = N mod base; prepend digit(r); N = ⌊N ÷ base⌋

The remainders, read from last to first, are the target representation. A value of 0 renders simply as 0.

To stay exact for arbitrarily long inputs, every calculation uses JavaScript BigInt rather than floating-point numbers, which would lose precision above 2⁵³ (about 9 quadrillion). As a credibility check, the tool computes the decimal value twice by independent code paths — Horner's method and the explicit positional sum above — and only marks a result verified when they agree. The four-panel binary / octal / decimal / hex readout and both working displays are all derived from that single shared integer, so the steps shown can never disagree with the answer.

• ECMA-262 — Number.prototype.toString(radix): canonical 2–36 digit alphabet
• MDN — Number.prototype.toString() radix range & digit set
• MDN — parseInt(): radix parsing reference

The digit alphabet and radix range were last cross-checked against the ECMA-262 specification on 2026-06-09. The conversion math (positional expansion and repeated division) is standard place-value arithmetic and does not change.