Number Base Converter
Convert integers between any base (Binary, Octal, Hex, Base64) or custom alphabets with arbitrary precision using BigInt logic.
About
This Number Base Converter is a high-precision tool designed to translate integers between different counting systems (radices). Unlike standard calculators that fail with large numbers due to floating-point errors, this tool uses BigInt arithmetic, allowing for arbitrary precision. This means you can convert numbers with hundreds of digits without losing accuracy.
It supports standard bases like Binary (Base 2), Octal (Base 8), and Hexadecimal (Base 16), as well as modern encoding standards like Base58 (used in Bitcoin) and Base64. Additionally, the "Custom" mode allows you to define your own set of symbols, making it useful for cryptography puzzles or esoteric programming languages.
Formulas
To convert a number string S from Base b to Decimal (Base 10), we sum the value of each digit d multiplied by the base raised to the power of its position p (starting from 0 on the right):
To convert a Decimal Value V to a Target Base t, we repeatedly apply the modulo operator to find the remainder (which becomes the digit) and divide the integer:
Reference Data
| Base Name | Radix r | Alphabet / Symbols | Example (Value 255) |
|---|---|---|---|
| Binary | 2 | 0, 1 | 11111111 |
| Octal | 8 | 0-7 | 377 |
| Decimal | 10 | 0-9 | 255 |
| Hexadecimal | 16 | 0-9, A-F | FF |
| Base32 | 32 | A-Z, 2-7 | HY |
| Base58 (Bitcoin) | 58 | 1-9, A-Z, a-z (no 0, O, I, l) | 5Q |
| Base64 (URL) | 64 | A-Z, a-z, 0-9, -, _ | 3_ |