Universal Base Converter
Perform high-precision conversions between any base from 2 to 36. Essential for cryptographic analysis, low-level programming, and theoretical mathematics.
The Mechanics of Positional Notation
Base conversion is the process of translating a number's representation from one system of positional notation to another. While decimal (Base-10) is our daily standard, the underlying logic of computation demands alternatives like Binary (Base-2), Octal (Base-8), and Hexadecimal (Base-16).
In any base b, a number is represented as a sum of coefficients multiplied by powers of b. For example, in Hexadecimal, the value `0x1A` represents `(1 * 16¹) + (10 * 16⁰)`, which equals 26 in decimal.
Standard Bases Comparison
| Base | Name | Digits |
|---|---|---|
| 2 | Binary | 0, 1 |
| 8 | Octal | 0-7 |
| 10 | Decimal | 0-9 |
| 16 | Hexadecimal | 0-9, A-F |
When to Use Higher Bases?
Bases like 32 and 36 are often used for URL shortening or Identifier generation. Base-32 is popular in security contexts (like TOTP secrets) because it avoids ambiguous characters like '0', '1', 'O', and 'I'. Base-36 uses the full alphanumeric set (0-9 and A-Z), providing the most compact representation using standard characters.
Precision & Large Integers
Standard JavaScript number types use 64-bit floating points (IEEE 754), which can lose precision for integers larger than 2⁵³ - 1. Octal Works utilizes `BigInt` for all base conversions, ensuring that even extremely long sequences of digits remain 100% accurate across all transformations.