S3Softs

Arbitrary Custom Base Converter

A powerful utility for computer scientists and mathematicians to instantly translate numbers between any arbitrary base ranging from Base 2 up to Base 36.

Input Base 10

Output Base 2

The Mathematics Behind It

How do Custom Bases work?

Standard number systems use well-known anchors: Binary (Base 2) uses digits 0-1, Decimal (Base 10) uses 0-9, and Hexadecimal (Base 16) uses 0-9 plus A-F. However, mathematics allows for any arbitrary base up to Base 36 (using the entire english alphabet `A-Z` to represent digits 10 through 35).

The Algorithm: To convert from Base-N to Base-M, we first parse the string using Base-N mathematics to find its true absolute integer value (Base 10 Anchor). We then divide that absolute integer repeatedly by M, collecting the remainders to construct the final Base-M string.

Frequently Asked Questions

What is the maximum base supported?

This tool supports up to Base 36. Base 36 is the mathematical limit for standard single-character alphabetic representation (10 numeric digits + 26 english alphabet letters = 36 possible characters).

Is this tool safe for extremely large numbers?

We utilize Javascript's native `parseInt(val, radix)` which guarantees precise translation up to the safe integer limit (9,007,199,254,740,991).

Related Tools & Utilities