Number Base Converter

A Number Base Converter is a mathematical translation utility used to transform numbers between different "radices" (bases). While humans think in Decimal (Base-10), computers think in Binary (Base-2), and programmers often use Hexadecimal (Base-16) or Octal (Base-8). This tool allows for arbitrary conversion between any base from 2 to 36.

The conversion engine uses a multi-stage logic pipeline:

1. Normalization (Input to Decimal):
   • The tool takes your input (e.g., 1A in Hex).
   • It parses each digit based on its position power ($1 \times 16^1 + 10 \times 16^0 = 26$).
   • It creates a standard JavaScript integer (Decimal).
2. Serialization (Decimal to Output):
   • It takes the decimal number (26).
   • It repeatedly divides it by the target base (e.g., Binary, Base-2).
   • It collects the remainders to form the new string ($26 = 11010_2$).

The History of Bases

Why do we use Base-10?

• Base-10 (Decimal): Because we have 10 fingers.
• Base-12 (Duodecimal): Used by ancient Sumerians (counting finger joints). Still survives in clocks (12 hours) and measurements (12 inches).
• Base-20 (Vigesimal): Used by the Mayans.
• Base-60 (Sexagesimal): Used by Babylonians. Survives in time (60 seconds, 60 minutes) and geometry (360 degrees).

Common Computer Bases

Base	Name	Digits	Use Case
2	Binary	0, 1	Machine Language
8	Octal	0-7	Unix Permissions
10	Decimal	0-9	Human Math
16	Hex	0-9, A-F	Colors / Memory
32	Base32	A-Z, 2-7	File Encoding
64	Base64	A-Z, a-z, 0-9, +/	Email Attachments

Technical Depth: Arbitrary Precision

JavaScript numbers are floating point (IEEE 754), which means they lose precision after 15 digits. If you try to convert a massive 20-digit ID, standard math will fail. Our tool detects large inputs and switches to BigInt arithmetic, ensuring that your cryptographic keys and database IDs are converted with bit-perfect accuracy.