Base Converter – Convert Numbers Between Any Base System

Imagine you’re learning computer science. Your textbook shows a number in binary, but your calculator only works in decimal. Or maybe you’re a programmer dealing with hexadecimal color codes and need to quickly check their decimal values. Doing the math by hand works for small numbers, but once fractions and negative values appear, it gets messy.

That’s when a Base Converter becomes a lifesaver. With a couple of clicks, you can convert numbers between any base — from binary (base-2) to hexadecimal (base-16), or even unusual systems like base-7 or base-36. It’s fast, accurate, and saves you from manual mistakes.

Why Base Conversion Matters

Different fields use different number systems:

• Binary (base-2): the language of computers (1s and 0s).
  
• Octal (base-8): compact way to represent binary in older systems.
  
• Decimal (base-10): everyday human counting system.
  
• Hexadecimal (base-16): common in programming, networking, and color coding.
  
• Custom bases (up to base-36): useful for encoding, data compression, or puzzles.
  

A converter is important because it:

• Helps students check homework in maths, computer science, or electronics.
  
• Saves programmers time when debugging or translating between systems.
  
• Allows engineers to handle fractional and negative base conversions without manual error.
  

What the Calculator Asks You

To keep things simple yet flexible, the base converter usually asks for:

• Input Number: The number you want to convert (can include decimals or negatives).
  
• From Base: The system the input is written in (2 to 36).
  
• To Base: The target system you want to convert to (2 to 36).
  
• Letter Case: Whether A–F in hexadecimal should be uppercase or lowercase.
  
• Fraction Precision: How many digits to keep after the decimal point in the result.
  

The Conversion Logic

At its core, conversion works in two stages:

1. From base → decimal:
   Multiply each digit by its base raised to the power of its position.
   Example: 1011.101 in base-2 =
   (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) + (1×2⁻¹) + (0×2⁻²) + (1×2⁻³)
   = 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125 = 11.625
   
2. From decimal → target base:
   
   • For the integer part: repeatedly divide by the new base and record remainders.
     
   • For the fractional part: repeatedly multiply by the new base and take whole numbers.
     Stop once you reach the precision limit.
     

This two-step process works for any base between 2 and 36.

How the Calculator Works Step by Step

1. You enter the number. Example: 1A.F.
   
2. Select the input base. Here, base-16 (hexadecimal).
   
3. Select the target base. Say, base-2.
   
4. The tool parses each digit. A=10, F=15.
   
5. It converts to decimal. 1×16¹ + 10×16⁰ + 15×16⁻¹ = 26.9375.
   
6. It converts decimal → binary.
   
   • Integer 26 → 11010.
     
   • Fraction .9375 → multiply by 2 repeatedly → .1111.
     
7. Final result: 11010.1111.
   

Examples

• Binary to Decimal: 1011.101 (base-2) → decimal = 11.625.
  
• Hexadecimal to Binary: 1A.F (base-16) → binary = 11010.1111.
  
• Decimal to Hexadecimal: -123.45 → base-16 = -7B.7333… (rounded).