The Base Conversion Calculator helps you convert numbers between different number bases such as binary (base 2), decimal (base 10), hexadecimal (base 16), octal (base 8), and more. This is essential for computer science, digital electronics, and programming. The calculator provides step-by-step explanations showing how numbers are converted from one base to another, making it perfect for students learning number systems and professionals working with different number representations.

Required Inputs & Typical Use Cases

• Source Base

  Select the base of the input number (binary, decimal, hexadecimal, octal, etc.).

• Target Base

  Select the base you want to convert to.

• Number

  Enter the number you want to convert. For hexadecimal, use digits 0-9 and letters A-F.

Common scenarios: (1) Convert binary 1010 to decimal; (2) Convert decimal 255 to hexadecimal; (3) Convert octal 777 to binary; (4) Convert hexadecimal FF to decimal; (5) Convert between any number bases for programming and digital systems.

The Formula

Binary to Decimal: Σ(digit × base^position)
Decimal to Binary: Divide by 2, collect remainders
Hexadecimal to Decimal: Use base 16 powers
Decimal to Hexadecimal: Divide by 16, collect remainders
General: Convert to decimal first, then to target base

• base

  The number base (2, 8, 10, 16, etc.)

• digit

  Individual digits in the number

• position

  Position of the digit (starting from 0)

• Result

  Converted number in target base

Worked Example

1. Step 1: Select bases

   Choose the source base and target base for conversion.

2. Step 2: Enter number

   Input the number you want to convert.

3. Step 3: Convert to decimal

   First convert the number to decimal (base 10).

4. Step 4: Convert to target base

   Convert from decimal to the target base.

Tips, Assumptions & Limitations

• Binary uses only digits 0 and 1.
• Hexadecimal uses digits 0-9 and letters A-F (case insensitive).
• Octal uses digits 0-7.
• Always verify your conversion by converting back to the original base.
• Use the calculator to practice and understand the conversion process.