How it works

Our Number Base Converter helps you quickly switch numbers between common bases: Decimal (Base 10), Binary (Base 2), Octal (Base 8), and Hexadecimal (Base 16). Whether you're studying computer science, digital electronics, or just curious about different number systems, this tool makes conversions straightforward.

The Formula

To convert a number from any base (b) to decimal:
Decimal = d_n * b^n +. + d_1 * b^1 + d_0 * b^0 To convert from decimal to another base (b):
Repeatedly divide the decimal number by b and record the remainders. The result is the remainders read from bottom to top.

Worked Example

1. Converting 25 (Decimal) to Binary

   Let's convert the decimal number 25 to its binary equivalent. 1. Divide 25 by 2: 25 ÷ 2 = 12 remainder 1 2. Divide 12 by 2: 12 ÷ 2 = 6 remainder 0 3. Divide 6 by 2: 6 ÷ 2 = 3 remainder 0 4. Divide 3 by 2: 3 ÷ 2 = 1 remainder 1 5. Divide 1 by 2: 1 ÷ 2 = 0 remainder 1 Reading the remainders from bottom to top, 25 (decimal) is 11001 (binary).

Tips, Assumptions & Limitations

• Ensure your input number uses only valid digits for its 'From Base' (e.g., 0s and 1s for Binary).
• Hexadecimal numbers use A-F for values 10-15. Our tool will output these as uppercase.
• This converter handles whole numbers only. For fractional parts, the conversion process is more complex.