How base conversion works
A number like 1011 in binary means 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal. The converter performs exactly this expansion for the source base to recover the plain decimal value, then repeatedly divides by the target base to build up the digits of the answer.
Because every conversion passes through decimal, switching between, say, binary and hexadecimal is exact and reversible.
Digits beyond 9
Bases larger than 10 need extra digit symbols. By convention the letters A–Z stand for the values 10–35, so hexadecimal (base 16) uses 0–9 then A–F, and base 36 uses the full 0–9 and A–Z set.
- Binary (base 2): digits 0 and 1.
- Hexadecimal (base 16): 0–9 then A–F.
- Base 36: 0–9 then A–Z.
Using the converter
Enter your number, pick the base it is written in, and pick the base you want it in. The result shows both the target-base value and the underlying decimal so you can check the conversion.
Caveats and common mistakes
The digits you type must be valid for the source base — a "2" is not a legal binary digit, for example. This tool handles non-negative whole numbers only, so fractional and negative inputs are not supported.
Formula
value = Σ digitᵢ × base^iFrequently asked questions
- Why does hexadecimal use letters?
- Bases above 10 need single symbols for values past 9, so letters A–Z represent 10–35. Hexadecimal uses A–F for 10–15.