# Online Bases converter

Convert a number between bases.
Base from :
Base to :
0

## What a base (Radix) ?

The radix or base is the number of unique digits, used to represent numbers.
If the base is larger than $10$ we use caracters 'A', 'B', 'C', ... as the digits 10, 11, 12 ...
To represent a number $n$ in a base $b$ we use the notation : $$n = \overline{d_{k} d_{k-1} \cdots d_{1}}^{(b)}$$ Examples:
The binary system :
Used internally by nearly all computers, is base 2. The two digits are "0" and "1".
Example : $\overline{31}^{(10)} = \overline{11111}^{(2)}$

The Octal system :
The eight digits are "0"–"7".
Example : $\overline{31}^{(10)} = \overline{37}^{(8)}$

The Decimal system :
The most used system of numbers in the world, is used in arithmetic. Its ten digits are "0"–"9".

The Duodecimal (dozenal) system :
Sometimes advocated due to divisibility by 2, 3, 4, and 6. It was traditionally used as part of quantities expressed in dozens and grosses.
Its 12 digits are "0"–"9" and "A"-"B" or "a"-"b".
Example : $\overline{31}^{(10)} = \overline{27}^{(12)}$

Example : $\overline{31}^{(10)} = \overline{1F}^{(16)}$
Example : $\overline{31}^{(10)} = \overline{1B}^{(20)}$