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 Decimal system :
The most used system of numbers in the world, is used in arithmetic. Its ten digits are "0"–"9".
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 Hexadecimal system :
Often used in computing as a more compact representation of binary (1 hex digit per 4 bits).
The sixteen digits are "0"–"9" followed by "A"–"F" or "a"–"f".
Example : $\overline{31}^{(10)} = \overline{1F}^{(16)}$
