Examples

Different characteristics that define a number system include the number of independent digits used in the number system, the place values of the different digits constituting the number and the maximum numbers that can be written with the given number of digits. Among the three characteristic parameters, the most fundamental is the number of independent digits or symbols used in the number system. It is known as the radix or base of the number system.
The decimal number system with which we are all so familiar can be said to have a radix of 10 as it has 10 independent digits, i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
the binary number system with only two independent digits, 0 and 1, is a radix-2 number system. The octal and hexadecimal number systems have a radix (or base) of 8 and 16 respectively.

We will see in the following sections that the radix of the number system also determines the other two characteristics. The place values of different digits in the integer part of the number are given by r0, r1, r2, r3 and so on, starting with the digit adjacent to the radix point. For the fractional part, these are r?1, r?2, r?3 and so on, again starting with the digit next to the radix point. Here, r is the radix of the number system. Also, maximum numbers that can be written with n digits in a given number system are equal to rn.