Number system is fundamental system to understand how various systems operate. Different characteristics that define a number system includes,
- The number of digits used in the number system,
- The place values of the different digits which constitute the number
- The maximum numbers that are written with the given number of digits.
Among above three parameters, the most fundamental parameter is the number of symbols used in the number system which is known as the radix or base of the number system.
The decimal number system with which we are more familiar is having radix of 10. i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Similarly, the binary number system as 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.
The radix of the number system determines the other two characteristics, 1) integer part of the number given by r0, r1, r2, r3, …. and 2) fractional part, r−1, r−2, r−3 and etc.