Number Systems

A number system defines a set of values used to represent quantity. We talk about the number of people attending classes, the number of modules taken per student and also use numbers to represent grades achieved by students in tests.

Quantifying values and items in relation to each other is helpful for us to make sense of our environment. We do this at an early age; figuring out if we have more toys to play with, more presents, more dollies and so on.

The study of number systems is not just limited to computers. We apply numbers every day and knowing how numbers work will give us an insight into how a computer manipulates and stores numbers.

Mankind through the ages has used signs or symbols to represent numbers.

Important Definitions Related to All Numbering Systems:

All the numbering systems have a few common elements as follows:

The number of values that a digit (one character) can assume is equal to the base of the system: It is also called as the Radix of the system.

For example for a decimal system, the base is "10" hence every digit can assume 10 values (0, 1, 2, . . ., 9).

The largest value of a digit is always one less than the base:

For example, the largest digit in a decimal system is 9. (One less than the base 10).

Each digit position (place) represents a different multiple of base i.e. the numbers have positional importance. For example consider the decimal number (349.25)₁₀.

Hence we can implement a common rule for all the numbering systems as follows. For a general number, we have to multiply each of digit by some power of base (B) or radix as shown in figure below.