Number systems: Introduction, types

Number systems are used in different areas with various types. Now we mostly use positional number systems.

Number systems

Number systems are a collection of digits and symbols.  Digits are various symbols. In our life, for counting, we have to use different types of number systems.

Previously we have discussed the history of number invention.


There are two basic types of number systems.
  1. Non-positional number systems
  2. Positional number systems

Number system introduction

Non-positional number systems


Use symbols such as I for 1, II for 2, III for 3, IIII for 4, IIIII for 5, etc.
Each symbol represents the same value regardless of its position in the number.
The symbols are simply added to find out the value of a particular number.


It is difficult to perform arithmetic with such a number system.

Number system introduction

Positional number systems


Use only a few symbols called digits.
These symbols represent different values depending on the position they occupy the number.

The value of each digit is determined by:
  • The digit itself
  • The position of the digit in the number
  • The base of the number system


The base is the total number of digits in the number system.

The maximum value of a single digit is always equal to one less than the value of the base.

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