The number system which uses eight symbols or digits is referred to as octal number system.

This number system uses only the digits ranging from zero(

**0**) to seven(

**7**) for counting as well as performing various arithmetic operations.

Even though the name of the number system is octal number system, the digit 8 is not used in this number system.

The radix or base in octal number system is 8

**since it involves eight (**

**8**) symbols.

In this number system the weights are all powers of 8.

The generic format for representing any number in binary number system is as show below

**8**

^{4}8^{3}8^{2}8^{1}8^{0}8^{-1}8^{-2}8^{-3}8^{-4 }←**Weights**

S_{4 } | S_{3 } | S_{2 } | S_{1 } | S_{0 } | . | S_{-1 } | S_{-2 } | S_{-3 } | S_{-4 } |

**↑**

**↑**

**↑**

**MSD Octal point LSD**

where

**MSD i the most significant digit**

**LSD is the least significant digit**

**S**

_{1}**,S**

_{2}**,S**

_{3 ....}**Sn**

_{ }**are values assigned.**

Representing larger numbers in binary number system was a difficult task and hence the other two number systems namely octal number system and hexadecimal number system were introduced.