# What is Octal Number system? DLD digital logic design

Last modified on May 26th, 2018 at 2:08 pm

**What is Octal Number system?**

- The Octal number is a number system with base 8 and digits range is from 0 to 7.
- Octal number system was used in past and now a days it is not used in modern digital systems.
- Each Octal Number digit is basically 2
^{3}=8 and represent a 3-bit Binary Number. - Binary Numbers and the Octal equivalents are discussed in the table below;

Decimal | Binary | Octal |

0 | 000 | 0 |

1 | 001 | 1 |

2 | 010 | 2 |

3 | 011 | 3 |

4 | 100 | 4 |

5 | 101 | 5 |

6 | 110 | 6 |

7 | 111 | 7 |

Table: Octal Equivalents of Binary and decimal Numbers

**Counting in Octal Number System**

- The maximum value that can be represented by a one single octal digit is 7 because it starts from 0 and octal means 0 to 8.
- Decimal 8 can be represented by a combination of 10
_{8}. - The subscript 8 in 10
_{8}indicates that the number is Octal. - Some of the Octal Numbers for Decimal numbers 8 to 30 are discussed in table below;

Decimal | Octal | Decimal | Octal | Decimal | Octal | ||

8 | 10 | 16 | 20 | 24 | 30 | ||

9 | 11 | 17 | 21 | 25 | 31 | ||

10 | 12 | 18 | 22 | 26 | 32 | ||

11 | 13 | 19 | 23 | 27 | 33 | ||

12 | 14 | 20 | 24 | 28 | 34 | ||

13 | 15 | 21 | 25 | 29 | 35 | ||

14 | 16 | 22 | 26 | 30 | 36 | ||

15 | 17 | 23 | 27 | 31 | 37 | ||

Table: | Octal Numbers upper than 0 to 7 |

**Thanks:** Hopefully you are now able to understand the octal number systems