What is Octal Number system? DLD digital logic design

By Prof. Fazal Rehman Shamil
Last modified on May 27th, 2019

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 108.
  • The subscript 8 in 108 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

Prof.Fazal Rehman Shamil (Available for Professional Discussions)
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