HowTo: Convert Octal numbers to other number systems

 

Octal number system is a system with base or radix 8, meaning there are only 8 digits in this system, them being 0-7. In this post we will see how to convert Octal numbers to decimal, binary and hexadecimal number systems.

Octal To Decimal 

To convert Octal numbers into the Decimal system, all we have to do is multiply each digit of the Octal number with its place value, that is 8ⁿ or 8^-n. Eg:-

To convert 127(8) to decimal number system, we do:

1 * 8² + 2 * 8¹ + 7 * 8⁰ which is equal to 87. That is 127(8) = 87(10).

Octal To Binary

To convert Octal numbers to the binary systems, we have to convert each digit of the Octal number into its corresponding 3 bit Binary equivalent. Eg:-

To convert 127(8) to its binary equivalent, we do:

1(8) = 001(2)

2(8) = 010(2)

7(8) = 111(2)  

Therefore, 127(8) = 001010111(2) or simply 1010111(2).

 

Octal To Hexadecimal  

To convert Octal numbers to Hexadecimal number systems, we have to first convert the Octal number to its binary equivalent, and then convert that into its hexadecimal equivalent. To know how to convert Binary to Hexadecimal, click here