How to Convert Octal to Binary Number System

 

The octal number system is a base-8 number system. This means that it has a total of 8 symbols, 0,1,2,3,4,5,6,7 for representing the values and The binary number system, on the other hand, is a base-2 number system. This means that it has a total of 2 symbols, 0 and 1, for representing the values. In this article, you will learn the conversion of octal to binary with the help of examples. Here, the following conversion of octal to binary is explained.

Converting a number from Octal to Binary Number System

There are two ways to convert octal to binary, which are explained below.

1- The direct method of octal to binary conversion

2- Convert octal to decimal and then decimal to binary 

1- Direct method

 To convert the numbers from octal to binary, proceed with the steps given below:

◆ Step 1 −  Convert each octal digit to its 3-digit binary representation from the table. Each of the digits must be treated as a decimal value.

◆ Step 2 − Combine these binary representations to form a single binary number.

To obtain binary equivalent of any octal number, individual digits of octal number should be converted

to binary in groups of 3digits as given in the table below:

Examples  - 

Example 1 -

Calculate the Binary equivalent of the Octal number (305)₈ 

(305)₈ = (011  000  101)₂

= (011000101)₂

             

Example 2 -

Calculate the Binary equivalent of the Octal number (133.66)₈ 

(133.66)₈ = (001  011  011.110  110)₂

= (001011011.110110)₂

2- Convert octal to decimal and then decimal to binary 

 In this method , We will first convert a number from octal to decimal (base 10), Then convert that decimal number to binary . To convert a number from octal to decimal , we multiply its digits starting from the right with 8 raised to exponents from 0 and then add the values. So, the first digit from right will be multiplied by 8⁰ , Which is equal to 1, the second digit will be multiplied by 8¹ = 8, and so on.

Example

Calculate the Binary equivalent of the Octal number (56)₈ .

First, we convert octal to decimal

(56)₈ = 6 × 8⁰ = 5 × 8¹

= 6 × 1 + 5 × 8

= 6 + 40

= 46

(56)₈ = (46)₁₀

then , Convert (46)₁₀ to binary  number system

(46)₁₀ = (101110)₂

So, (56)₈ = (101110)₂

At the end of this article We will use Logic Kit app to show you an example of octal to binary conversion,

So you can Download "Logic Kit" app on App Store to have help  with Number System conversion and all the topics of number system and Boolean algebra with steps. 

 Click here to download the app.