Methods to Convert Octal to Binary Number System with Examples

Octal to Binary conversion is part of the Number System. Number system is a set of values used to represent different quantities and they use different number bases, and a number base indicates how many different digits are available when using a particular numbering system. Example: a number system can represent the number of students in class or viewers watching a certain TV program.

What are Binary Numbers?

Binary numbers constitute only two digits that are 0 and 1. Computers manipulate and store all of their data, including numbers, words, films, pictures, and music, using the binary number system.

What are Octal Numbers?

Octal numbers can be represented with a base of 8 and use digits from 0 to 7 i.e., 0, 1, 2, 3, 4, 5, 6, and 7 to represent numbers. The term octal is used to describe numbers with an eight-digit base.

Methods to Convert Octal to Binary

Octal number system makes it simple to convert huge binary values into smaller, more compact groups. A binary number can be converted to an octal number in different ways.

There are 2 methods to convert an octal number to a binary number:

• Method 1: Octal to Decimal and Then Decimal to Binary
• Method 2: Direct Method of Octal to Binary Conversion

Method 1: Octal to Decimal and Then Decimal to Binary

In this method, firstly convert an octal number into its equivalent decimal number, then convert the decimal number to a binary number. The steps for this are as follows:

Step 1: Convert an octal number to a decimal number.

Step 2: Convert the decimal number to a binary number.

• Take the obtained value from step 1 which is a decimal number and divide it by 2.
• Note down the remainder.
• Similarly, continue the above two steps for the quotient until the quotient is zero.
• Note down the remainder in the reverse order.
• The obtained number is the equivalent binary number for the given octal number.

Method 2: Direct Method of Octal to Binary Conversion

There is a direct method to convert an octal number to a binary number. Since there are only 8 symbols (i.e., 0, 1, 2, 3, 4, 5, 6, 7) in octal number system and its base (i.e., 8) is equivalent to 23 = 8. So, we can represent each digit of the octal number in a group of 3 bits in a binary number.

This method is simple and also works as the reverse of binary to octal conversion. The steps are explained as follows:

• Step 1: Take the given octal number as input.
• Step 2: Convert each digit of the octal number into a binary number by using the octal to binary table.
• Step 3: This will be the equivalent binary number.

Convert Octal to Binary Using Table

Octal to binary conversion can also be done by using the octal to the binary table to convert the number from base 8 to a number with base 2. Using this table we can also convert the binary number to an octal number.

The given table is used for octal to binary conversion:

Octal Number	Binary Number
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

Solved Examples

Example 1: Convert .

Solution: Binary representation of each digit of 123 is:

1 – 001

2 – 010

3 – 011

Therefore, .

Example 2: Convert .

Solution: Binary representation of each digit of 4321 is:

4 – 100

3 – 011

2 – 010

1 – 001

Therefore, .

Example: Convert (24)₈ to a binary number.

Solution:
Break the octal number 24 into individual digits:

• 2 in binary is 010
• 4 in binary is 100

Now, join them together:
(24)₈ = (010100)₂

Example 4: Convert (62)₈ to a binary number.

Solution:
Break the octal number 62 into digits:

• 6 in binary is 110
• 2 in binary is 010

Now, join them together:
(62)₈ = (110010)₂

If you are checking Octal to Binary article, also check related maths articles:
Convert Octal to Binary	Binary Number System
Octal Number System	Types of Number System
Binary Multiplication	Decimal to Octal Conversion

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