Convert Octal to Binary

Dhristi JEE 2022-24

Octal to Binary Conversion

The octal number system is a base - 8 number system. It implies that this number system includes a total of 8 symbols such as 0, 1, 2, 3, 4, 5, 6, and 7 to represent any values. In computer, the octal number system is represented as:

  • Writing 8 as a suffix of the value (eg. 765₈).

On the other hand, the binary number system is a base-2 number system that primarily includes only 2 symbols such as 0 and 1 to represent any values. In computer, the binary number system is represented as:

  • Writing 2 as a suffix of the value (eg. 765₂).

Read on to know how to convert the octal number system to the binary number system. 


How to Convert Octal to Binary?

Conversion of octal to binary is a straightforward process because octal numbers are shortened versions of binary strings. For the process of conversion, every digit in the given octal number should be converted to a 3-bit binary number and hence arriving at the binary equivalent of the octal number. Octal numbers can also be converted to the equivalent binary number indirectly (first decimal then binary). Following is the table representation for the conversion of octal numbers into binary numbers and vice versa directly.

Octal

Binary

0

000

1

001

2

010

3

011

4

100

5

101

6

110

7

111


Let us understand octal to binary numbers using the direct method with an example:


Example 1:

Convert 76 to Its Equivalent Binary Number.

Solution:

Given an octal number i.e. 76₈. With the help of the table given below, we can write 76₈ in binary number as 111110₂. 

Therefore, 76₈ = 111110₂.


Octal to Binary Conversion (Indirect Method)

Conversion of octal to binary using an indirect method is a two-way process. In the indirect method, we will first convert the given octal number into its equivalent decimal number and in the next step, we will convert the decimal number into its equivalent binary number. 

Let us first understand Octal to Decimal conversion. 

To convert the octal number (base - 8) to the decimal number (base - 10), we will use the octal place value to add the base-10 value of each digit.

Each time you move towards the left in the octal number system, the value increases eight times. 


Octal Place Value

8⁵

32,768

8⁴

4,096

512

64

8

1

2

7

5

4

9

4


In the octal number, the digit values go from 0 to 7, the numbers 8 and 9 are not allowed. 


Decimal to Binary Conversion

Following are the steps to convert the obtained decimal number into its equivalent binary number.

  • Step 1: Divide the obtained decimal number by 2 and write down the remainder.

  • Step 2: Now, divide the quotient that is obtained in the above steps by 2, and note the remainder again.

  • Step 3: Repeat the above two steps until you get 0 as the quotient.

  • Step 4: Now, list down the remainder in such a way that the last remainder is written first, followed by the rest in the reverse order.

This process can also be understood in another way which states that the Least Significant Bit (LSB) of the binary number will be placed at the top and the Most Significant Bit (MSB) will be placed at the bottom. This number obtained will be the binary value of the given decimal number.


Octal To Binary Conversion Example (Indirect Method)

Convert 634₈ to a binary number.

Solution:

We will first convert the given octal number into its equivalent decimal number. Let us learn the steps.

Step 1: Write down the given octal number, expressing it as a power of 8 starting from right to left for each integer value. The power of 8 from the right side starts with 0 as shown below.

6 x 8² + 3 x 8¹ + 4 x 8º

Step 2:  Write down the place value of each digit of the given octal number.

  • 8º  = 4

  • 8¹ = 3 

  • 8²  = 6

Step 3: Multiply the above-obtained power of 8 values with its respective octal digit as shown below:

  • 6 x 64  = 384

  • 3 x 8 = 24

  • 4 x 1 = 4

Step 4: Sum up the resultant values obtained in the above step after the multiplication of each octal digit and the octal weights or power of 8 values.

= 384 + 24 + 4

= 412

Hence,  634₈ = 412₁₀

Now, we will convert the resultant decimal number into its equivalent binary number.

Decimal Number = 412₁₀


Divide by 2

Result

Remainder

Binary Value

412 ÷ 2

206

0

0 (LSB)

206 ÷ 2

103

0

0

103 ÷ 2

51

1

1

51 ÷ 2

25

1

1

25 ÷ 2

12

1

1

12 ÷ 2

6

0

0

6 ÷ 2

3

0

0

3 ÷ 2

1

1

1

1 ÷ 2

0

1

1 (MSB)


Therefore, the binary equivalent for the given octal number 634₈ is 110011100₂.

634₈ = 110011100₂


Octal to Binary Converter

Octal to binary converter is an easy-to-use online converter that enables you to convert the given octal numbers into their equivalent binary number in a fraction of seconds. To operate the octal to binary converter given below, you must enter a given octal number in the input field below and hit the Convert button. The converter will give you the binary equivalent of the given octal number.


Octal Value


Convert


Binary Value


Solved Example

1. Convert (305)₈ to its Equivalent Binary Number Using the Direct Method.

Solution:

Given an octal number i.e. (305)₈. With the help of the table given below, we can write (305)₈ in binary number as (011 000 101)₂. 

Therefore, (305)₈ = (011 000 101)₂.


2. Convert (145)₈ to a Binary Number Using the Indirect Method.

Solution:

We will first convert the given octal number into its equivalent decimal number. Let us learn the steps.

Step 1: Write down the given octal number, expressing it as a power of 8 starting from right to left for each integer value. The power of 8 from the right side starts with 0 as shown below.

1 x 8² + 4 x 8¹ + 5 x 8⁰

Step 2:  Write down the place value of each digit of the given octal number.

  • 8  = 1

  • 8¹ = 4

  • 8²  = 5

Step 3: Multiply the above-obtained power of 8 values with its respective octal digit as shown below:

  • 1 x 64  = 64

  • 4 x 8 = 32

  • 5 x 1 = 1

Step 4: Sum up the resultant values obtained in the above step after the multiplication of each octal digit and the octal weights or power of 8 values.

= 64 + 32 + 5

= 101

Hence, (145)₈ = (101)₁₀

Now, we will convert the resultant decimal number into its equivalent binary number.

Decimal Number = (101)₁₀


Divide by 2

Result

Remainder

Binary Value

101 ÷ 2

50

1

1

50 ÷ 2

25

0

0

25÷ 2

12

1

1

12 ÷ 2

6

0

0

6 ÷ 2

3

0

0

3 ÷ 2

1

1

1

1 ÷ 2

0

1

1


Therefore, the binary equivalent for the given octal number (145)₈ is (1100101)₂

(145)₈ =  (1100101)₂

FAQs on Convert Octal to Binary

1. What is Octal to Binary Converter?

Ans: Octal to binary converter is a free online tool specifically designed to convert the given octal number into binary number and vice versa at no time. 

2. What is the Drawback of the Octal to Number System?

Ans: The main drawback of octal numbers is that computers do not understand the octal number system so there is an additional requirement of octal to binary converters before it is applied to computers.  

3. What are the Symbols Used in the Octal Number System?

Ans: The octal number system is a number system of base 8 which implies that we require 8 different symbols i.e. 0, 1, 2, 3,4, 5, 6, and 7 to represent any number in the octal number system. The smallest two-digit number in the octal number system is equivalent to 8.

4. What is the Use of the Octal Number System?

Ans: Octal number systems are widely used in the aviation sector and also in the computer application sector to use ers in the form of code. Octal number systems are also used in a programming language to do coding or write the encrypted language, which is only understood by a computing machine.

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