# How to Convert Binary Into Octal Number System

As you had seen in the previous blog, how to convert binary into a decimal number and decimal into binary. If you have not read our these blog, then go to this link โHow to Convert Binary to Decimal Numberโ and โHow to Convert Decimal to Binaryโ

So, today we will see โhow to convert binary into octal number systemโ. Before we start, let take a recap about Binary and Octal number.

Binary number: A binary number is a number that uses the digit only two-digit โ0โ and โ1โ and its base is 2. It is known as binary numbers. Here are some examples of binary numbers are: 101, 011, 1001, 1101, etc.

Octal number: A octal number is a number that uses the digit 0 to 7(0,1,2,3,4,5,6,7) and its base is 8. It is known as Octal Number. Here are some examples of octal numbers are: 128, 758, 2568, etc.

Example 1: Convert the binary number 1012 into Octal?

SOL:

Step 1: Firstly we have to convert 1012 into the decimal number. Letโs convert

= 1 x 22 + 0 x 21 + 1 x 20

= 510

Step 2: Now, we have to convert the number 510 into Octal form. Letโs convert

To covert this number, so we have to divide the decimal number by 8.

Hence, the octal number is 58.

Example 2: Convert the binary number 101100112 into Octal.

Sol:

Step 1: Firstly, we have to convert 101100112 into decimal form.

= 1 x 27 + 0 x 26 + 1 x 25 + 1 x 24 + 0 x 23 + 0 x 22 + 1 x 21 + 1 x 20

= 17910

Step 2: Now, we have to convert the number 17910 into Octal form. Letโs convert

To covert this number, so we have to divide the decimal number by 8.

Now, write the remainder downward to upward manner = 263

Hence, the octal number is 2638.

Example 3: Convert the Binary number 101110010012 into an Octal?

SOL:

Step 1: Firstly, we have to convert 101110010012 into decimal form.

(10111001001)โ = (1 ร 2ยนโฐ) + (0 ร 2โน) + (1 ร 2โธ) + (1 ร 2โท) + (1 ร 2โถ) + (0 ร 2โต) + (0 ร 2โด) + (1 ร 2ยณ) + (0 ร 2ยฒ) + (0 ร 2ยน) + (1 ร 2โฐ)

= (1481)โโ

Step 2: Now, we have to convert the number 1481 into Octal form. Letโs convert

To covert this number, so we have to divide the decimal number by 8.

Now, write the remainder downward to upward manner = 2711

Hence the Octal number isย (2711)8

Example 4: Convert the Binary number (1000010111111)2 into Octal?

SOL:

Step 1: Firstly, we have to convert 10000101111112 into decimal form.

=(1000010111111)โ = (1 ร 2ยนยฒ) + (0 ร 2ยนยน) + (0 ร 2ยนโฐ) + (0 ร 2โน) + (0 ร 2โธ) + (1 ร 2โท) + (0 ร 2โถ) + (1 ร 2โต) + (1 ร 2โด) + (1 ร 2ยณ) + (1 ร 2ยฒ) + (1 ร 2ยน) + (1 ร 2โฐ)

= (4287)โโ

Step 2: Now, we have to convert the number (4287)โโ into Octal form. Letโs convert

To covert this number, we have to divide the decimal number by 8.

Now, write the remainder downward to upward manner = 10277

Hence the Octal number is (10277)8.

Now, we are going to solve the decimal points question and see how they solve it.

Example 6: Convert the Binary number (100.01)2 into Octal?

SOL:

Step 1: Firstly, we have to convert (100.01)2 into decimal form. Letโs convert

=(100.01)โ = (1 ร 2ยฒ) + (0 ร 2ยน) + (0 ร 2โฐ) + (0 ร 2โปยน) + (1 ร 2โปยฒ)

= (4.25)โโ

Step 2: Now, we have to convert the number (4.25)โโ into Octal form. Letโs convert

In the decimal point question, we have to do multiply the decimal no. by 8 until the decimal is not finished.

If you multiply 4.25 with 8 then you will get 34. It means the decimal is finish. So, now we can easily convert 34 into octal. Letโs convert

Step 3: Now, we have to convert 34 into octal.

Now, write the remainder downward to upward manner = 42.

(Note: 42 is not our answer, Our answer is 4.2. This is because we have finished the decimal point by multiplying by 8 only at one time. It means we have to put a decimal only one time in after 2. So, our answer is 4.2)

Hence the octal number is (4.2)8

Example 7: Convert the Binary number (1011.001)2 into Octal?

SOL:

Step 1: Firstly, we have to convert (1011.001)2 into decimal form. Letโs convert

=(1011.001)โ = (1 ร 2ยณ) + (0 ร 2ยฒ) + (1 ร 2ยน) + (1 ร 2โฐ) + (0 ร 2โปยน) + (0 ร 2โปยฒ) + (1 ร 2โปยณ)

= (11.125)โโ

Step 2: Now, we have to convert the number (11.125)โโ into Octal form.

To convert this, firstly we have to multiply with 8 until the decimal is not finished.

If you multiply 11.125 with 8 then you will get 89. It means the decimal is finish. So, now we can easily convert 89 into octal. Letโs convert

Step 3: Now, we have to convert 89 into octal.

Now, write the remainder downward to upward manner = 131.

(Note: 131 is not our answer, Our answer is 13.1. This is because we have finished the decimal point by multiplying by 8 only at one time. It means we have to put a decimal only one time in after 1. So, our answer is 13.1)

Hence the octal number is (13.1)8

Example 8: Convert the Binary number (1011011101.001101)2 into Octal?

SOL:

Step 1: Firstly, we have to convert (1011011101.001101)2 into decimal form. Letโs convert

= (1011011101.001101)โ

= (1 ร 2โน) + (0 ร 2โธ) + (1 ร 2โท) + (1 ร 2โถ) + (0 ร 2โต) + (1 ร 2โด) + (1 ร 2ยณ) + (1 ร 2ยฒ) + (0 ร 2ยน) + (1 ร 2โฐ) + (0 ร 2โปยน) + (0 ร 2โปยฒ) + (1 ร 2โปยณ) + (1 ร 2โปโด) + (0 ร 2โปโต) + (1 ร 2โปโถ)

= (733.203125)โโ

Step 2: Now, we have to convert the number (733.203125)โโ into Octal form.

To convert this, firstly we have to multiply with 8 until the decimal is not finished.

If you multiply 733.203125 with 8 then you will get 5865.625. It still not finished the decimal point, so we have to multiply this number with 8.

When we multiply the number 5865.625 with 8 then itโll give us 46925. It means the decimal point is now is finish. So, now we can easily convert 46925 into octal. Letโs convert

Step 3: Now, we have to convert 46925 into octal. So, letโs convert it

Now, write the remainder downward to upward manner = 133515

(Note: As you know that 133515 is not our answer, Our answer is 1335.15. This is because we have finished the decimal point by multiplying by 8 at two time. It means we have to put a decimal two time in after 15. So, our answer is 1335.15)

Hence the octal number is (1335.15)8

## Conclusion:

I have told you that how to convert the binary number into octal number. If you do not understand, then tell me in the comment section so that I come with a new method for you. I know this method is a bit lengthy and the same is explained in easy way on other website. So, Donโt worry guys, I will come with the table method in the upcoming so that you can learn both the method.

So, thatโs for todayโs blog guys. We will meet again with the new topic, till then you read our old blog and tell me that if I have made any mistake in my content so please tell me in the comment section so that I will fix it as soon as possible. And, also give us your feedback about this website.

Thanks for reading our blog, I hope you guyโs liked our todayโs blog๐. Keep learning with computerstudypoint.com

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Top 13 Must have soft skills to Add in your resumeย  10 Best computer science skills to add in your resume 8 object oriented programming languages to learn in 2024 Top 9 Programming Projects to enhance your resume