How to Convert a Decimal Number into an Octal number | Number System

In this blog, we will learn to convert a decimal number into an octal number.

Before, start this topic let’s take a recap on what is a decimal number or an octal number.

Decimal Number – Decimal Number are those number who uses 10 digits of a number system 0 to 9 (0,1,2,3,4,5,6,7,8,9) and the base of a decimal number is 10. Example: 9₁₀, 25₁₀, 48₁₀, 152₁₀ etc. These numbers are known as “Decimal Number”

Octal Number – Octal Number are those number who uses 8 digits of a number system 0 to 7 (0,1,2,3,4,5,6,7) and the base of the octal number is 8. Example: 6₈, 13₈, 24₈ etc. This number is known as “Octal Number”

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As always let start with the example.

Example 1: Convert a Decimal Number (9)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process.

Decimal no. ÷ by 8	Quotient	Remainder
9 ÷ 8	1	1
1 ÷ 8	0	1

Now, write all the remainder from downward to the upward manner like this 1 and 1 = 11.

Hence, the conversion of decimal to octal is (11)₈

Example 2: Convert a Decimal Number (26)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process.

Decimal no. ÷ by 8	Quotient	Remainder
26 ÷ 8	3	2
3 ÷ 8	0	3

Now, write all the remainder from downward to the upward manner like this 3 and 2 = 32

Hence, the conversion of decimal to octal is (32)₈

Example 3: Convert the Decimal Number (93)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process.

Decimal no. ÷ by 8	Quotient	Remainder
93 ÷ 8	11	5
11 ÷ 8	1	3
1 ÷ 8	0	1

Now, write all the remainder from downward to the upward manner like this 1, 3, and 5 = 135.

Hence, the conversion of decimal to octal is (135)₈

Example 4: Convert the Decimal Number (176)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process

Decimal no. ÷ by 8	Quotient	Remainder
176 ÷ 8	22	0
22 ÷ 8	2	6
2 ÷ 8	0	2

Now, write all the remainder from downward to the upward manner like this 2, 6, and 0 = 260.

So, our answer is (260)₈

Hence, the conversion of decimal to octal is (260)₈

Example 5: Convert the Decimal Number (242)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process

Decimal no. ÷ by 8	Quotient	Remainder
242 ÷ 8	30	2
30 ÷ 8	3	6
3 ÷ 8	0	3

Now, write all the remainder from downward to the upward manner like this 3, 6, and 2 = 362.

So, our answer is (362)₈.

Hence, the conversion of decimal to octal is (362)₈.

Example 6: Convert the Decimal Number (758)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process

Decimal no. ÷ by 8	Quotient	Remainder
758 ÷ 8	94	6
94 ÷ 8	11	6
11 ÷ 8	1	3
1 ÷ 8	0	1

Now, write all the remainder from downward to the upward manner like this 1, 3, 6, and 6 = 1366.

So, our answer is (1366)₈.

Hence, the conversion of decimal to octal is (1366)₈.

Example 7: Convert the Decimal Number (1472)₁₀ into Octal?

Sol:

To convert this number, we have to divide the given number by 8 until the quotients come to 0. So, let start the dividing process

Decimal no. ÷ by 8	Quotient	Remainder
1472 ÷ 8	184	0
184 ÷ 8	23	0
23 ÷ 8	2	7
2 ÷ 8	0	2

Now, write all the remainder from downward to the upward manner like this 2, 7, 0, and 0 = 2700.

So, our answer is (2700)₈.

Hence, the conversion of decimal to octal is (2700)₈.

Conclusion:

Today I have told you about how to convert a decimal number into an Octal Number. I hope you understand very well. In case If you have any problem understanding something then let me know in the comment section, I will try to help you by replying to your comment.

So, that’s for today’s blog guys. We will meet again with the new topic,

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