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Convert Decimal to Octal

We frequently use the decimal number system in our daily lives. Other number systems, such as binary, octal, and hexadecimal, are essential in the realm of computers and digital systems. Anyone interested in computer science, electronics, or programming needs to know how to convert numbers between these systems. The conversion from decimal to octal is one such significant conversion. This manual takes you step-by-step through the entire idea in an easy-to-follow format.

Table of Content

Definition
What is Decimal?
What is Octal?
How to Convert Decimal to Octal
Decimal to Octal Table
Solved Examples
Practice Questions
Real Life Examples
Conclusion
FAQs on Convert Decimal to Octal

Definition

Changing a number from base-10 (decimal) to base-8 (octal) is known as conversion from decimal to octal. Because octal representations are shorter than binary and simpler for humans to read, this is helpful in computing.

What is Decimal?

The standard method for identifying both integer and non-integer numbers is the decimal number system. Because it is based on ten digits - 0 through 9 - it is also referred to as the base-10 system. A power of 10 is represented by each position in a decimal number.

For example:

524 in decimal = 5 x 10^2 + 2 x 10^1 + 4 x 10^0 = 500 + 20 + 4

What is Octal?

Base-8, another name for the octal number system, has eight digits: 0 through 7. A power of eight is represented by each place value. Because each octal digit precisely corresponds to three binary digits, octal numbers are frequently used in computing as a more readable representation of binary code.

For example:

Octal number 725 = 7 x 8^2 + 2 x 8^1 + 5 x 8^0 = 448 + 16 + 5 = 469 in decimal

How to Convert Decimal to Octal

Use these procedures to change a decimal number to an octal number:

Step 1: Divide the decimal number by eight.

Step 2: Write down what's left.

Step 3: Divide by 8 once more using the quotient from Step 1.

Step 4: Continue until the quotient equals zero.

Step 5: Write the remainders from last to first in reverse order. The octal number will be this.

Decimal to Octal Table

Decimal	Octal	Decimal	Octal
0	0	10	12
1	1	11	13
2	2	12	14
3	3	13	15
4	4	14	16
5	5	15	17
6	6	16	20
7	7	20	24
8	10	25	31
9	11	30	36

Solved Examples

Example 1: Convert 45 to octal.

45 ÷ 8 = 5 remainder 5
5 ÷ 8 = 0 remainder 5
Read remainders from bottom to top: 55

Answer: 45 in decimal = 55 in octal

Example 2: Convert 100 to octal.

100 ÷ 8 = 12 remainder 4
12 ÷ 8 = 1 remainder 4
1 ÷ 8 = 0 remainder 1
Read remainders: 144

Answer: 100 in decimal = 144 in octal

Example 3: Convert 255 to octal.

255 ÷ 8 = 31 remainder 7
31 ÷ 8 = 3 remainder 7
3 ÷ 8 = 0 remainder 3
Read remainders: 377

Answer: 255 in decimal = 377 in octal

Example 4: Convert 64 to octal

64 ÷ 8 = 8 remainder 0
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Read remainders: 100

Answer: 64 in decimal = 100 in octal

Example 5: Convert 128 to octal

128 ÷ 8 = 16 remainder 0
16 ÷ 8 = 2 remainder 0
2 ÷ 8 = 0 remainder 2
Read remainders: 200

Answer: 128 in decimal = 200 in octal

Example 6: Convert 300 to octal

300 ÷ 8 = 37 remainder 4
37 ÷ 8 = 4 remainder 5
4 ÷ 8 = 0 remainder 4
Read remainders: 454

Answer: 300 in decimal = 454 in octal

Example 7: Convert 512 to octal

512 ÷ 8 = 64 remainder 0
64 ÷ 8 = 8 remainder 0
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Read remainders: 1000

Answer: 512 in decimal = 1000 in octal

Example 8: Convert 90 to octal

90 ÷ 8 = 11 remainder 2
11 ÷ 8 = 1 remainder 3
1 ÷ 8 = 0 remainder 1
Read remainders: 132

Answer: 90 in decimal = 132 in octal

Practice Questions

Convert 64 to octal
Convert 128 to octal
Convert 75 to octal
Convert 200 to octal
Convert 300 to octal
Convert 512 to octal
Convert 350 to octal
Convert 23 to octal
Convert 90 to octal
Convert 1000 to octal

Real Life Examples

Digital Clocks and Timers: When working with bits and binary-coded formats, embedded system programming occasionally uses octal values.
Unix File Permissions: Octal numbers (such as chmod 755) are used by Unix and Linux file permission systems to indicate read, write, and execute permissions.
Programming in Assembly Language: Octal representations make it easier to understand machine instructions in low-level programming.
Old Computers and Hardware: Memory addresses and instructions were frequently represented in octal rather than hexadecimal by earlier computing systems.

Conclusion

In computer science and digital electronics, knowing how to convert decimal numbers to octal is essential. It connects machine-level instructions with human-readable numbers. Although decimal numbers are simpler for people to comprehend, octal offers a more readable and compact representation of binary. For developers, engineers, and students working with digital systems, embedded programming, and data encoding, mastering this conversion process is crucial.

Anyone can easily learn to convert decimal numbers into octal with regular practice and comprehension of the step-by-step procedure. It develops a solid foundation in number systems used in contemporary computing in addition to improving numerical literacy.

Related Links:

Conversions: Fractions to Decimals, Decimals to Fractions -Click & learn more about conversion of decimals!

Decimal to Binary Numbers -Convert Decimal to Binary Numbers Quickly – Learn Rules, Methods, and Practice Questions!

Frequently Asked Questions on Converting Decimal to Octal

1. How to convert a decimal to octal?

Use these procedures to change a decimal number to an octal one:

First, divide the decimal number's integer component by 8.
Step 2: Put the rest in writing.
Step 3: Keep dividing the quotient by 8 until it equals zero.
Step 4: Determine the octal number by reading the remainders backwards.
For decimals that contain a fraction, take the integer portion of each result after repeatedly multiplying the fractional part by 8 (until the fraction becomes 0 or you get enough digits).