103 LearnersLast updated on July 9th, 2025
Decimal to Octal Conversion
Numbers can be represented in different numeral systems such as decimal, binary, octal, and hexadecimal. The decimal system, which is base 10, is the most commonly used system in everyday life, consisting of the digits 0 to 9. The octal system, which is base 8, uses the digits 0 to 7. Sometimes, it is necessary to convert numbers from decimal to octal for various applications in computing and digital electronics. In this topic, we will learn how to convert decimal numbers to octal.
What is Decimal?
A decimal is a number in the base-10 numeral system, which is the standard system for denoting integers and non-integer numbers. It is based on the powers of 10 and includes the digits 0 through 9. Decimal numbers are widely used in everyday life for counting and basic arithmetic. The decimal system is intuitive for humans because it is likely based on the use of ten fingers for counting.
What is Octal?
The octal numeral system, or base-8 number system, uses eight symbols: 0 to 7. It is sometimes used in computing and digital electronics because it is more compact than binary and can easily be converted to and from binary. Each octal digit represents three binary digits (bits), making conversions between these systems straightforward.
Decimal to Octal Formula
To convert a decimal number to octal, you repeatedly divide the decimal number by 8 and record the remainders. The octal number is formed by the remainders read in reverse order.
Steps:
1. Divide the decimal number by 8.
2. Record the remainder.
3. Use the quotient as the new number to divide by 8.
4. Repeat this process until the quotient is zero.
5. The octal equivalent is the remainders read from bottom to top.
How to Convert Decimal to Octal?
Converting a decimal number to octal involves using repeated division by 8. Here's a step-by-step guide:
1. Write down the decimal number.
2. Divide the number by 8 and write down the remainder.
3. Take the quotient and divide it again by 8, noting the new remainder.
4. Continue this process until the quotient is zero.
5. The octal number is the string of remainders read in reverse order.
Decimal to Octal Conversion Chart
When converting between numeral systems, charts can be helpful. Below is a chart that shows decimal numbers and their corresponding octal equivalents for reference. This can help in understanding how numbers are represented differently in each system.
Common Mistakes and How to Avoid Them in Decimal to Octal Conversion
When converting decimal numbers to octal, students often make mistakes. Here are some common errors to be aware of and how to address them.
Mistake 1
Using incorrect division
Students sometimes use the wrong divisor. Remember that for decimal to octal conversion, you must divide by 8, not any other number.
Mistake 2
Misreading the remainders
It’s crucial to read the remainders in reverse order to get the correct octal representation. Some students mistakenly read them in the order they were found.
Mistake 3
Ignoring leading zeros
Students may ignore leading zeros in the octal result, which can cause errors in certain contexts where the number of digits is significant. Always consider the full representation.
Mistake 4
Confusion with binary conversion
Since both octal and binary systems are used in computing, students may confuse the two and use binary conversion methods instead of octal.
Mistake 5
Rounding errors
Some students might incorrectly round the division results instead of taking the integer quotient and remainder, leading to wrong conversions.
Decimal to Octal Conversion Examples
Problem 1
Convert 156 to Octal
156 in decimal is 234 in octal.
Explanation
Divide 156 by 8:
156 ÷ 8 = 19 remainder 4
19 ÷ 8 = 2 remainder 3
2 ÷ 8 = 0 remainder 2 Octal: 234
Problem 2
Convert 27 to Octal
27 in decimal is 33 in octal.
Explanation
Divide 27 by 8: 27 ÷ 8 = 3 remainder 3
3 ÷ 8 = 0 remainder 3 Octal: 33
Problem 3
Convert 512 to Octal
512 in decimal is 1000 in octal.
Explanation
Divide 512 by 8: 512 ÷ 8 = 64 remainder 0
64 ÷ 8 = 8 remainder 0
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1 Octal: 1000
Problem 4
The decimal number 100 is what in octal?
100 in decimal is 144 in octal.
Explanation
Divide 100 by 8: 100 ÷ 8 = 12 remainder 4
12 ÷ 8 = 1 remainder 4
1 ÷ 8 = 0 remainder 1 Octal: 144
Problem 5
Convert 345 to Octal
345 in decimal is 531 in octal.
Explanation
Divide 345 by 8: 345 ÷ 8 = 43 remainder 1
43 ÷ 8 = 5 remainder 3
5 ÷ 8 = 0 remainder 5 Octal: 531
FAQs on Decimal to Octal
1.How is 1 in decimal represented in octal?
2.What is 64 in octal?
3.Why do we use octal numbers?
4.How do I convert 255 from decimal to octal?
Important Glossaries for Decimal to Octal Conversion
- Conversion: The process of changing a number from one numeral system to another, such as decimal to octal.
- Remainder: The number left after division when one integer does not divide the other exactly.
- Base: The number of unique digits, including zero, used to represent numbers in a positional numeral system. Decimal is base-10, and octal is base-8.
- Quotient: The result of division, not including the remainder.
- Numeral System: A writing system for expressing numbers; includes decimal, octal, binary, etc.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
