101 LearnersLast updated on July 15th, 2025
Binary to Octal Conversion
We often need to convert numbers from one base to another in mathematics and computer science. Binary and octal are two different number systems. The binary system is a base-2 system, which uses only two digits: 0 and 1. It is used internally by almost all modern computers and computer-based devices because it is straightforward to implement with digital electronic circuitry. The octal system is a base-8 system, which uses digits from 0 to 7. Converting binary numbers to octal numbers is a common task in computing, and it helps to simplify binary numbers. In this topic, we will learn how to convert binary numbers to octal numbers.
What is Binary?
A binary number is a number expressed in the base-2 numeral system, which uses only two symbols: 0 and 1.
The binary system is the foundation of all binary code, which is used to write data and instructions in computing.
Each digit in a binary number is called a bit.
The binary system is used because it is simple to implement with electronic circuits using logic gates.
What is Octal?
The octal numeral system, or oct for short, is the base-8 number system and uses the digits 0 to 7.
It is sometimes used in computing and digital electronics because it can be easily represented with groups of three binary digits (bits).
Each octal digit corresponds to three bits, which makes it simpler to convert between binary and octal.
Binary to Octal Conversion Formula
To convert binary numbers to octal, we use a straightforward method of grouping and conversion.
We group each set of three binary digits (bits) starting from the right to left (adding zeros to the left if necessary), and then convert each group to its corresponding octal digit.
Conversely, to convert from octal to binary, we convert each octal digit to a three-bit binary number.
How to Convert Binary to Octal?
Converting binary numbers to octal numbers is simple using a standard approach.
Since one octal digit corresponds to three binary bits, we can convert binary to octal by grouping binary digits in sets of three from right to left.
Steps to convert binary to octal: Write down the binary number. If necessary, add leading zeros to make the number of digits a multiple of three.
Group the binary digits in sets of three. Convert each group into the corresponding octal digit.
Binary to Octal Conversion Chart
When working with binary and octal numbers, it's useful to have a chart to quickly convert between the two.
Below is a chart that shows us the binary-to-octal conversions for groups of three bits.
Common Mistakes and How to Avoid Them in Binary to Octal Conversion
When converting binary numbers to octal, students often make mistakes.
Here are some common mistakes to get a better understanding of the concepts of conversions.
Mistake 1
Not grouping binary digits correctly
Students might forget to group the binary digits in sets of three, leading to incorrect octal values. Always start grouping from the right.
Mistake 2
Missing leading zeros
Students often neglect to add leading zeros to make the number of binary digits a multiple of three, which can lead to incorrect groupings.
Mistake 3
Incorrect bit-to-octal conversion
When converting groups of three binary digits to octal, students might make mistakes in calculating the equivalent octal digit. Practice converting small groups to avoid errors.
Mistake 4
Confusing binary with decimal
Students sometimes confuse binary numbers with decimal numbers. Remember, binary is base-2, not base-10.
Mistake 5
Overlooking the leftmost group
When the leftmost group of binary digits has fewer than three bits, students might overlook this group. Remember to add leading zeros to complete the group.
Binary to Octal Conversion Examples
Problem 1
Convert 101101110 to Octal
101101110 in binary is 556 in octal.
Explanation
Group the binary number in sets of three from right to left: 101 101 110.
Convert each group: - 101 = 5 - 101 = 5 - 110 = 6 Thus, 101101110 = 556 in octal.
Problem 2
Convert 110011 to octal.
Solution: Converting 110011 to octal gives us 63.
Explanation
Group the binary number in sets of three: 011 001 1. Add leading zeros if necessary: 011 001 001. Convert each group: - 011 = 3 - 001 = 1 So, 110011 = 63 in octal.
Problem 3
A binary number 111001010 is given. What is its octal equivalent?
The octal equivalent is 712.
Explanation
Group the binary number in sets of three: 111 001 010. Convert each group: - 111 = 7 - 001 = 1 - 010 = 2 Thus, 111001010 = 712 in octal.
Problem 4
Convert 1001110 to octal.
The octal equivalent is 116.
Explanation
Group the binary number in sets of three: 010 011 110.
Add leading zeros if necessary: 010 011 110.
Convert each group: - 010 = 2 - 011 = 3 - 110 = 6 So, 1001110 = 116 in octal.
Problem 5
Converting 101010 to Octal
101010 in binary is 52 in octal.
Explanation
Group the binary number in sets of three: 010 101 010. Add leading zeros: 010 101 010. Convert each group: - 010 = 2 - 101 = 5 So, 101010 = 52 in octal.
FAQs on Binary to Octal
1.How do you convert binary to octal?
2.What is the octal equivalent of binary 1011?
3.Is 1101 a valid octal number?
4.How do you convert 111000 to octal?
Important Glossaries for Binary to Octal Conversion
- Binary: A base-2 numeral system using digits 0 and 1.
- Octal: A base-8 numeral system using digits 0 to 7.
- Bit: The smallest unit of data in computing, represented as 0 or 1 in binary.
- Grouping: The process of organizing binary digits into sets of three for conversion to octal.
- Conversion: The process of changing a number from one numeral system to another, such as from binary to octal.
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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
