102 LearnersLast updated on July 16th, 2025
Octal to Binary Conversion
In the realm of number systems, we encounter different bases like decimal, binary, octal, and hexadecimal. Each base is used for various applications, especially in computing and digital electronics. The octal system has a base of 8 and uses digits from 0 to 7, while the binary system is base 2, using only digits 0 and 1. Sometimes, we need to convert numbers from octal to binary to simplify calculations or for specific applications in digital systems. In this topic, we will learn how to convert octal numbers to binary.
What is the Octal System?
The octal system is a base-8 number system used in computing and digital electronics.
It uses eight digits, ranging from 0 to 7.
Octal is sometimes used as a shorthand or intermediate step in computing due to its easy conversion to binary.
Each octal digit corresponds to a unique 3-bit binary sequence, making conversions straightforward.
What is the Binary System?
The binary system is a base-2 number system fundamental to computer systems and digital electronics.
It uses only two digits, 0 and 1, to represent numbers. Each binary digit is called a bit.
Binary is used because it aligns well with the two-state nature of electronic circuits, which can be either on or off.
Octal to Binary Conversion Formula
To convert octal to binary, we use the following approach:
Each octal digit is converted into its equivalent 3-digit binary number.
Binary = So, to convert from octal to binary, replace each octal digit with its 3-bit binary equivalent.
This process is straightforward due to the direct mapping between octal and binary.
How to Convert Octal to Binary?
Converting octal to binary is simple using direct mapping.
Since each octal digit converts directly to a 3-bit binary sequence, we can convert octal to binary by replacing each octal digit with its corresponding binary equivalent.
Steps to convert octal to binary: Write down the octal number. Replace each octal digit with its 3-digit binary equivalent. Example: Octal 7 = Binary 111
Octal to Binary Conversion Chart
When working with number systems, sometimes we use octal and sometimes binary.
We use simple conversions to understand how an octal number translates to binary.
Below is a chart that shows us the octal-to-binary conversions.
Common Mistakes and How to Avoid Them in Octal to Binary Conversion
When converting octal to binary, students often make mistakes. Here are some common mistakes to help understand the concepts of conversions better.
Mistake 1
Using the wrong binary equivalent
Students get confused and use incorrect binary values for conversion, such as representing octal 5 as 1010 instead of 101.
Mistake 2
Omitting leading zeros
Students might omit necessary leading zeros in binary numbers, leading to incorrect results.
For example, they might write octal 4 as binary 100 instead of 100.
Mistake 3
Misplacing binary bits
Students can misplace binary bits, which leads to incorrect values. For example, instead of writing the binary for octal 3 as 011, they might write it as 110.
Mistake 4
Incorrect grouping of bits
Students sometimes group bits incorrectly when converting larger numbers. Each octal digit should map to exactly three binary bits.
Mistake 5
Misunderstanding the base systems
Students often get confused about the base systems. They might think octal 8 exists, but it doesn't. Remember, octal only uses digits 0 to 7.
Octal to Binary Conversion Examples
Problem 1
Convert octal 345 to binary.
Octal 345 = Binary 011 100 101
Explanation
We know the conversion: Octal 3 = Binary 011 Octal 4 = Binary 100 Octal 5 = Binary 101 Now, placing them together: 345 in octal = 011 100 101 in binary.
Problem 2
Convert octal 17 to binary.
Solution: Converting octal 17 to binary gives us 001 111.
Explanation
Use the conversion: Octal 1 = Binary 001 Octal 7 = Binary 111 Now, place them together: 17 in octal = 001 111 in binary.
Problem 3
A digital sensor outputs octal 701. What is the output in binary?
The binary output is 111 000 001.
Explanation
Convert each octal digit to binary: Octal 7 = Binary 111 Octal 0 = Binary 000 Octal 1 = Binary 001 Output = 111 000 001 in binary.
Problem 4
The memory address is given in octal 256. What is its binary equivalent?
The binary equivalent is 010 101 110.
Explanation
Convert each octal digit to binary: Octal 2 = Binary 010 Octal 5 = Binary 101 Octal 6 = Binary 110 Address = 010 101 110 in binary.
Problem 5
Converting octal 74 to binary.
Octal 74 = Binary 111 100
Explanation
Step 1: Convert each digit: Octal 7 = Binary 111 Octal 4 = Binary 100 Step 2: Combine them: 74 in octal = 111 100 in binary.
FAQs on Octal to Binary Conversion
1.How do you convert octal to binary?
2.What is octal 10 in binary?
3.How do you convert binary back to octal?
4.What is the binary equivalent of octal 12?
Important Glossaries for Octal to Binary Conversion
- Binary: A base-2 number system that uses digits 0 and 1.
- Bit: The smallest unit of data in a computer, representing a binary digit.
- Octal: A base-8 number system that uses digits 0 to 7.
- Conversion: The process of changing a number from one base to another.
- Digit: A single numerical symbol used to represent numbers in different bases.
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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
