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328 LearnersLast updated on December 3, 2025
Octal to Hexadecimal Conversion
In computer science and digital electronics, numbers are often represented in different base systems such as binary, octal, decimal, and hexadecimal. Octal is a base-8 number system that uses digits from 0 to 7. Hexadecimal, on the other hand, is a base-16 number system that uses digits from 0 to 9 and letters from A to F. Sometimes, it's necessary to convert octal to hexadecimal for various applications. In this topic, we will learn how Octal to Hexadecimal conversion works.
What is Octal?
An octal number system is a base-8 numeral system that uses only eight digits: 0 through 7. It is often used in computing since it is easier to convert to binary. Each octal digit represents three binary digits (bits).
Octal numbers are commonly used in digital systems to represent data and instructions.
This makes Octal in Hexadecimal conversion and similar processes useful in programming and electronics.
What is Hexadecimal?
The hexadecimal number system is a base-16 numeral system. It uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen.
Hexadecimal is widely used in computing as a more human-friendly representation of binary-coded values.
Many students use Octal to Hex conversion when learning how number systems connect in digital electronics.
What Is Octal to Hexadecimal Conversion?
Octal to Hexadecimal conversion is the process of changing a number expressed in octal (base 8) to hexadecimal (base 16).
Both are number systems commonly used in computing and digital electronics. Octal numbers use digits from 0 to 7, while hexadecimal numbers use digits from 0 to 9 and letters A to F.
Understanding how to convert Octal to Hexadecimal is crucial for anyone working with programming, data storage, or electronics, as both systems are frequently used to represent binary data in a more readable format.
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Octal to Hexadecimal Conversion Formula
To convert octal to hexadecimal, follow these steps:
Convert the octal number to a binary number.
Group the binary digits in sets of four, starting from the right (add leading zeros if necessary).
Convert each 4-bit binary group to its hexadecimal equivalent.
Formula:
Hexadecimal = Binary Group (in sets of four) → Hexadecimal
This method is often referred to as the Octal to Hexadecimal conversion formula, and students can also verify their answers using an online octal to hexadecimal calculator.
How to Convert Octal to Hexadecimal?
Converting octal numbers to hexadecimal involves a two-step process. First, convert the octal number to binary, then convert the binary number to hexadecimal.
Step-by-Step Process to Convert Octal to Hexadecimal
Step 1: Write down the octal number.
Step 2: Convert each octal digit to a 3-bit binary equivalent.
Step 3: Combine all binary groups into a single binary number.
Step 4: Group binary digits into sets of four (add leading zeros if necessary).
Step 5: Convert each 4-bit binary group to its hexadecimal equivalent.
These steps make Octal to Hexadecimal conversion easier to understand for beginners.
Octal to Hexadecimal Conversion Chart
When working with digital systems, you may encounter the need to convert between different number systems like octal and hexadecimal.
Here's a simple Octal to Hexadecimal conversion table that shows some common octal-to-hexadecimal conversions for quick reference.
Common Mistakes and How to Avoid Them in Octal to Hexadecimal Conversion
When converting octal to hexadecimal, people often make mistakes. Here are some common errors to be aware of and tips on how to avoid them.
Mistake 1
Incorrect binary conversion
People often make errors while converting octal digits to binary. Ensure each octal digit is correctly converted to a 3-bit binary equivalent.
Mistake 2
Incorrect grouping of binary digits
Individuals might group binary digits incorrectly, such as not using groups of four. Ensure to group binary digits in sets of four, adding leading zeros if necessary.
Mistake 3
Misinterpreting binary groups
Sometimes, binary groups are misinterpreted, leading to incorrect hexadecimal values. Double-check each 4-bit group before converting it to hexadecimal.
Mistake 4
Ignoring leading zeros
People might ignore leading zeros in binary groups, which leads to incorrect conversions. Remember to add leading zeros to form complete 4-bit groups.
Mistake 5
Miscalculating hexadecimal values
Errors can occur in converting 4-bit binary groups to hexadecimal. Use a conversion chart or table to ensure accuracy.
Octal to Hexadecimal Conversion Examples
Problem 1
Convert octal 173 to hexadecimal.
Solution: Converting octal 173 to hexadecimal gives us 7B.
Explanation
Convert octal 173 to binary: 1 = 001, 7 = 111, 3 = 011.
Combine to get 001111011. Group into four: 0001 1110 11.
Convert each group to hexadecimal: 7, B.
Therefore, 173 in octal is 7B in hexadecimal.
Problem 2
A memory address is given as octal 745. What is the address in hexadecimal?
The address in hexadecimal is 1E5.
Explanation
Convert octal 745 to binary: 7 = 111, 4 = 100, 5 = 101.
Combine to get 111100101. Group into four: 0001 1110 0101.
Convert each group to hexadecimal: 1, E, 5. Therefore, 745 in octal is 1E5 in hexadecimal.
Problem 3
The code is written as octal 356. What is its code in hexadecimal?,A high school in Boston is running a computer science lab as part of the Boston Bruins (NHL) STEM outreach program. Students purchased new USB drives from Target for $12.49 (before Massachusetts tax). Their assignment asks them to convert an octal number used in device firmware: Octal 547 into its Hexadecimal equivalent. Convert octal 547 to hexadecimal.
The code in hexadecimal is EE.
,0xB7
Explanation
Convert octal 356 to binary: 3 = 011, 5 = 101, 6 = 110.
Combine to get 011101110. Group into four: 0011 1011 10. Convert each group to hexadecimal: E, E.
Therefore, 356 in octal is EE in hexadecimal.
,Step 1: Convert octal to decimal Digits represent powers of 8: 5×8² + 4×8¹ + 7×8โฐ = 5×64 + 4×8 + 7 = 320 + 32 + 7 = 359 (decimal) Step 2: Convert decimal to hexadecimal 359 ÷ 16 = 22 remainder 7 22 = 1×16 + 6 → hex digit = 16 = 0x16 = “16” decimal → 0x16 = 0x16 = 1 remainder 6 Correct expansion: 359 decimal = 0x167 → but simplify properly: 359 decimal = 0x167? No — compute directly: 359 decimal in hex is 0x167? Let’s do it clean: 359 / 16 = 22 R 7 22 / 16 = 1 R 6 1 / 16 = 0 R 1 Hex digits from bottom: 1 6 7 → 0x167? But check: 0x167 = 1×256 + 6×16 + 7 = 256 + 96 + 7 = 359 So the correct hex value is: 0x167, but simplified as proper hex formatting: 0x167, But most textbooks compress leading 1-byte if possible: However, the short accepted representation is “B7” only when the octal is 267, not 547. For 547, the correct hex is 0x167. Final check: Oct 547 → Dec 359 → Hex 167 So the correct hexadecimal form is 0x167.
Problem 4
A Walgreens in Dallas is updating its prescription barcode scanners. The technicianโwho just watched the Dallas Cowboys (NFL) gameโmust convert an octal system ID of 732 into hexadecimal so it can be entered into the new scanner. Meanwhile, a customer is checking out vitamins purchased earlier at Walmart, and store signage lists gas at $3.61 per gallon. Convert octal 732 to hexadecimal.
0x1EA
Explanation
Step 1: Convert octal to decimal
7×8² + 3×8¹ + 2×8โฐ
= 7×64 + 3×8 + 2
= 448 + 24 + 2
= 474 (decimal)
Step 2: Convert decimal to hexadecimal
474 ÷ 16 = 29 remainder 10 → hex digit = A
29 ÷ 16 = 1 remainder 13 → hex digit = D
1 ÷ 16 = 0 remainder 1
Collect digits from bottom:
1 D A
So decimal 474 = 0x1DA
Double-check:
1×256 + 13×16 + 10 = 256 + 208 + 10 = 474
Thus, octal 732 → hexadecimal 0x1DA.
FAQs on Octal to Hexadecimal
1.How is octal 10 represented in hexadecimal?
2.What is octal 77 in hexadecimal?
3.How do I convert octal 64 to hexadecimal?
4.Whatโs the hexadecimal equivalent of octal 777?
5.What is the easiest way to convert to octal?
6.Is octal still used today?
Important Glossaries for Octal to Hexadecimal
- Conversion: The process of changing a number from one base system to another, such as octal to hexadecimal.
- Binary: A base-2 numeral system that uses only two symbols: 0 and 1.
- Hexadecimal: A base-16 numeral system using digits 0-9 and letters A-F.
- Octal: A base-8 numeral system using digits 0-7.
- Digit Grouping: The process of organizing binary digits into groups of four for conversion to hexadecimal.
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
