Octal to Hexadecimal Converter – Table and Examples

Number bases are important for the representation and processing of data in digital systems and programming. The move from octal to hexadecimal is one such significant change. This blog focuses on the complexities of octal to hexadecimal conversion, emphasising how it can be applied in real life. 

What is Octal?

Before proceeding with the octal-to-hexadecimal conversion, we must first briefly understand the fundamentals of the octal and hexadecimal number systems. The Octal Number System is a number system with an eight-digit base and digits ranging from 0 to 7. A number system is a system of relating, representing, or expressing figures in colourful forms. There are four abecedarian ways to represent figures: the octal number system, the double number system, the decimal number system, and the hexadecimal number system. The octal number system is commonly used in computing, particularly in Unix file permissions and addressing.

Octal numbers can be directly converted to binary numbers in the number system, but we cannot directly convert binary numbers to octal numbers. We will first need to convert the binary number to a decimal number and then later convert that decimal number to an octal number.

Current Use of Octal

Although octal numbers may not be as popular in today’s computing world as decimal or hexadecimal systems, they are still relevant in certain areas. The Octal number system is frequently used in computer applications. The current computer systems use 16-bit, 32-bit, or 64-bit words, which are then further subdivided. The aviation industry widely uses octal numbers. Some other uses of Ocral are

Unix-like File Permissions: In Unix and Unix-like operating systems (including Linux), file permissions are typically specified in octal notation. In the octal system, each permission (read, write, and execute) is represented by a number, making it a compact and efficient approach to managing permissions.

Embedded Systems and Low-Level Programming: Due to their close connection with binary representation, octal numbers are employed for memory addressing or hardware setups in some embedded systems and low-level programming scenarios. However, this utilisation has decreased over time due to the development of hexadecimal and binary representations.

Legacy Systems: The older generation of computer systems and programming languages may still use octal representation for particular purposes. These could be legacy systems that have not yet been upgraded to more current number systems.

History of Octal

In 1801, James Anderson condemned the French for creating the metric system based on decimal arithmetic. He proposed base 8 and invented the name Octal. His work was supposed to be entirely recreational mathematics, but he suggested ditching the current systems of weights and measures and switching to a purely octal system. Interestingly enough, he noted that our current English units were already close to being an octal system.

What is Hexadecimal?

​​Hexadecimal, also called “hex”, is a base-16 numbering system used in mathematics and computer science to represent and process binary-coded data effectively. Due to its close affinity with binary representation and simplicity of conversion, it is widely used in computers.

In the hexadecimal system, numbers are represented using sixteen symbols: the digits 0 to 9 and the letters A to F, where the letter A stands for 10, the letter B stands for 11, the letter C for 12, the letter D for 13, the letter E for 14, and the letter F for 15. Each hexadecimal digit corresponds to four binary digits (bits), which makes it particularly convenient for representing and converting binary data.

Current Use of Hexadecimal?

Programmers commonly use hexadecimal numbering to simplify the binary numbering system. A linear relationship exists between 2 and 16, as 16 equals 24. As a result, the four binary digits are equal to one hexadecimal digit. Humans reduce and simplify the binary numbering systems used by computers with hexadecimal numbering systems. The following uses of Hexadecimal are:

Define Locations in Memory: When using binary to define places in memory, Hexadecimal may categorise each byte as merely two hexadecimal digits instead of eight digits.

Defining Colors: Hexadecimal defines the colours used on the website. Two hexadecimal digits describe primary colours, red, green, and blue. The format used is #RRGGBB, where RR represents red, GG represents green, and BB represents blue.

Media Access Control (MAC) Addresses: MAC addresses comprise 12 hexadecimal digits. The format is either MM:MM:MM:SS:SS:SS: SS or MMMM-MMSS-SSSS. The first six digits of the MAC address reflect the adapter manufacturer’s ID, while the final six numbers represent the adapter’s serial number.

Display Errors: Hexadecimals are useful for programmers in finding and fixing errors, as they define the memory location of the error.

History of Hexadecimal

​​In the history of early computers, there was no universal agreement on representing more than nine points. Some preferred using digits 0 to 5 with a Macron character to denote values 10–15, while others disagreed. One mathematician, Bruce A. Martin, suggested a completely new set of symbols based on bit locations, but it did not gain much acceptance. Martin also found the option of using letters A to F illogical. 

IBM introduced the current hexadecimal system in 1963 in the field of computing. A former representation with 0–9 and U–Z, the Bendix G-15, was used by computers in 1956.

Relationship Between Octal and Hexadecimal

The fact that both octal and hexadecimal are widely used as intermediate notations for binary data accounts for their similarities. Both bases were used because they are simple to convert between and work well with binary representation. Octal still has certain uses, particularly on antiquated systems with Unix file permissions. Hexadecimal has gained support due to its simpler representation and close alignment with binary.

How to Convert Octal to Hexadecimal?

Octal numbers cannot be converted directly. Here is a breakdown of the process of converting octal to hexadecimal:

Step 1: Octal to Binary Conversion
Step 2: Binary to Hexadecimal Conversion

In a nutshell, the conversion from octal to hexadecimal can be accomplished in two steps: first, the octal number is converted to binary, and then the binary number is converted to hexadecimal. You may get the octal value using the hexadecimal number system with the help of this technique.

Octal to Hexadecimal Conversion Table

With the help of the table, locate the corresponding octal value for the hexadecimal digit in the left column. Let’s say you are looking for the octal equivalent of “E.” Check the table to find that it is “16.” The same goes for “F,” which has an octal equivalent of “17.”

Please keep in mind that this database only contains individual hexadecimal digits. When converting larger hexadecimal numbers to octal, each digit must be changed to its octal equivalent before forming the final octal representation.

Formulas and Examples of Octal to Hexadecimal Conversion

Octal numbers are a base-8 number system. This means eight symbols are needed to represent values: 0, 1, 2, 3, 4, 5, 6, 7. When the subscript 8 is applied to the end of a number, it is used to distinguish an octal number.

In contrast to the decimal number system, the hexadecimal number system has a base of 16 characters. It uses 16 symbols, namely 0, 1, 2, 3, 4,5, 6, 7, 8, 9, A, B, C, D, E, and F. Attaching the subscript 16 at the end is customary to denote a number expressed in hexadecimal.

Example 1: Convert Octal (73) to Hexadecimal:

• Convert Octal to Binary:

7 (octal) = 111 (binary)

3 (octal) = 011 (binary)

Combine: 111011 (binary)

• Convert Binary to Hexadecimal:

Group binary digits in sets of four from right to left: 0011 1011

Convert each group to hexadecimal:

0011 = 3 (hexadecimal)

1011 = B (hexadecimal)

Combine: 3B (hexadecimal)

The octal number 73 corresponds to the hexadecimal number 3B.

Example 2: Convert Octal (625) to Hexadecimal:

• Convert Octal to Binary:

6 (octal) = 110 (binary)

2 (octal) = 010 (binary)

5 (octal) = 101 (binary)

Combine: 110010101 (binary)

• Convert Binary to Hexadecimal:

Group binary digits in sets of four from right to left: 0011 0010 1010

Convert each group to hexadecimal:

0011 = 3 (hexadecimal)

0010 = 2 (hexadecimal)

1010 = A (hexadecimal)

Combine: 32A (hexadecimal)

So, the octal number 625 is equivalent to the hexadecimal number 32A.

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Difference Between Octal and Hexadecimal

Octal and hexadecimal numbers represent and handle binary-coded data in computers and mathematics. They differ, however, in terms of basis, symbols utilised, and applications. Here are the fundamental distinctions between octal and hexadecimal:

Both octal and hexadecimal represent binary-coded data; however, they are more extensively used and adaptable on current computers due to their compactness and conversion efficiency. Although it is still used occasionally, octal has become irrelevant over time.

Conclusion

When engaging in computer science, programming, or digital systems, individuals discover converting from octal to hexadecimal as an invaluable skill. This proficiency permits one to traverse diverse numerical bases proficiently, expanding their comprehension of data representation and manipulation across various settings. Whether you are a seasoned programmer, a skilled network administrator, or simply an enthusiast of number systems, delving into the captivating process of transforming octal to hexadecimal is an enthralling expedition worthy of pursuit.

FAQ’s about Octal to Hexadecimal