Octal to Hexadecimal Conversion Examples
Octal to hexadecimal conversion is an essential concept in number systems used in computer science, digital electronics, and programming. It helps simplify data representation by converting base-8 numbers into base-16 format efficiently.
Understanding this conversion allows students to work easily with memory addresses, machine-level programming, and digital systems.
What is Octal to Hexadecimal Conversion?
Octal to hexadecimal conversion is the process of converting a base-8 number into its equivalent base-16 number using systematic methods. This conversion is widely used in computing to represent binary data in a compact and readable format. The list of conversion methods is given below:
1. Direct Method (Using Binary Conversion)
This is the most common and accurate method where octal numbers are first converted into binary and then into hexadecimal.
- Each octal digit is converted into a 3-bit binary number
- Combine all binary digits
- Group binary digits into sets of 4 (from right)
- Convert each group into hexadecimal
2. Indirect Method (Using Decimal Conversion)
In this method, the octal number is first converted into decimal and then into hexadecimal.
- Convert octal to decimal using powers of 8
- Convert decimal to hexadecimal using division by 16
Steps for Octal to Hexadecimal Conversion
Octal to hexadecimal conversion becomes easy when you follow a step-by-step approach. These steps ensure accuracy and clarity while solving problems. The detailed steps are given below:
1. Convert Octal to Binary
Each octal digit is replaced by its equivalent 3-bit binary value.
- Example: 7 → 111, 5 → 101
2. Group Binary Digits
Binary digits are grouped into sets of 4 starting from the right side.
- Add leading zeros if needed
3. Convert Binary to Hexadecimal
Each group of 4 binary digits is converted into a hexadecimal digit.
- Example: 1111 → F, 1010 → A
Octal to Hexadecimal Conversion Table
This table helps students quickly understand the relationship between octal, binary, and hexadecimal numbers.
| Octal | Binary | Hexadecimal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 2 | 010 | 2 |
| 3 | 011 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
Octal to Hexadecimal Conversion Examples
These examples help students clearly understand the step-by-step process of converting octal numbers into hexadecimal format. The list of solved examples is given below:
1. Example: Convert (17)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the hexadecimal number (17)8 into its equivalent decimal number.
Description:
Step 1: Convert Octal to Binary
Each octal digit is converted into its 3-bit binary equivalent:
1₈ = 001₂
7₈ = 111₂
(17)₈ = (001111)₂
Step 2: Group Binary Digits into 4 Bits
Group the binary number from right to left and add leading zeros if needed:
(001111)₂ = (0000 1111)₂
Step 3: Convert Each Group to Hexadecimal
0000₂ = 0₁₆
1111₂ = F₁₆
Final Answer:
(17)₈ = (0F)₁₆
2. Example: Convert (245)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (245)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
Each octal digit is converted into its 3-bit binary equivalent:
2₈ = 010₂
4₈ = 100₂
5₈ = 101₂
(245)₈ = (010100101)₂
Step 2: Group Binary Digits into 4 Bits
Group the binary number from right to left and add leading zeros if needed:
(010100101)₂ = (0000 1010 0101)₂
Step 3: Convert Each Group to Hexadecimal
0001₂ = 5₁₆
1010₂ = A₁₆
0000₂ = 0₁₆
Final Answer:
(245)₈ = (A5)₁₆
3. Example: Convert (736)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (736)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
3₈ = 011₂
6₈ = 110₂
(736)₈ = (111011110)₂
Step 2: Group Binary Digits into 4 Bits
(111011110)₂ = (0001 1101 1110)₂
Step 3: Convert Each Group to Hexadecimal
0001₂ = 1₁₆
1101₂ = D₁₆
1110₂ = E₁₆
Final Answer:
(736)₈ = (1DE)₁₆
4. Example: Convert (1234)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (1234)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
(1234)₈ = (001010011100)₂
Step 2: Group Binary Digits into 4 Bits
(001010011100)₂ = (0010 1001 1100)₂
Step 3: Convert Each Group to Hexadecimal
0010₂ = 2₁₆
1001₂ = 9₁₆
1100₂ = C₁₆
Final Answer:
(1234)₈ = (29C)₁₆
5. Example: Convert (5671)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (5671)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
5₈ = 101₂
6₈ = 110₂
7₈ = 111₂
1₈ = 001₂
(5671)₈ = (101110111001)₂
Step 2: Group Binary Digits into 4 Bits
(101110111001)₂ = (1011 1011 1001)₂
Step 3: Convert Each Group to Hexadecimal
1011₂ = B₁₆
1011₂ = B₁₆
1001₂ = 9₁₆
Final Answer:
(5671)₈ = (BB9)₁₆
6. Example: Convert (7043)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (7043)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
0₈ = 000₂
4₈ = 100₂
3₈ = 011₂
(7043)₈ = (111000100011)₂
Step 2: Group Binary Digits into 4 Bits
(111000100011)₂ = (1110 0010 0011)₂
Step 3: Convert Each Group to Hexadecimal
1110₂ = E₁₆
0010₂ = 2₁₆
0011₂ = 3₁₆
Final Answer:
(7043)₈ = (E23)₁₆
7. Example: Convert (12345)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (12345)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
5₈ = 101₂
(12345)₈ = (001010011100101)₂
Step 2: Group Binary Digits into 4 Bits
(001010011100101)₂ = (0001 0100 1110 0101)₂
Step 3: Convert Each Group to Hexadecimal
0001₂ = 1₁₆
0100₂ = 4₁₆
1110₂ = E₁₆
0101₂ = 5₁₆
Final Answer:
(12345)₈ = (14E5)₁₆
8. Example: Convert (76543)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (76543)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
6₈ = 110₂
5₈ = 101₂
4₈ = 100₂
3₈ = 011₂
(76543)₈ = (111110101100011)₂
Step 2: Group Binary Digits into 4 Bits
(111110101100011)₂ = (0111 1101 0110 0011)₂
Step 3: Convert Each Group to Hexadecimal
0111 ₂ = 7₁₆
1101 ₂ = D₁₆
0110 ₂ = 6₁₆
0011₂ = 3₁₆
Final Answer:
(76543)₈ = (7D63)₁₆
9. Example: Convert (456721)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (456721)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
7₈ = 111₂
2₈ = 010₂
1₈ = 001₂
(456721)₈ = (100101110111010001)₂
Step 2: Group Binary Digits into 4 Bits
(100101110111010001)₂ = (0010 0101 1101 1101 0001)₂
Step 3: Convert Each Group to Hexadecimal
0010₂ = 2₁₆
0101₂ = 5₁₆
1101₂ = D₁₆
1101₂ = D₁₆
0001₂ = 1₁₆
Final Answer:
(456721)₈ = (25DD1)₁₆
10. Example: Convert (1234567)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (1234567)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
7₈ = 111₂
(1234567)₈ = (001010011100101110111)₂
Step 2: Group Binary Digits into 4 Bits
(001010011100101110111)₂ = (0101 0011 1001 0111 0111)₂
Step 3: Convert Each Group to Hexadecimal
0101₂ = 5₁₆
0011₂ = 3₁₆
1001₂ = 9₁₆
0111₂ = 7₁₆
0111₂ = 7₁₆
Final Answer:
(1234567)₈ = (53977)₁₆
11. Example: Convert (7654321)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (7654321)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
6₈ = 110₂
5₈ = 101₂
4₈ = 100₂
3₈ = 011₂
2₈ = 010₂
1₈ = 001₂
(7654321)₈ = (111110101100011010001)₂
Step 2: Group Binary Digits into 4 Bits
(111110101100011010001)₂ = (0001 1111 0101 1000 1101 0001)₂
Step 3: Convert Each Group to Hexadecimal
0001₂ = 1₁₆
1111₂ = F₁₆
0101₂ = 5₁₆
1000₂ = 8₁₆
1101₂ = D₁₆
0001₂ = 1₁₆
Final Answer:
(7654321)₈ = (1F58D1)₁₆
12. Example: Convert (23456710)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (23456710)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
7₈ = 111₂
1₈ = 001₂
0₈ = 000₂
(23456710)₈ = (010011100101110111001000)₂
Step 2: Group Binary Digits into 4 Bits
(010011100101110111001000)₂ = (0100 1110 0101 1101 1100 1000)₂
Step 3: Convert Each Group to Hexadecimal
0100₂ = 4₁₆
1110₂ = E₁₆
0101₂ = 5₁₆
1101₂ = D₁₆
1100₂ = C₁₆
1000₂ = 8₁₆
Final Answer:
(23456710)₈ = (4E5DC8)₁₆
13. Example: Convert (70123456)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (70123456)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
0₈ = 000₂
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
(70123456)₈ = (111000001010011100101110)₂
Step 2: Group Binary Digits into 4 Bits
(111000001010011100101110)₂ = (1110 0000 1010 0111 0010 1110)₂
Step 3: Convert Each Group to Hexadecimal
1110₂ = E₁₆
0000₂ = 0₁₆
1010₂ = A₁₆
0111₂ = 7₁₆
0010₂ = 2₁₆
1110₂ = E₁₆
Final Answer:
(70123456)₈ = (E0A72E)₁₆
14. Example: Convert (123456701)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (123456701)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
5₈ = 101₂
6₈ = 110₂
7₈ = 111₂
0₈ = 000₂
1₈ = 001₂
(123456701)₈ = (001010011100101110111000001)₂
Step 2: Group Binary Digits into 4 Bits
(0001 0100 1110 0101 1101 1100 0001)₂ = (0001 0100 1110 0101 1101 1100 0001)₂
Step 3: Convert Each Group to Hexadecimal
0001 ₂ = 1₁₆
0100₂ = 4₁₆
1110 ₂ = E₁₆
0101 ₂ = 5₁₆
1101 ₂ = D₁₆
1100 ₂ = C₁₆
0001₂ = 1₁₆
Final Answer:
(123456701)₈ = (14E5DC1)₁₆
15. Example: Convert (7654321076)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (7654321076)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
6₈ = 110₂
5₈ = 101₂
4₈ = 100₂
3₈ = 011₂
2₈ = 010₂
1₈ = 001₂
0₈ = 000₂
7₈ = 111₂
6₈ = 110₂
(7654321076)₈ = (111110101100011010001000111110)₂
Step 2: Group Binary Digits into 4 Bits
(111110101100011010001000111110)₂ = (0011 1110 1011 0001 1010 0010 0011 1110)₂
Step 3: Convert Each Group to Hexadecimal
0011₂ = 3₁₆
1110₂ = E₁₆
1011₂ = B₁₆
0001₂ = 1₁₆
1010₂ = A₁₆
0010₂ = 2₁₆
0011₂ = 3₁₆
1110₂ = E₁₆
Final Answer:
(7654321076)₈ = (3EB1A23E)₁₆
Octal Fraction to Hexadecimal Conversion Examples
Octal fractions can also be converted into hexadecimal by extending the same binary method. This is useful for representing precise values in computing systems. The list of fractional examples is given below:
Fractional Example 1: Convert (45.27)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (45.27)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
4₈ = 100₂
5₈ = 101₂
.2₈ = .010₂
7₈ = 111₂
(45.27)₈ = (100101.010111)₂
Step 2: Group Binary Digits into 4 Bits
(100101.010111)₂ = (0010 0101 . 0101 1100)₂
Step 3: Convert Each Group to Hexadecimal
0010₂ = 2₁₆
0101₂ = 5₁₆
0101₂ = 5₁₆
1100₂ = C₁₆
Final Answer:
(45.27)₈ = (25.5C)₁₆
Fractional Example 2: Convert (123.45)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (123.45)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
1₈ = 001₂
2₈ = 010₂
3₈ = 011₂
.4₈ = .100₂
5₈ = 101₂
(123.45)₈ = (001010011.100101)₂
Step 2: Group Binary Digits into 4 Bits
(001010011.100101)₂ = (0000 0101 0011 . 1001 0100)₂
Step 3: Convert Each Group to Hexadecimal
0000₂ = 0₁₆
0101₂ = 5₁₆
0011₂ = 3₁₆
1001₂ = 9₁₆
0100₂ = 4₁₆
Final Answer:
(123.45)₈ = (053.94)₁₆
Fractional Example 3: Convert (7.123)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (7.123)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
7₈ = 111₂
.1₈ = .001₂
2₈ = 010₂
3₈ = 011₂
(7.123)₈ = (111.001010011)₂
Step 2: Group Binary Digits into 4 Bits
(111.001010011)₂ = (0111 . 0010 1001 1000)₂
Step 3: Convert Each Group to Hexadecimal
0111₂ = 7₁₆
0010₂ = 2₁₆
1001₂ = 9₁₆
1000₂ = 8₁₆
Final Answer:
(7.123)₈ = (7.298)₁₆
Fractional Example 4: Convert (56.701)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (56.701)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
5₈ = 101₂
6₈ = 110₂
.7₈ = .111₂
0₈ = 000₂
1₈ = 001₂
(56.701)₈ = (101110.111000001)₂
Step 2: Group Binary Digits into 4 Bits
(101110.111000001)₂ = (0010 1110 . 1110 0000 1000)₂
Step 3: Convert Each Group to Hexadecimal
0010₂ = 2₁₆
1110₂ = E₁₆
1110₂ = E₁₆
0000₂ = 0₁₆
1000₂ = 8₁₆
Final Answer:
(56.701)₈ = (2E.E08)₁₆
Fractional Example 5: Convert (234.567)₈ to Hexadecimal
Solution:
The following diagram shows the conversion of the octal number (234.567)₈ into its equivalent hexadecimal number.
Description:
Step 1: Convert Octal to Binary
2₈ = 010₂
3₈ = 011₂
4₈ = 100₂
.5₈ = .101₂
6₈ = 110₂
7₈ = 111₂
(234.567)₈ = (010011100.101110111)₂
Step 2: Group Binary Digits into 4 Bits
(010011100.101110111)₂ = (0000 1001 1100 . 1011 1011 1000)₂
Step 3: Convert Each Group to Hexadecimal
0000₂ = 0₁₆
1001₂ = 9₁₆
1100₂ = C₁₆
1011₂ = B₁₆
1011₂ = B₁₆
1000₂ = 8₁₆
Final Answer:
(234.567)₈ = (09C.BB8)₁₆
Common Mistakes in Octal to Hexadecimal Conversion
Students often make errors while converting between number systems, especially when dealing with grouping and binary conversions. Avoiding these mistakes can improve accuracy. The list of common mistakes is given below:
1. Incorrect Binary Conversion
Each octal digit must be converted into exactly 3 binary bits.
- Do not skip leading zeros
2. Wrong Grouping of Binary Digits
Binary digits must be grouped in sets of 4 from right to left.
- Always add leading zeros if required
3. Ignoring Fractional Grouping
For fractional parts, grouping should be done from left to right after the decimal.
- Maintain consistency in grouping
Applications of Octal to Hexadecimal Conversion
This conversion plays an important role in various fields of computer science and electronics. It helps simplify complex binary data. The list of applications is given below:
1. Memory Addressing
Hexadecimal numbers are widely used to represent memory locations.
2. Digital Electronics
Conversion helps in designing and understanding digital circuits.
3. Programming and Debugging
Programmers use hexadecimal for debugging and low-level coding.
Conclusion
Octal to hexadecimal conversion is a crucial concept that simplifies working with number systems in computing. By using binary as an intermediate step, students can easily perform accurate conversions for both integers and fractional numbers.
Mastering this topic not only strengthens your understanding of number systems but also builds a strong foundation for programming, digital electronics, and computer architecture.