Hexadecimal to Octal Conversion Examples
Hexadecimal to octal conversion is an important concept in number systems used in computer science, digital electronics, and programming. It helps transform base-16 numbers into base-8 format, making data easier to interpret in certain computing environments.
Understanding this conversion allows students and professionals to efficiently work with low-level programming, memory representation, and digital system design.
What is Hexadecimal to Octal Conversion?
Hexadecimal to octal conversion is the process of converting a base-16 number into its equivalent base-8 number using systematic methods. This conversion is commonly used to simplify binary data representation in different formats.
The main methods for conversion are given below:
1. Direct Method (Using Binary Conversion)
This is the most common and reliable method where hexadecimal numbers are first converted into binary and then into octal.
- Each hexadecimal digit is converted into a 4-bit binary number
- Combine all binary digits
- Group binary digits into sets of 3 (from right)
- Convert each group into octal
2. Indirect Method (Using Decimal Conversion)
In this method, the hexadecimal number is first converted into decimal and then into octal.
- Convert hexadecimal to decimal using powers of 16
- Convert decimal to octal using division by 8
Steps for Hexadecimal to Octal Conversion
Hexadecimal to octal conversion becomes simple when you follow a step-by-step approach. These steps ensure accuracy and clarity.
1. Convert Hexadecimal to Binary
Each hexadecimal digit is replaced by its equivalent 4-bit binary value.
Example:
A → 1010,
F → 1111
2. Group Binary Digits
Binary digits are grouped into sets of 3 starting from the right side.
- Add leading zeros if necessary
3. Convert Binary to Octal
Each group of 3 binary digits is converted into an octal digit.
Example:
111 → 7,
010 → 2
Hexadecimal to Octal Conversion Table
This table helps in understanding the relationship between hexadecimal, binary, and octal numbers.
| Hexadecimal | Binary | Octal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 10 |
| 9 | 1001 | 11 |
| A | 1010 | 12 |
| B | 1011 | 13 |
| C | 1100 | 14 |
| D | 1101 | 15 |
| E | 1110 | 16 |
| F | 1111 | 17 |
Hexadecimal to Octal Conversion Examples
These examples help students clearly understand the step-by-step process of converting hexadecimal numbers into octal format. The list of solved examples is given below:
1. Example: Convert (3A)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (3A)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
Each hexadecimal digit is converted into its 4-bit binary equivalent:
3₁₆ = 0011₂
A₁₆ = 1010₂
(3A)₁₆ = (00111010)₂
Step 2: Group Binary Digits into 3 Bits
Group the binary number from right to left and add leading zeros if needed:
(00111010)₂ = (000 111 010)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
111₂ = 7₈
010₂ = 2₈
Final Answer:
(3A)₁₆ = (072)₈
2. Example: Convert (7F)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (7F)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
Each hexadecimal digit is converted into its 4-bit binary equivalent:
7₁₆ = 0111₂
F₁₆ = 1111₂
(7F)₁₆ = (01111111)₂
Step 2: Group Binary Digits into 3 Bits
Group the binary number from right to left and add leading zeros if needed:
(01111111)₂ = (001 111 111)₂
Step 3: Convert Each Group to Octal
001₂ = 1₈
111₂ = 7₈
111₂ = 7₈
Final Answer:
(7F)₁₆ = (177)₈
3. Example: Convert (A5)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (A5)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
A₁₆ = 1010₂
5₁₆ = 0101₂
( A5 )₁₆ = (10100101)₂
Step 2: Group Binary Digits into 3 Bits
(10100101)₂ = (010 100 101)₂
Step 3: Convert Each Group to Octal
010₂ = 2₈
100₂ = 4₈
101₂ = 5₈
Final Answer:
(A5)₁₆ = (245)₈
4. Example: Convert (2B)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (2B)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
2₁₆ = 0010₂
B₁₆ = 1011₂
(2B)₁₆ = (00101011)₂
Step 2: Group Binary Digits into 3 Bits
(00101011)₂ = (000 101 011)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
101₂ = 5₈
011₂ = 3₈
Final Answer:
(2B)₁₆ = (053)₈
5. Example: Convert (F2)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (F2)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
F₁₆ = 1111₂
2₁₆ = 0010₂
( F2 )₁₆ = (11110010)₂
Step 2: Group Binary Digits into 3 Bits
(11110010)₂ = (011 110 010)₂
Step 3: Convert Each Group to Octal
011₂ = 3₈
110₂ = 6₈
010₂ = 2₈
Final Answer:
(F2)₁₆ = (362)₈
6. Example: Convert (1C7)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (1C7)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
1₁₆ = 0001₂
C₁₆ = 1100₂
7₁₆ = 0111₂
(1C7)₁₆ = (000111000111)₂
Step 2: Group Binary Digits into 3 Bits
(000111000111)₂ = (000 111 000 111)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
111₂ = 7₈
000₂ = 0₈
111₂ = 7₈
Final Answer:
(1C7)₁₆ = (0707)₈
7. Example: Convert (3AF)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (3AF)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
3₁₆ = 0011₂
A₁₆ = 1010₂
F₁₆ = 1111₂
(3AF)₁₆ = (001110101111)₂
Step 2: Group Binary Digits into 3 Bits
(001110101111)₂ = (001 110 101 111)₂
Step 3: Convert Each Group to Octal
001₂ = 1₈
110₂ = 6₈
101₂ = 5₈
111₂ = 7₈
Final Answer:
(3AF)₁₆ = (1657)₈
8. Example: Convert (9B2E)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (9B2E)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
9₁₆ = 1001₂
B₁₆ = 1011₂
2₁₆ = 0010₂
E₁₆ = 1110₂
(9B2E)₁₆ = (1001101100101110)₂
Step 2: Group Binary Digits into 3 Bits
(1001101100101110)₂ = (001 001 101 100 101 110)₂
Step 3: Convert Each Group to Octal
001₂ = 1₈
001₂ = 1₈
101₂ = 5₈
100₂ = 4₈
101₂ = 5₈
110₂ = 6₈
Final Answer:
(9B2E)₁₆ = (115456)₈
9. Example: Convert (4D3A7)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (4D3A7)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
4₁₆ = 0100₂
D₁₆ = 1101₂
3₁₆ = 0011₂
A₁₆ = 1010₂
7₁₆ = 0111₂
(4D3A7)₁₆ = (01001101001110100111)₂
Step 2: Group Binary Digits into 3 Bits
(01001101001110100111)₂ = (000 100 110 100 111 010 011 1)₂
= (000 100 110 100 111 010 011 001)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
100₂ = 4₈
110₂ = 6₈
100₂ = 4₈
111₂ = 7₈
010₂ = 2₈
011₂ = 3₈
001₂ = 1₈
Final Answer:
(4D3A7)₁₆ = (04647231)₈
10. Example: Convert (1A3F7C)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (1A3F7C)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
1₁₆ = 0001₂
A₁₆ = 1010₂
3₁₆ = 0011₂
F₁₆ = 1111₂
7₁₆ = 0111₂
C₁₆ = 1100₂
(1A3F7C)₁₆ = (000110100011111101111100)₂
Step 2: Group Binary Digits into 3 Bits
(000110100011111101111100)₂ = (000 110 100 011 111 101 111 100)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
110₂ = 6₈
100₂ = 4₈
011₂ = 3₈
111₂ = 7₈
101₂ = 5₈
111₂ = 7₈
100₂ = 4₈
Final Answer:
(1A3F7C)₁₆ = (06437574)₈
11. Example: Convert (ABC123)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (ABC123)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
1₁₆ = 0001₂
2₁₆ = 0010₂
3₁₆ = 0011₂
(ABC123)₁₆ = (101010111100000100100011)₂
Step 2: Group Binary Digits into 3 Bits
(101010111100000100100011)₂ = (101 010 111 100 000 100 100 011)₂
Step 3: Convert Each Group to Octal
101₂ = 5₈
010₂ = 2₈
111₂ = 7₈
100₂ = 4₈
000₂ = 0₈
100₂ = 4₈
100₂ = 4₈
011₂ = 3₈
Final Answer:
(ABC123)₁₆ = (52740443)₈
12. Example: Convert (7F2A9B)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (7F2A9B)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
7₁₆ = 0111₂
F₁₆ = 1111₂
2₁₆ = 0010₂
A₁₆ = 1010₂
9₁₆ = 1001₂
B₁₆ = 1011₂
(7F2A9B)₁₆ = (011111110010101010011011)₂
Step 2: Group Binary Digits into 3 Bits
(011111110010101010011011)₂ = (011 111 110 010 101 010 011 011)₂
Step 3: Convert Each Group to Octal
011₂ = 3₈
111₂ = 7₈
110₂ = 6₈
010₂ = 2₈
101₂ = 5₈
010₂ = 2₈
011₂ = 3₈
011₂ = 3₈
Final Answer:
(7F2A9B)₁₆ = (37625233)₈
13. Example: Convert (1234ABCD)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (1234ABCD)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
1₁₆ = 0001₂
2₁₆ = 0010₂
3₁₆ = 0011₂
4₁₆ = 0100₂
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
D₁₆ = 1101₂
(1234ABCD)₁₆ = (00010010001101001010101111001101)₂
Step 2: Group Binary Digits into 3 Bits
(00010010001101001010101111001101)₂
= (000 001 001 000 110 100 101 010 111 100 110 1)₂
= (000 001 001 000 110 100 101 010 111 100 110 001)₂
Step 3: Convert Each Group to Octal
000₂ = 0₈
001₂ = 1₈
001₂ = 1₈
000₂ = 0₈
110₂ = 6₈
100₂ = 4₈
101₂ = 5₈
010₂ = 2₈
111₂ = 7₈
100₂ = 4₈
110₂ = 6₈
001₂ = 1₈
Final Answer:
(1234ABCD)₁₆ = (011064527461)₈
14. Example: Convert (9ABCDE12)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (9ABCDE12)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
9₁₆ = 1001₂
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
D₁₆ = 1101₂
E₁₆ = 1110₂
1₁₆ = 0001₂
2₁₆ = 0010₂
(9ABCDE12)₁₆ = (10011010101111001101111000010010)₂
Step 2: Group Binary Digits into 3 Bits
(10011010101111001101111000010010)₂
= (001 001 101 010 111 100 110 111 100 001 001 0)₂
= (001 001 101 010 111 100 110 111 100 001 001 000)₂
Step 3: Convert Each Group to Octal
001₂ = 1₈
001₂ = 1₈
101₂ = 5₈
010₂ = 2₈
111₂ = 7₈
100₂ = 4₈
110₂ = 6₈
111₂ = 7₈
100₂ = 4₈
001₂ = 1₈
001₂ = 1₈
000₂ = 0₈
Final Answer:
(9ABCDE12)₁₆ = (115274674110)₈
15. Example: Convert (ABCDEF1234)₁₆ to Octal
Solution:
The following steps show the conversion of the hexadecimal number (ABCDEF1234)₁₆ into its equivalent octal number.
Description:
Step 1: Convert Hexadecimal to Binary
A₁₆ = 1010₂
B₁₆ = 1011₂
C₁₆ = 1100₂
D₁₆ = 1101₂
E₁₆ = 1110₂
F₁₆ = 1111₂
1₁₆ = 0001₂
2₁₆ = 0010₂
3₁₆ = 0011₂
4₁₆ = 0100₂
(ABCDEF1234)₁₆ = (1010101111001101111011110001001000110100)₂
Step 2: Group Binary Digits into 3 Bits
(1010101111001101111011110001001000110100)₂
= (001 010 101 111 001 101 111 011 110 001 001 000 110 100)₂
Step 3: Convert Each Group to Octal
001₂ = 1₈
010₂ = 2₈
101₂ = 5₈
111₂ = 7₈
001₂ = 1₈
101₂ = 5₈
111₂ = 7₈
011₂ = 3₈
110₂ = 6₈
001₂ = 1₈
001₂ = 1₈
000₂ = 0₈
110₂ = 6₈
100₂ = 4₈
Final Answer:
(ABCDEF1234)₁₆ = (12571573611064)₈