Octal to Hexadecimal Converter
Enter the octal number you want to convert to hexadecimal.
Table of Contents
- How does octal to hexadecimal conversion work?
- Octal to hexadecimal conversion formula
- Conversion process
- Examples
- Octal to hexadecimal conversion table
- Frequently Asked Questions
How does octal to hexadecimal conversion work?
The octal system is base 8 and the hexadecimal system is base 16. To convert an octal number to hexadecimal, first convert the octal number to binary (each octal digit is replaced with its 3-bit binary equivalent). Then, group the resulting bits into sets of 4 (from right to left) to form the base-16 number.
Octal to hexadecimal conversion formula
For an octal number with n digits:
N₈ = ∑(oi × 8i) → N₁₀ → N₁₆Where oi is each octal digit (0–7) in position i. The octal number is first converted to its decimal equivalent, and then the decimal value is converted to base 16 (hexadecimal).
Conversion process
- Write the octal number.
- Convert the octal number to its decimal value by multiplying each digit by its corresponding power of 8 (80 on the right).
- Take the decimal result and convert it to hexadecimal by successively dividing by 16 and noting the remainders (0–9, A–F).
- Read the remainders in reverse order to obtain the base-16 number.
Examples
17₈ to hexadecimal| Octal | Intermediate decimal | Hexadecimal |
|---|---|---|
| 17₈ | 15₁₀ | F₁₆ |
Conversion: 17₈ → 15₁₀ → F₁₆.
Result: 17₈ = F₁₆.
25₈ to hexadecimal| Octal | Intermediate decimal | Hexadecimal |
|---|---|---|
| 25₈ | 21₁₀ | 15₁₆ |
Conversion: 25₈ → 21₁₀ → 15₁₆.
Result: 25₈ = 15₁₆.
Octal to hexadecimal conversion table
Quick reference values for simple conversions between octal and hexadecimal numbers.
| Octal | Hexadecimal |
|---|---|
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
10 | 8 |
11 | 9 |
12 | A |
13 | B |
14 | C |
15 | D |
16 | E |
17 | F |
20 | 10 |
40 | 20 |
100 | 40 |
Frequently Asked Questions
How is the conversion from octal to hexadecimal performed?
To convert an octal number to hexadecimal, first convert the octal number to binary by replacing each octal digit with its 3-bit equivalent. Then, group the bits into sets of 4 (from right to left) and convert each group into its hexadecimal value.
Why is the binary system used in the conversion from octal to hexadecimal?
Because the binary system serves as a natural intermediate between base 8 and base 16. Each octal digit equals 3 bits, and each hexadecimal digit equals 4 bits, making the process accurate and straightforward.