Octal to Decimal Converter
Enter the octal number you want to convert to decimal.
Table of Contents
- How does octal to decimal conversion work?
- Octal to decimal conversion formula
- Conversion process
- Examples
- Octal to decimal conversion table
- Frequently Asked Questions
How does octal to decimal conversion work?
The octal system is base 8 and the decimal system is base 10. To convert an octal number to decimal, multiply each octal digit by the corresponding power of 8 (starting from the right with 80) and add the results. This method provides the direct equivalent value in base 10.
Octal to decimal conversion formula
For an octal number with n digits:
N₈ = ∑(oi × 8i)Where oi is each octal digit (0–7) in position i, and each is multiplied by 8i. The sum of all products gives the equivalent value in base 10.
Conversion process
- Write the octal number and assign powers of 8 to each digit (80 on the right).
- Multiply each digit by its corresponding power of 8.
- Add all the products to get the equivalent value in base 10.
Examples
17₈ to decimal| Octal Digit | Power of 8 | Product |
|---|---|---|
| 7 | 80 = 1 | 7 × 1 = 7 |
| 1 | 81 = 8 | 1 × 8 = 8 |
Total sum: 8 + 7 = 15.
Result: 17₈ = 15₁₀.
25₈ to decimal| Octal Digit | Power of 8 | Product |
|---|---|---|
| 5 | 80 = 1 | 5 × 1 = 5 |
| 2 | 81 = 8 | 2 × 8 = 16 |
Total sum: 16 + 5 = 21.
Result: 25₈ = 21₁₀.
Octal to decimal conversion table
Quick reference values for short octal numbers.
| Octal | Decimal |
|---|---|
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
10 | 8 |
11 | 9 |
12 | 10 |
20 | 16 |
40 | 32 |
100 | 64 |
200 | 128 |
400 | 256 |
1000 | 512 |
2000 | 1024 |
Frequently Asked Questions
How do you convert an octal number to decimal?
To convert an octal number to decimal, multiply each digit by a power of 8 according to its position (starting with 8⁰ from the right) and sum the results.
Why does the octal system use powers of 8?
Because each position in the octal system represents a multiple of 8. It’s a base-8 system where valid digits range from 0 to 7.