Octal to Decimal Converter
Convert octal numbers to decimal with step-by-step calculation. Simple and accurate octal to decimal conversion tool.
Octal to Decimal Converter
Convert octal numbers to decimal format. This tool provides step-by-step calculation showing how each octal digit is multiplied by powers of 8 to get the decimal equivalent.
What is octal to decimal conversion?
Octal to decimal conversion is the process of converting a base-8 number to a base-10 number. Each digit is multiplied by 8 raised to the power of its position, starting from the rightmost digit (8⁰).
How do you convert octal to decimal?
To convert octal to decimal:
1. Write down the octal number
2. Multiply each digit by 8 raised to the power of its position (from right to left, starting with 0)
3. Add all the results together
Example: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15₁₀
What is the formula for octal to decimal conversion?
The formula is: Decimal = dₙ×8ⁿ + dₙ₋₁×8ⁿ⁻¹ + ... + d₁×8¹ + d₀×8⁰
Where dₙ is the nth digit from the right, and n is the position (starting from 0).
Why use octal instead of decimal?
Octal is useful in computing because:
- Easy conversion to binary (3 octal digits = 9 binary digits)
- More compact than binary
- Used in Unix file permissions
- Common in some programming contexts
Octal to Decimal Conversion Table
| Octal | Decimal | Binary | Hex |
|---|---|---|---|
| 0 | 0 | 000 | 0 |
| 1 | 1 | 001 | 1 |
| 2 | 2 | 010 | 2 |
| 3 | 3 | 011 | 3 |
| 4 | 4 | 100 | 4 |
| 5 | 5 | 101 | 5 |
| 6 | 6 | 110 | 6 |
| 7 | 7 | 111 | 7 |
| 10 | 8 | 1000 | 8 |
| 11 | 9 | 1001 | 9 |
| 12 | 10 | 1010 | A |
| 17 | 15 | 1111 | F |
| 20 | 16 | 10000 | 10 |
| 40 | 32 | 100000 | 20 |
| 100 | 64 | 1000000 | 40 |
| 200 | 128 | 10000000 | 80 |
| 377 | 255 | 11111111 | FF |
| 400 | 256 | 100000000 | 100 |