Decimal to Octal Converter
Convert decimal (base-10) numbers to octal (base-8) instantly
Step-by-step Calculation:
📚 Decimal to Octal Conversion Details
What is Decimal?
Decimal (base-10) is our everyday number system using digits 0-9. Each position represents a power of 10.
What is Octal?
Octal (base-8) uses digits 0-7. Each position represents a power of 8. Commonly used in computing.
Conversion Method
Divide the decimal number by 8 repeatedly, keeping track of remainders. Read remainders in reverse order.
Common Uses
- Computer programming
- Unix file permissions
- Digital electronics
- Number system education
📏 How to Convert Decimal to Octal
Follow these steps to convert any decimal number to octal:
- Divide the decimal number by 8
- Record the remainder (0-7)
- Use the quotient as the new number
- Repeat until quotient is 0
- Read remainders in reverse order
100 ÷ 8 = 12 remainder 4 ← LSD
12 ÷ 8 = 1 remainder 4
1 ÷ 8 = 0 remainder 1 ← MSD
// Read remainders from bottom to top:
// 100₁₀ = 144₈
📊 Conversion Table
| Decimal | Octal | Calculation |
|---|---|---|
| 8 | 10₈ | 8÷8=1R0, 1÷8=0R1 |
| 16 | 20₈ | 16÷8=2R0, 2÷8=0R2 |
| 32 | 40₈ | 32÷8=4R0, 4÷8=0R4 |
| 64 | 100₈ | 64÷8=8R0, 8÷8=1R0, 1÷8=0R1 |
| 100 | 144₈ | 100÷8=12R4, 12÷8=1R4, 1÷8=0R1 |
| 255 | 377₈ | 255÷8=31R7, 31÷8=3R7, 3÷8=0R3 |
❓ Frequently Asked Questions
A: The largest digit in octal is 7. After 7 comes 10 (which represents 8 in decimal).
A: Octal was historically used because it's easier to convert to/from binary (3 bits = 1 octal digit).
A: Multiply each digit by 8 raised to its position power, starting from right (8⁰, 8¹, 8², etc.) and sum them.
A: Octal is base-8 (0-7), hexadecimal is base-16 (0-9, A-F). Hex is more compact for large numbers.