Decimal to Octal Converter
Enter the decimal number you want to convert to octal.
Table of Contents
- How does decimal to octal conversion work?
- Decimal to octal conversion formula
- Conversion process
- Examples
- Decimal to octal conversion table
- Frequently Asked Questions
How does decimal to octal conversion work?
The decimal system is base 10 and the octal system is base 8. To convert a decimal number to octal, repeatedly divide the number by 8 and record the remainders. Then, read the remainders in reverse order (from bottom to top) to obtain the base-8 number.
Decimal to octal conversion formula
To convert a decimal number N to octal:
Where the coefficients oi (remainders) take values from 0 to 7, obtained by successively dividing N by 8. The octal number is formed by reading the remainders from bottom to top.
Conversion process
- Divide the decimal number by 8 and note the remainder (0–7).
- Take the quotient obtained and repeat the division by 8 until you reach 0.
- Write the remainders in reverse order (from bottom to top) to obtain the octal number.
Examples
25₁₀ to octal| Division | Quotient | Remainder |
|---|---|---|
| 25 ÷ 8 | 3 | 1 |
| 3 ÷ 8 | 0 | 3 |
Reading the remainders from bottom to top: 31₈.
Result: 25₁₀ = 31₈.
100₁₀ to octal| Division | Quotient | Remainder |
|---|---|---|
| 100 ÷ 8 | 12 | 4 |
| 12 ÷ 8 | 1 | 4 |
| 1 ÷ 8 | 0 | 1 |
Reading the remainders from bottom to top: 144₈.
Result: 100₁₀ = 144₈.
Decimal to octal conversion table
Quick reference values for small decimal numbers.
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 16 | 20 |
| 32 | 40 |
| 64 | 100 |
| 128 | 200 |
| 256 | 400 |
| 512 | 1000 |
| 1024 | 2000 |
Frequently Asked Questions
How do you convert a decimal number to octal?
To convert a decimal number to octal, repeatedly divide the number by 8, write down the remainders, and then read them from bottom to top.
Why is base 8 used in the octal system?
Because each octal digit represents exactly 3 binary bits, which makes conversions between binary and octal quick and straightforward.