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In digital electronics and computer programming, octal (base 8) is sometimes used as a numerical system.
If you need to convert a decimal number to octal, follow these steps: divide the decimal number by 8, get the integer quotient, and repeat until the quotient is zero.
In this guide, we’ll provide examples and include a conversion table for reference.
To convert a decimal number to octal, follow these steps:
Example #1: Convert 756210 to Octal
Division by 8:
| Division by 8 | Quotient (integer) | Remainder (decimal) | Remainder (octal) | Digit # | |
|---|---|---|---|---|---|
| 1 | 7562/8 | 945 | 2 | 2 | 0 |
| 2 | 945/8 | 118 | 1 | 1 | 1 |
| 3 | 118/8 | 14 | 6 | 6 | 2 |
| 4 | 14/8 | 1 | 6 | 6 | 3 |
| 5 | 1/8 | 0 | 1 | 1 | 4 |
Therefore, 756210 in decimal is equivalent to 166128 in octal.
Example #2: Convert 3563110 to Octal
Division by 8:
| Division by 8 | Quotient | Remainder (decimal) | Remainder (octal) | Digit # | |
|---|---|---|---|---|---|
| 1 | 35631/8 | 4453 | 7 | 7 | 0 |
| 2 | 4453/8 | 556 | 5 | 5 | 1 |
| 3 | 556/8 | 69 | 4 | 4 | 2 |
| 4 | 69/8 | 8 | 5 | 5 | 3 |
| 5 | 8/8 | 1 | 0 | 0 | 4 |
| 6 | 1/8 | 0 | 1 | 1 | 5 |
Therefore, 3563110 in decimal is equivalent to 1054578 in octal.
Decimal to Octal Conversion Table
To help with decimal to octal conversions, use this table as a reference:
| Decimal (base 10) | Octal (base 8) |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |
| 16 | 20 |
| 17 | 21 |
| 18 | 22 |
| 19 | 23 |
| 20 | 24 |
| 21 | 25 |
| 22 | 26 |
| 23 | 27 |
| 24 | 30 |
| 25 | 31 |
| 26 | 32 |
| 27 | 33 |
| 28 | 34 |
| 29 | 35 |
| 30 | 36 |
| 40 | 50 |
| 50 | 62 |
| 60 | 74 |
| 70 | 106 |
| 80 | 120 |
| 90 | 132 |
| 100 | 144 |
| 200 | 310 |
| 1000 | 1750 |
| 2000 | 3720 |
Converting decimal to octal is a straightforward process that can be done by following a few simple steps. Remember to use the conversion table provided for reference and to double-check your results.
With this knowledge, you’ll be able to work with octal numbers in various applications with ease.