Octal representations can shorten lengthy binary sequences and are frequently used in computer programming and systems for easy visualization of data. Also, knowing how to convert between different bases enhances your numerical literacy and strengthens your foundational skills in various programming languages.
How to convert from decimal to octal
Let’s go through the division-remainder method, which is a reliable and systematic way to convert decimal numbers to octal.
Step 1: Divide the Decimal Number by 8
- Take the decimal number you want to convert and divide it by 8.
- Write down the quotient and the remainder.
Step 2: Repeat the Division
- Use the quotient from the previous division as the new number to divide by 8 again.
- Continue dividing until the quotient becomes zero, recording each remainder.
Step 3: Write the Octal Number
- The octal number is formed by reading the remainders from the bottom up. The last remainder (when the quotient is zero) will be the leftmost digit in the octal representation.
Example: Converting Decimal to Octal
Let’s convert 156 (decimal) to octal.
- 156 ÷ 8 = 19, remainder = 4
- 19 ÷ 8 = 2, remainder = 3
- 2 ÷ 8 = 0, remainder = 2
Reading the remainders from the bottom up, we get 234 in octal.
So, 156 (decimal) is 234 (octal).
Tools for Decimal to Octal Conversion
While learning how to convert manually is essential, with our online tools you can instantly convert decimal numbers to octal, which is useful when dealing with larger 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 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |