Convert Binary to Octal
Need to change a binary number to octal? Use our free binary to octal converter to instantly transform base-2 values into base-8. Just enter a number using 0s and 1s below to see the result.
Binary to octal calculator
Quick Reference
Binary to Octal Conversion Table
Need a quick reference instead of a binary to octal calculator? This chart shows exactly how common base-2 numbers map to base-8, helping you complete a fast binary to octal conversion.
| Binary | Grouping | Octal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 10 | 010 | 2 |
| 11 | 011 | 3 |
| 100 | 100 | 4 |
| 101 | 101 | 5 |
| 110 | 110 | 6 |
| 111 | 111 | 7 |
| 1000 | 001 000 | 10 |
| 1010 | 001 010 | 12 |
| 1111 | 001 111 | 17 |
| 10000 | 010 000 | 20 |
| 11001 | 011 001 | 31 |
| 111111 | 111 111 | 77 |
| 11111111 | 011 111 111 | 377 |
Step-by-Step
How to Convert Binary to Octal
Wondering how to convert binary to octal by hand? The process is surprisingly straightforward once you learn to group the digits.
The Method
To change a binary number to octal, you take advantage of the fact that three binary digits (bits) perfectly match one octal digit. Binary is a base-2 system (using only 0 and 1), and octal is a base-8 system (using 0 through 7).
Starting from the rightmost side, split the binary number into groups of three digits. If your final group on the left is short, just add leading zeros.
How to Change Binary to Octal Manually
Write the binary number
Take the binary value you want to convert. For example, let's use 1010.
Group digits into threes
From right to left, split the number into groups of three. Our number 1010 becomes 001 010.
Convert each group to octal
Use a basic chart. 001 = 1 and 010 = 2, so combining them means 1010₂ = 12₈.
Binary vs Octal
Understanding the Binary Octal Relationship
Why even do a bin to octal conversion? Computers process all data in binary code—endless strings of 0s and 1s. However, these long sequences are tough for humans to read, write, or debug.
By converting them into octal (a system using numbers 0 through 7), the digits become much shorter and easier to manage. Because exactly three binary digits fit into a single octal digit, making a binary octal translation preserves the underlying bit structure perfectly without doing complex math.
For example, transforming the long binary string 111111 results in a clean and simple 77 in octal.
Worked Examples
Binary to Octal Conversion Examples
Here is how you use the grouping method to perform a bin to oct conversion on common numbers.
10 in binary to octal
10 → 010 = 2. So 10₂ = 2₈.
101 in binary to octal
101 = 5. So 101₂ = 5₈.
1000 in binary to octal
1000 → 001 000 = 10. So 1000₂ = 10₈.
1010 in binary to octal
1010 → 001 010 = 12. So 1010₂ = 12₈.
1111 in binary to octal
1111 → 001 111 = 17. So 1111₂ = 17₈.
10000 in binary to octal
10000 → 010 000 = 20. So 10000₂ = 20₈.
11001 in binary to octal
11001 → 011 001 = 31. So 11001₂ = 31₈.
11111111 in binary to octal
11111111 → 011 111 111 = 377. So 11111111₂ = 377₈.
FAQ
Frequently Asked Questions
Answers to common questions about base-2 and base-8 numbers.