Binary to Octal Converter
Enter the binary number you want to convert to octal.
Table of Contents
- How does binary to octal conversion work?
- Binary to octal conversion formula
- Conversion process
- Examples
- Binary to octal conversion table
- Frequently Asked Questions
How does binary to octal conversion work?
The binary system is base 2 and the octal system is base 8. To convert a binary number to octal, group the binary digits into blocks of 3 starting from the right (adding zeros to the left if necessary). Then, replace each group of 3 bits with its equivalent octal value (0–7).
Binary to octal conversion formula
For a binary number of n digits:
Where each block of 3 bits is converted into an octal digit Oj (0–7).
Conversion process
- Write the binary number and group it into blocks of 3 digits starting from the right (add zeros to the left if necessary).
- Convert each block of 3 bits into its decimal equivalent value (from 0 to 7).
- Combine the obtained values to form the number in base 8 (octal).
Examples
101110₂ to octal101110₂ → group into blocks of 3 bits: 101 110
101₂ = 5₈, 110₂ = 6₈
Result: 101110₂ = 56₈.
1110011₂ to octal1110011₂ → group into blocks of 3 bits: 111 001 011
111₂ = 7₈, 001₂ = 1₈, 011₂ = 3₈
Result: 1110011₂ = 713₈.
Binary to octal conversion table
Quick reference values for short binary numbers.
| Binary | Octal |
|---|---|
0 | 0 |
1 | 1 |
10 | 2 |
11 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
1000 | 10 |
1001 | 11 |
1010 | 12 |
1011 | 13 |
1100 | 14 |
1101 | 15 |
1110 | 16 |
1111 | 17 |
10000 | 20 |
100000 | 40 |
1000000 | 100 |
10000000 | 200 |
100000000 | 400 |
1000000000 | 1000 |
10000000000 | 2000 |
Frequently Asked Questions
How do you convert a binary number to octal?
To convert a binary number to octal, group the binary digits into blocks of 3 starting from the right. Then, replace each block with its equivalent octal value (0–7).
Why are bits grouped in sets of 3?
Because each octal digit represents exactly 3 bits. This makes the conversion between binary and octal straightforward and easy.
Cite this page
You can use the following citation format when referencing this calculator in academic or professional work.
Ramos, J., Binary to octal converter, Available at: https://calcuclub.com/convert/binary-to-octal/ (Accessed: 27 November 2025).