Binary to octal converter
Type a binary number to get its octal value. Every 3 bits make one octal digit, so 11111111 becomes 377. Enter several numbers on separate lines to convert them all at once.
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How to convert binary to octal
- Start from the right and split the bits into groups of 3.
- Add zeros on the left of the last group if it has fewer than 3 bits.
- Turn each group into a digit from 0 to 7 with the table below.
- Write the digits in the same order.
It works because 8 is 23, so each octal digit lines up with exactly 3 bits. No division is needed. Hex follows the same idea with groups of 4 bits, which is how binary to hex works.
Binary to octal conversion table
| Binary | Octal | Binary | Octal |
|---|---|---|---|
| 000 | 0 | 100 | 4 |
| 001 | 1 | 101 | 5 |
| 010 | 2 | 110 | 6 |
| 011 | 3 | 111 | 7 |
Inside each group the bits are worth 4, 2 and 1. So 101 is 4 + 1 = 5 and 110 is 4 + 2 = 6.
Worked examples
| Binary | Groups of 3 | Octal |
|---|---|---|
| 1010 | 001 010 | 12 |
| 101110 | 101 110 | 56 |
| 11111111 | 011 111 111 | 377 |
| 111101101 | 111 101 101 | 755 |
| 1000000000 | 001 000 000 000 | 1000 |
Take 101110. From the right, the groups are 110 and 101. 110 is 6 and 101 is 5, so the answer is 56. Check it with the binary to decimal converter: 101110 is 46, and 5 × 8 + 6 = 46.
Where octal is used
The best-known use today is Unix file permissions. In chmod 755, each digit is 3 bits for read, write and execute, as the GNU manual on numeric modes spells out. 7 is 111 (rwx) for the owner, and each 5 is 101 (r-x) for the group and everyone else. Octal also appears in number literals, written 0755 in C and 0o755 in Python, in some older computers with 12, 24 or 36-bit words, and in avionics transponder codes.
Binary to octal with fractions
For bits after the point, group from the point to the right and pad with zeros on the right. So 0.1011 becomes .101 100, which is 0.54 in octal. The converter handles this for you when you type a number with a point. To go back, octal to binary writes each octal digit as 3 bits.
Frequently asked questions
Why group binary in threes for octal?
Because 23 = 8. Three bits hold exactly the values 0 to 7, which are the octal digits.
What is 1111 in octal?
17. The groups are 001 and 111, which are 1 and 7.
What is 11111111 in octal?
377. It is also 255 in decimal and FF in hex.
Can I convert several numbers at once?
Yes. Put each binary number on its own line or separate them with spaces.