Binary to Octal Converter
Convert binary numbers to octal format
Tip: Enter a binary number (0s and 1s only). The conversion happens in real-time.
Runs in your browserBinary Octal
Binary to octal, step by step
Convert binary to octal
Type a binary number and the octal result appears as you type. Results longer than four digits are also shown in groups of three, the window bar shows the bit length, and Copy takes the plain digits.
Each octal digit stands for exactly three bits, so octal is a shorter way to write the same bits. It is still used for Unix file permissions, where each digit holds the read, write and execute bits of one group of users.
How to convert binary to octal by hand
Split the bits into groups of three from the right, pad the leftmost group with zeros, and write each group as one octal digit. For 1011101110:
| Group of three bits | Octal digit |
|---|---|
| 001 | 1 |
| 011 | 3 |
| 101 | 5 |
| 110 | 6 |
Join the digits: 1011101110 is 1356 in octal. To check it, 1 × 512 + 3 × 64 + 5 × 8 + 6 = 750, and 1011101110 is 750 in decimal too. The step-by-step window above splits the bits you type in the same way.
Three-bit groups as octal digits and permissions
| Bits | Octal | Permission |
|---|---|---|
| 000 | 0 | --- |
| 001 | 1 | --x |
| 010 | 2 | -w- |
| 011 | 3 | -wx |
| 100 | 4 | r-- |
| 101 | 5 | r-x |
| 110 | 6 | rw- |
| 111 | 7 | rwx |
In a permission the three bits are read, write and execute, worth 4, 2 and 1. So 111 101 101 is 755: the owner can read, write and execute, and everyone else can read and execute.
Starting from an octal number?
The octal to binary converter writes each octal digit back as its three bits.
To group the same bits in fours instead, use the binary to hex converter, or the number system converter for all four bases at once.
Binary to octal questions
755. The groups 111, 101 and 101 are 7, 5 and 5, which is the permission rwxr-xr-x.
Because 8 is 2 × 2 × 2. Three bits have exactly eight combinations, one for each octal digit from 0 to 7.
No. Missing zeros are added on the left of the first group, so 1010 is read as 001 010 and gives 12.
Yes, if it has a minus sign: -1010 gives -12. A bit pattern without a sign, such as a two's complement value, is read as a positive number.
No. The conversion runs in your browser.