Octal to Binary Converter
Type an octal number to see its bits: every octal digit becomes exactly three binary digits.
Octal uses only the digits 0–7
In binary (base 2)
111101101
Octal 755 is 1 1110 1101 in binary (base 2).
256 + 128 + 64 + 32 + 8 + 4 + 1 = 493
Tap a bit to flip it. Each tile is worth its digit × 2n.
Bytes in memory2 bytes, big- and little-endian
The +0, +1 … under each byte is its address offset. Big-endian puts the most significant byte first; little-endian puts it last.
How to convert octal to binary
Write every octal digit as three bits and join them. Keep all three bits for each digit, even when they start with zeros: 1 is 001 and 2 is 010.
For 644: 6 = 110, 4 = 100, 4 = 100, so the bits are 110 100 100. Read as permissions that is rw- r-- r--: the owner can read and write, everyone else can only read.
This is the reverse of grouping binary in threes, and the quickest check of a permission mode: each digit expands into the read, write and execute flags directly.
1 octal digit = 3 bits; 4 = 100, 6 = 110, 7 = 111
- Octal permission digits are sums of 4 (read), 2 (write) and 1 (execute), so 6 is read and write. Source: POSIX chmod, The Open Group Base Specifications.
Octal numbers in binary
Octal values with their bits, grouped in threes so each digit lines up with its own group.
| Octal | Binary (3 bits per digit) | Decimal |
|---|---|---|
| 7 | 111 | 7 |
| 10 | 001 000 | 8 |
| 17 | 001 111 | 15 |
| 20 | 010 000 | 16 |
| 52 | 101 010 | 42 |
| 77 | 111 111 | 63 |
| 100 | 001 000 000 | 64 |
| 144 | 001 100 100 | 100 |
| 177 | 001 111 111 | 127 |
| 200 | 010 000 000 | 128 |
Show all 15 rowsShow fewer
| 377 | 011 111 111 | 255 |
| 644 | 110 100 100 | 420 |
| 755 | 111 101 101 | 493 |
| 777 | 111 111 111 | 511 |
| 1777 | 001 111 111 111 | 1023 |
Frequently Asked Questions
What is 7 in binary?
Seven is 111, the largest three-bit value; it is also rwx, every permission on.
What is the octal number 777 in binary?
777 becomes 111 111 111: nine bits, all on. As a permission that means anyone can read, write and run the file.
Can octal digits contain 8 or 9?
No. Octal digits run from 0 to 7; a number with an 8 or 9 in it is decimal (or a typo), and the converter will say so.