Octal to Binary Converter
Type a octal number of any length to see it in binary, with every step of the working.
Octal to binary table
| Octal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 7 | 111 |
| 10 | 1000 |
| 12 | 1010 |
| 17 | 1111 |
| 20 | 10000 |
| 40 | 100000 |
| 100 | 1000000 |
| 144 | 1100100 |
| 177 | 1111111 |
| 200 | 10000000 |
| 377 | 11111111 |
| 400 | 100000000 |
| 1750 | 1111101000 |
| 2000 | 10000000000 |
Worked examples
10 in binary
12 (octal)
1010 (binary)
Decimal value 10.
255 in binary
377 (octal)
11111111 (binary)
Decimal value 255.
2026 in binary
3752 (octal)
11111101010 (binary)
Decimal value 2026.
About Octal to Binary Converter
This converter turns octal numbers into binary and shows how. To convert octal to binary, replace each octal digit with its 3 bit binary pattern. For example, 12 in octal is 1010 in binary, and 3752 is 11111101010.
Octal packs three bits into each digit. It is best known today from Unix file permissions, where 755 means read, write and execute for the owner and read and execute for everyone else. Binary is the language of computers: every value in memory is a pattern of bits, each one a 0 or a 1. Numbers of any length are converted exactly, because the tool works with whole numbers digit by digit instead of rounding.
How to use Octal to Binary Converter
- Type or paste a octal number into the first box. Spaces, underscores and prefixes such as 0x are ignored.
- Read the binary result straight away in the second box, grouped for easier reading if you leave the box ticked.
- Look at the working table to see each step of the method.
- Copy the result, or use the swap button to convert binary back to octal.
Common uses
- Setting Unix and Linux file permissions such as 755 or 644
- Reading older computing documentation
- Computer science homework on number bases
- Checking escape codes in some programming languages
Frequently asked questions
How do I convert octal to binary by hand?
Replace each octal digit with its 3 bit binary pattern. The working table on this page shows exactly these steps for the number you type.
What is 377 in binary?
377 in octal is 11111111 in binary. In decimal it is 255, the largest number that fits in one byte.
What is 3752 in binary?
3752 in octal is 11111101010 in binary.
Can it convert very large numbers?
Yes. Whole numbers with up to 4,096 digits are converted exactly. The working table shows the first rows when a number is very long.
Does it handle fractions or negative numbers?
Negative whole numbers are converted with their minus sign kept. Fractions are not supported, because many fractions that end in one base repeat for ever in another.