Octal to Binary Converter
Type a base-8 number and get its binary form, one 3-bit group per digit.
Binary
| Binary | Decimal | Hex | Octal |
|---|
Going the other way? Use the binary to octal converter.
To convert octal to binary, replace each octal digit with its 3-bit binary group and keep the order. For octal 65, the 6 expands to 110 and the 5 to 101. Joined in order that gives 110101, worth 53 in decimal.
How it works
Octal is base 8, and since eight is two to the third power, every octal digit corresponds to exactly three binary digits. That correspondence is independent per digit: a 6 always expands to the same three bits no matter what sits next to it. So the whole conversion is reading the table once per digit.
Worked example with octal 65. The digit 6 is worth 6, which as three bits is 110. The digit 5 is worth 5, which is 101. Write the groups in the same order as the digits: 110101. Sanity check the long way: octal 65 means 6 eights plus 5 ones, which is 53, and converting 53 to binary lands on the same answer.
One caution: octal looks like decimal but is not. The octal number 65 and the decimal number 65 are different values (53 versus 65). If a number came from a chmod command, a Unix permission listing, or a leading-zero literal like 0755 in older programming languages, it is octal. If it came from ordinary human counting, it is decimal and belongs in the decimal to binary converter instead.
The expansion trick is also why octal ever existed: on early machines with 12-bit, 24-bit, and 36-bit words, a word split evenly into 3-bit groups, so octal printed nicely. Modern bytes are eight bits, which split into two hex digits instead, and hex mostly took over.
The digit table: all 8 expansions
| Octal | Binary | Decimal |
|---|---|---|
| 0 | 000 | 0 |
| 1 | 001 | 1 |
| 2 | 010 | 2 |
| 3 | 011 | 3 |
| 4 | 100 | 4 |
| 5 | 101 | 5 |
| 6 | 110 | 6 |
| 7 | 111 | 7 |
FAQ
How do I convert octal to binary?
Replace each octal digit with its 3-bit binary group, keeping the order. For octal 65, the 6 expands to 110 and the 5 expands to 101, giving 110101. No arithmetic is involved, just substitution from the eight-row table.
How is this different from decimal to binary?
Octal converts by substitution because eight is a power of two: each digit becomes exactly three bits, independently of its neighbors. Decimal has no such shortcut, since ten is not a power of two, so decimal conversion needs repeated division. Octal 65 and decimal 65 are also different values entirely.
What do octal permission numbers like 755 mean in binary?
Each digit expands to three bits meaning read, write, execute. The 7 becomes 111, all three allowed, and 5 becomes 101, read and execute only. So 755 spells rwx for the owner and r-x for everyone else.