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Convert decimal numbers (base-10) to octal numbers (base-8) instantly. Used in Unix file permissions, computing, and digital systems.
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 7 | 7 |
| 8 | 10 |
| 16 | 20 |
| 64 | 100 |
| 100 | 144 |
| 128 | 200 |
| 255 | 377 |
| 256 | 400 |
| 512 | 1000 |
| 1000 | 1750 |
Octal (base-8) is a number system that uses eight digits: 0-7. It was popular in early computing because three binary digits (bits) can be represented by one octal digit (2³ = 8). Today, octal is primarily used in Unix/Linux file permissions and some specialized programming contexts.
Divide the decimal number by 8 repeatedly and record the remainder. Continue until the quotient is 0. The octal number is the remainders read from bottom to top (or right to left).
Example: Convert 83 to octal
83 ÷ 8 = 10 remainder 3
10 ÷ 8 = 1 remainder 2
1 ÷ 8 = 0 remainder 1
Result: 123 (reading remainders from bottom to top)
Octal is primarily used in Unix/Linux file permissions. For example, chmod 755 sets read/write/execute for owner and read/execute for group and others. While less common than hexadecimal in modern computing, it remains important for system administration and legacy code.
Unix permissions use three octal digits: one for owner, group, and others. Each digit is the sum of read (4), write (2), and execute (1) permissions. For example, 7 (4+2+1) means rwx, 6 (4+2) means rw-, and 5 (4+1) means r-x. So 755 means rwxr-xr-x.
Octal is base-8, meaning it uses 8 unique digits (0-7). Once you reach 7, the next number is 10 in octal (which equals 8 in decimal). This is similar to how decimal uses 0-9 and then goes to 10, but octal "rolls over" one digit earlier.
In many programming languages (C, C++, JavaScript), octal literals start with 0. For example, 0755 is octal for 493 in decimal. Python uses 0o prefix (0o755). This notation helps distinguish octal from decimal numbers in source code.
Hexadecimal (base-16) became more popular because modern computers use 8-bit bytes, and two hex digits represent exactly one byte (4 bits per hex digit). Octal digits represent 3 bits, which doesn't align as cleanly with byte boundaries. However, octal remains useful for Unix permissions and some specialized applications.