Octal to Decimal Calculator

Octal is a base-8 number system that uses digits 0 through 7. Each octal digit represents exactly three binary digits (bits), since 2^3 = 8. Octal was used in early computing because older computers processed data in 6-bit or 12-bit groups, which are multiples of 3. Today, octal is mainly used in Unix/Linux file permissions (e.g., chmod 755) and some networking contexts.

Multiply each octal digit by 8 raised to the power of its position (from right, starting at 0), then sum the results. For example, 755 in octal: 5 x 8^0 = 5, 5 x 8^1 = 40, 7 x 8^2 = 448. Total = 5 + 40 + 448 = 493 in decimal.

chmod 755 is a Unix/Linux file permission setting using octal notation. The three digits represent the permissions for owner (7), group (5), and others (5). Each digit is the sum of read (4), write (2), and execute (1) permissions. 7 = 4+2+1 = read, write, execute. 5 = 4+0+1 = read, no write, execute. So 755 means the owner can read, write, and execute; group and others can only read and execute.

One octal digit represents exactly three binary bits, making conversion between the two very simple. To convert binary to octal, group binary digits in threes from the right and convert each group: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. For example, binary 110 111 101 = octal 675. This is why octal was convenient before hexadecimal became standard.

Octal is less common than it once was but is still used in specific contexts: Unix/Linux file permissions (chmod), some escape sequences in programming languages (e.g., \077 in C), embedded systems programming, and some network equipment configuration. Hexadecimal has largely replaced octal for most computing uses because processors now commonly work with 4-bit nibbles (hexadecimal) rather than 3-bit groups (octal).