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The octal system is a base-8 numeral system, which uses eight symbols: 0, 1, 2, 3, 4, 5, 6, and 7. It is less commonly used than the decimal (base-10) or hexadecimal (base-16) systems, but it has historical significance and practical applications in computing. The octal system is particularly useful in computing because it can directly represent groups of three binary digits, making it easier to convert between binary and octal.

In the octal system, each digit's position represents a power of 8. For example, the number 357 in octal can be expressed as:

3 * 8^2 + 5 * 8^1 + 7 * 8^0 = 3 * 64 + 5 * 8 + 7 * 1 = 192 + 40 + 7 = 239

The octal system is often used in computing for file permissions in Unix-like operating systems, where each permission is represented by a three-digit octal number. For instance, the permission 755 means the owner has read, write, and execute permissions, while the group and others have read and execute permissions.

The octal system is also used in digital electronics and computer programming, particularly in low-level programming languages and hardware description languages. It provides a more compact representation of binary data, making it easier to work with certain types of data and perform bitwise operations.

Despite its practical uses, the octal system is not as widely used as the decimal or hexadecimal systems. However, its unique properties and historical significance make it an important topic in the study of numeral systems and computing.