An octal number is a numeral system that uses base 8, meaning it consists of eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. Each digit in an octal number represents a power of 8, similar to how decimal numbers use base 10. For example, the octal number 17 represents 1 \times 8^1 + 7 \times 8^0, which equals 15 in decimal. Octal numbers are often used in computing and digital electronics because they can represent binary numbers more compactly. Each octal digit corresponds to three binary digits (bits), making it easier to read and write large binary values. This relationship is particularly useful in programming and systems like Unix, where file permissions are often expressed in octal format.