Octal numbers are a base-8 numeral system that uses digits from 0 to 7. Each digit in an octal number represents a power of 8, making it different from the more commonly used decimal system, which is 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), simplifying the conversion between the two systems. This makes octal useful in contexts like Unix file permissions and computer programming.