The hexadecimal number system is a base-16 numeral system that uses sixteen distinct symbols: the digits 0-9 and the letters A-F. In this system, A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15. It is commonly used in computing and digital electronics because it can represent large binary numbers in a more compact and readable form. Each digit in the hexadecimal system represents a power of 16, similar to how each digit in the decimal system represents a power of 10. For example, the hexadecimal number 1A3 translates to (1 × 16²) + (10 × 16¹) + (3 × 16⁰), which equals 419 in decimal. This system simplifies the representation of binary data, making it easier for programmers and engineers to work with.