The hexadecimal system is a base-16 number system that uses sixteen distinct symbols: the digits 0-9 represent values zero to nine, while the letters A-F represent values ten to fifteen. This system is commonly used in computing and digital electronics because it can represent large binary numbers in a more compact and readable form. In the hexadecimal system, each digit's place value is a power of 16, similar to how the decimal system uses powers of 10. For example, the hexadecimal number 1A3 can be converted to decimal by calculating 1 \times 16^2 + 10 \times 16^1 + 3 \times 16^0, which equals 419 in decimal.