Hexadecimal

Hexadecimal is a base-16 numeral system used in mathematics and computing. It uses sixteen distinct digits: the decimal digits 0 through 9 and the letters A through F (case-insensitive) to represent values zero to fifteen. In positional notation, each hex digit represents four binary bits, or a nibble, so a pair of hex digits corresponds to a byte.

Hex numbers are commonly written with prefixes such as 0x or 0X in programming languages; some contexts use a trailing h (for example 2FA3h) or a dollar sign in others. This reflects its roots in binary data, where each hex digit maps neatly to a 4-bit group.

Conversions: to decimal, sum each digit times 16 raised to the digit's position from right to left. For example, 2FA3 hex equals 2×4096 + 15×256 + 10×16 + 3 = 12195. To binary, each hex digit corresponds to four bits: 2→0010, F→1111, A→1010, 3→0011, so 2FA3 becomes 0010 1111 1010 0011.

Applications: hex is widely used to represent memory addresses, machine code, and other binary data in a compact, human-readable form. In web design, color codes use six hex digits after a hash, such as #RRGGBB; shorthand #RGB is also common where each digit expands to double.

Overview: hexadecimal is a practical notation in computing and digital systems, enabling efficient conversion between binary and a readable string format.