Hexadecimal numbers

Hexadecimal

In mathematics and computing, hexadecimal(also base 16, or hex) is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a–f) to represent values ten to fifteen. Hexadecimal numerals are widely used by computer systems designers and programmers. Several different notations are used to represent hexadecimal constants in computing languages; the prefix "0x" is widespread due to its use in Unix and C (and related operating systems and languages). Alternatively, some authors denote hexadecimal values using a suffix or subscript. For example, one could write 0x2AF3 or 2AF3₁₆, depending on the choice of notation.

As an example, the hexadecimal number 2AF3₁₆ can be converted to an equivalent decimal representation. Observe that 2AF3₁₆is equal to a sum of (2000₁₆ + A00₁₆ + F0₁₆ + 3₁₆), by decomposing the numeral into a series of place value terms. Converting each term to decimal, one can further write: (2₁₆ × 16³) + (A₁₆ × 16²) + (F₁₆ × 16¹) + (3₁₆ × 16⁰),
(2 × 4096) + (10 × 256) + (15 × 16) + (3 × 1), or 10995.

Each hexadecimal digit represents four binary digits (bits), and the primary use of hexadecimal notation is a human-friendly representation of binary-coded values in computing and digital electronics. One hexadecimal digit represents a nibble, which is half of an octet or byte (8 bits). For example, byte values can range from 0 to 255 (decimal), but may be more conveniently represented as two hexadecimal digits in the range 00 to FF. Hexadecimal is also commonly used to represent computer memory addresses.