Hexadecimal

Hexadecimal (hex for short) is a positional numeral system for representing a numeric value as base 16. For the most common convention, a digit is represented as "0" to "9" like for decimal and as a letter of the alphabet from "A" to "F" (either upper or lower case) for the digits with decimal value 10 to 15. As typical computer hardware is binary in nature and that hex is power of 2, the hex representation is often used in computing as a dense representation of binary information. A hex digit represents 4 contiguous bits –known as a nibble. An 8-bit byte is two hex digits, such as 2C. Special notation is often used to indicate that a number is hex. In mathematics, a subscript is typically used to specify the base. For example, the decimal value 491 would be expressed in hex as 1EB16. In computer programming, various notations are used. In C and many related languages, the prefix 0x is used. For example, 0x1EB.

Written representation

Common convention Typically, a hex representation convention allows either lower or upper case letters and treats the letter the same regardless of its case. Often when rendering non-textual data, a value stored in memory is displayed as a sequence of hex digits with spaces between values. For instance, in the following hex dump, each 8-bit byte is a 2-digit hex number, with spaces between them, while the 32-bit offset at the start is an 8-digit hex number.

Identification There are several conventions for expressing that a number is represented as hex.

A decimal subscript can give the base explicitly. For example 15910 indicates decimal 159, 15916 indicates hex 159. Some prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h In C and many languages influenced by it, the prefix 0x indicates that the numeric literal after it is in hex, a character of a string or character literal can be expressed as hex with the prefix \x (for example '\x1B' represents the Esc control character) and to output an integer as hex via printf-like function, the format conversion code %X or %x is used In URIs (including URLs), character codes are written as hex pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the code for the space (blank) character, ASCII code point 20 in hex, 32 in decimal. In XML and XHTML, a character can be expressed as a hex numeric character reference using the notation &#xcode;, for instance T represents the character U+0054 (the uppercase letter "T"). If there is no x the number is decimal (thus T is the same character). In Intel-derived assembly languages and Modula-2, hex is denoted with a suffixed H or h: FFh or 05A3H. Some implementations require a leading zero when the first hex digit character is not a decimal digit, so one would write 0FFh instead of FFh. Some other implementations (such as NASM) allow C-style numbers (0x42) Other assembly languages (6502, Motorola), Pascal, Delphi, some versions of BASIC (Commodore), GameMaker Language, Godot and Forth use $ as a prefix: $5A3, $C1F27ED Some assembly languages (Microchip) use the notation H'ABCD' (for ABCD16); similarly, Fortran 95 uses Z'ABCD' Ada and VHDL enclose hex numerals in based "numeric quotes": 16#5A3#, 16#C1F27ED#. For bit vector constants VHDL uses the notation x"5A3", x"C1F27ED". Verilog represents hex constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hex constant The Icon and Smalltalk languages use the prefix 16r: 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#: 16#5A3, 16#C1F27ED Common Lisp uses the prefixes #x and #16r. Setting the variables *read-base* and *print-base* to 16 can also be used to switch the reader and printer of a Common Lisp system to hex representation for reading and printing numbers. Thus hex numbers can be represented without the #x or #16r prefix code, when the input or output base has been changed to 16. MSX BASIC, QuickBASIC, FreeBASIC and Visual Basic prefix hex numbers with &H: &H5A3 BBC BASIC and Locomotive BASIC use & for hex TI-89 and 92 series uses a 0h prefix: 0h5A3, 0hC1F27ED ALGOL 68 uses the prefix 16r to denote hex numbers: 16r5a3, 16rC1F27ED. Binary, quaternary (base-4), and octal numbers can be specified similarly. The most common format for hex on IBM mainframes (zSeries) and midrange computers (IBM i) running the traditional OS's (zOS, zVSE, zVM, TPF, IBM i) is X'5A3' or X'C1F27ED', and is used in Assembler, PL/I, COBOL, JCL, scripts, commands and other places. This format was common on other (and now obsolete) IBM systems as well. Occasionally quotation marks were used instead of apostrophes. Donald Knuth used a typewriter typeface to represent hex in his book The TeXbook, like: 5A3, C1F27ED

Implicit In some contexts, a number is always written as hex, and therefore, needs no identification notation.

In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+00A1 is the inverted exclamation point (¡). Color references in HTML, CSS and X Window can be expressed with six hex digits (two each for the red, green and blue components, in that order) prefixed with #: magenta, for example, is represented as #FF00FF. CSS also allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33, a golden orange. In MIME (e-mail extensions) quoted-printable encoding, character codes are written as hex pairs prefixed with =: Espa=F1a is "España" (F1hex is the code for ñ in the ISO/IEC 8859-1 character set).) PostScript binary data (such as image pixels) can be expressed as unprefixed consecutive hex pairs: AA213FD51B3801043FBC ... Any IPv6 address can be written as eight groups of four hex digits (sometimes called hextets), where each group is separated by a colon (:). This, for example, is a valid IPv6 address: 2001:0db8:85a3:0000:0000:8a2e:0370:7334 or abbreviated by removing leading zeros as 2001:db8:85a3::8a2e:370:7334 (IPv4 addresses are usually written in decimal). Globally unique identifiers are written as thirty-two hex digits, often in unequal hyphen-separated groupings, for example 3F2504E0-4F89-41D3-9A0C-0305E82C3301.

Alternative symbols

Notable other hexadecimal representations that use symbols other than letters "A" through "F" to represent the digits above 9 include:

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