In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. Its primary purpose is to represent the binary code in a format easier for humans to read, and acts as a form of shorthand, in which one hexadecimal digit stands in place of four binary bits. For example, the decimal numeral 79, whose binary representation is 01001111, is 4F in hexadecimal (4 = 0100, F = 1111). IBM introduced the current hexadecimal system to the computing world; an earlier version, using the digits 0–9 and u–z, had been introduced in 1956, and had been used by the Bendix G-15 computer. This article is about different methods of expressing numbers with symbols. ... I like cream cheese, it tastes good on toast. ... For other uses, see Arabic numerals (disambiguation). ... The Eastern Arabic numerals (also called Eastern Arabic numerals, Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Pakistan and parts of India, and also in the no longer used Ottoman Turkish... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... India has produced many numeral systems. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... The counting rods (Traditional Chinese: , Simplified Chinese: , pinyin: chou2) were used by ancient Chinese before the invention of the abacus. ... The Abjad numerals are a decimal numeral system which was used in the Arabic-speaking world prior to the use of the Hindu-Arabic numerals from the 8th century, and in parallel with the latter until Modern times. ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ... Note: This article contains special characters. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... Greek numerals are a system of representing numbers using letters of the Greek alphabet. ... The Sanskrit alphabetic numerals were created in about A.D. 510 by Ä€ryabhaa. ... Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodian. ... Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. ... The Etruscan numerals were used by the ancient Etruscans. ... Mayan numerals. ... Roman numerals are a numeral system originating in ancient Rome, adapted from Etruscan numerals. ... During the beginning of the Urnfield culture, around 1200 BC, a series of votive sickles of bronze with marks that have been interpreted as a numeral system, appeared in Central Europe. ... This is a list of numeral system topics, by Wikipedia page. ... A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... For other uses, see Decimal (disambiguation). ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... Quaternary is the base four numeral system. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... In computing, base64 is a data encoding scheme whereby binary-encoded data is converted to printable ASCII characters. ... Ternary or trinary is the base-3 numeral system. ... Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. ... Base 30 or trigesimal is a positional numeral system using 30 as the radix. ... Base 36 refers to a positional numeral system using 36 as the radix. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... In mathematics, the base or radix is the number of various unique symbols (digits), including zero, that a positional numeral system uses to represent numbers in a given counting system. ... 16 (sixteen) is the natural number following 15 and preceding 17. ... This article is about different methods of expressing numbers with symbols. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... The term binary code can mean several different things: There are a variety of different methods of coding numbers or symbols into strings of, including fixed-length binary numbers, prefix codes such as Huffman code, and other arithmetic coding. ... Shorthand is an abbreviated, symbolic writing method that improves speed of writing or brevity as compared to a normal method of writing a language. ... This article is about the unit of information. ... For other uses, see Decimal (disambiguation). ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... For other uses, see IBM (disambiguation) and Big Blue. ... The Bendix G-15 computer was introduced in 1956 by the Bendix Corporation, Computer Division, Los Angeles, California. ...

Uses

The sixteen nibbles the hexadecimal figures stand for, ordered in a Hasse diagram

Hexadecimal is primarily used in computing to represent a byte. Representing the 256 possible values has a number of problems: first, there are unprintable control characters; second, ASCII itself stops at 7 bits with the remainder being system-specific extensions; and finally, even if all characters in the machine's set were displayable as something, neither users nor input methods are generally prepared to handle 256 unique characters. For other senses of this word, see zero or 0. ... This article is about the number one. ... This article does not cite any references or sources. ... Look up three in Wiktionary, the free dictionary. ... This article discusses the number Four. ... Look up five in Wiktionary, the free dictionary. ... Look up six in Wiktionary, the free dictionary. ... Seven Days of Creation - 1765 book, title page 7 (seven) is the natural number following 6 and preceding 8. ... Look up eight in Wiktionary, the free dictionary. ... This article is about the number. ... This article is about the number 10. ... 11 (eleven) is the natural number following 10 and preceding 12. ... Look up twelve in Wiktionary, the free dictionary. ... 13 (thirteen) is the natural number after 12 and before 14. ... 14 (fourteen) is the natural number following 13 and preceding 15. ... 15 (fifteen) is the natural number following 14 and preceding 16. ... Image File history File links Hypercubeorder. ... Image File history File links Hypercubeorder. ... For other uses, see Nibble (disambiguation). ... In the mathematical discipline known as order theory, a Hasse diagram (pronounced HAHS uh, named after Helmut Hasse (1898–1979)) is a simple picture of a finite partially ordered set, forming a drawing of the transitive reduction of the partial order. ... For the computer industry magazine, see Byte (magazine). ...

Hex triplets

HTML and CSS use hexadecimal notation (hex triplets) to specify colors on web pages, with "#" standing for hexadecimal. Twenty-four-bit color is represented in the format #RRGGBB: where RR specifies the value of the Red component of the color, GG the Green component, and BB the Blue component. For example, a shade of red that is (238,9,63) in decimal is coded as #EE093F. This syntax is borrowed from the X Window System. HTML, an initialism of Hypertext Markup Language, is the predominant markup language for web pages. ... In web development, Cascading Style Sheets (CSS) is a stylesheet language used to describe the presentation of a document written in a markup language. ... Authors of web pages have a variety of options available for specifying colors for elements of web documents. ... “X11” redirects here. ...

Example of conversion from hexadecimal triplet to decimal triplet: Hexadecimal triplet: FFCF4B

Step 1: Separate the triplets: FF CF 4B

Step 2: Convert each hexadecimal value to a decimal representation:

• FF = 15*16 + 15*1 = 255
• CF = 12*16 + 15*1 = 207
• 4B = 4*16 + 11*1 = 75

Result: Hexadecimal triplet FFCF4B = Decimal triplet 255,207,75

Other common uses

In URLs, all characters can be coded hexadecimally, even those not normally permitted. This is specified in RFC 3986. Each 2-digit (1 byte) hexadecimal sequence is preceded by a percent sign and refers to a specific UTF-8 character code. For example, in the URL http://en.wikipedia.org/wiki/Main%20Page, the (hexadecimal) UTF-8 character code for a space (" ") is 20. A Uniform Resource Locator, URL (spelled out as an acronym, not pronounced as earl), or Web address, is a standardized address name layout for resources (such as documents or images) on the Internet (or elsewhere). ... In internetworking and computer network engineering, Request for Comments (RFC) documents are a series of memoranda encompassing new research, innovations, and methodologies applicable to Internet technologies. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ... UTF-8 (8-bit UCS/Unicode Transformation Format) is a variable-length character encoding for Unicode. ... UTF-8 (8-bit UCS/Unicode Transformation Format) is a variable-length character encoding for Unicode. ...

Some software programs will create unique order numbers by using a hexadecimal representation of the exact second the order was taken, based on the total number of seconds since the start of the 20th century. For example, C9BCE0F5 represents April 2, 2007 14:19:32. Computer software (or simply software) refers to one or more computer programs and data held in the storage of a computer for some purpose. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999...

Page numbers on teletext are written in hexadecimal, with available numbers being in the range of 100-8FF. However, page numbers with letters are only used for "hidden" and engineering pages. A BBC Ceefax page from January 9, 2007. ...

Representing hexadecimal

Some hexadecimal representations are indistinguishable from decimal representations (to humans and computers); therefore, some convention is usually used to flag them.

In typeset text, hexadecimal is often indicated by a subscripted suffix such as 5A3₁₆, 5A3_SIXTEEN, or 5A3_HEX. In computer programming languages (which are nearly always plain text without such typographical distinctions as subscript and superscript),a wide variety of alternative notations are used to indicate hexadecimal numbers. Computer files can be divided into two broad categories: binary and text. ...

The following are some of the most common representations:

• Ada and VHDL enclose hexadecimal numerals in based "numeric quotes", e.g. 16#5A3#. (Note: Ada accepts this notation for all bases from 2 through 16 and for both integer and real types.)
• C and languages with a similar syntax (such as C++, C#, Java and JavaScript) prefix hexadecimal numerals with 0x, e.g. 0x5A3. The leading 0 is used so that the parser can simply recognize a number, and the x stands for hexadecimal. The x in 0x can be either in upper or lower case but is almost always seen written in lower case. In some languages other than C or C++, 0b is used to prefix Binary numbers, and occasionally (in Haskell, for example) 0o is used for Octal.
• *nix shells use an escape character form F in expressions and 0xFF for constants.
• In HTML, hexadecimal character references also use the x: ֣ should give the same as ֣ – with your browser ֣ and ֣ respectively (Hebrew accent munah). Hexadecimal color references are prefixed with #, e.g. #FFFFFF (white).
• Some assemblers indicate hex by an appended h (if the numeral starts with a letter, then also with a preceding 0, to indicate that it is a number), e.g., 0A3Ch, 5A3h. The syntax may vary per assembly language. For example, the 6502 assembly language uses a $ as prefix, e.g. #$10FF (the # indicates an immediate numeric value).
• Postscript indicates hex by a prefix 16#.
• Common Lisp use the prefixes #x and #16r.
• Pascal, other assemblers (AT&T, Motorola), and some versions of BASIC and Forth use a prefixed $, e.g. $5A3.
• The Smalltalk programming language uses the prefix 16r. Note Smalltalk accepts the format <radix>r<digits> where radix is a number base from 2 upwards (i.e. 2r1110 is 10r14 or 16rE), with the practical limitation being within the ASCII character set range 0-9 and A-Z used to represent the digits. Some versions of Smalltalk allow fractional digits following a period character, ., enabling hexadecimal (and other base) representation of floating point numbers.
• Some versions of BASIC, notably Microsoft's variants including QBasic and Visual Basic, prefix hexadecimal numerals with &H, e.g. &H5A3; others such as BBC BASIC just used & (used for octal in Microsoft's BASIC).
• TI 89 and 92 series designate 0h (ex 0hA3)
• Notations such as X'5A3' are sometimes seen; PL/I uses such notation. This is the most common format for hexadecimal on IBM mainframes (zSeries) and minicomputers (iSeries) running the traditional OS's (zOS, zVSE, zVM, TPF, OS/400), and is used in Assembler, PL/1, Cobol, JCL, scripts, commands and other places. The most common exceptions are when using a language with a different native convention (C, Java, etc.). This format was common on other (and now obsolete) IBM systems as well.
• Microchip's MPASM assembler uses H'5A' to represent hexadecimal numbers as well as the more common 0x prefix.
• Donald Knuth introduced the use of different fonts to represent radices in his book The TeXbook. In his notation, hexadecimal representations are written in a typewriter type, e.g. 5A3

A hexadecimal multiplication table

There is no single agreed-upon standard, so all the above conventions are in use, sometimes even in the same paper. However, as they are quite unambiguous, little difficulty arises from this. Ada is a structured, statically typed, imperative, and object-oriented high-level computer programming language. ... VHDL, or VHSIC Hardware Description Language, is commonly used as a design-entry language for field-programmable gate arrays and application-specific integrated circuits in electronic design automation of digital circuits. ... The integers are commonly denoted by the above symbol. ... C is a general-purpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ... C++ (pronounced see plus plus, IPA: ) is a general-purpose programming language with high-level and low-level capabilities. ... C# (pronounced see-sharp) is an object-oriented programming language developed by Microsoft as part of their . ... Java language redirects here. ... JavaScript is a scripting language most often used for client-side web development. ... A parser is a computer program or a component of a program that analyses the grammatical structure of an input, with respect to a given formal grammar, a process known as parsing. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... Haskell is a standardized purely functional programming language with non-strict semantics, named after the logician Haskell Curry. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... A Unix-like operating system is one that behaves in a manner similar to a UNIX system, while not necessarily conforming to or being certified to any version of the Single UNIX Specification. ... HTML, an initialism of Hypertext Markup Language, is the predominant markup language for web pages. ... See the terminology section, below, regarding inconsistent use of the terms assembly and assembler. ... The MOS Technology 6502 is an 8-bit microprocessor that was designed by Chuck Peddle for MOS Technology in 1975. ... PostScript (PS) is a page description language used primarily in the electronic and desktop publishing areas. ... Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard X3. ... Pascal is a structured imperative computer programming language, developed in 1970 by Niklaus Wirth as a language particularly suitable for structured programming. ... This article is about the current AT&T. For the 1885-2005 company, see American Telephone & Telegraph. ... Motorola Inc. ... BASIC (Beginners All-purpose Symbolic Instruction Code) is a family of high-level programming languages. ... Forth is a programming language and programming environment, initially developed by Charles H. Moore at the US National Radio Astronomy Observatory in the early 1970s. ... For other uses, see Small talk. ... BASIC (Beginners All-purpose Symbolic Instruction Code) is a family of high-level programming languages. ... Microsoft Corporation, (NASDAQ: MSFT, HKSE: 4338) is a multinational computer technology corporation with global annual revenue of US$44. ... QBasic is an IDE and interpreter for a variant of the BASIC programming language which is based on QuickBasic. ... This article is about the Visual Basic language shipping with Microsoft Visual Studio 6. ... BBC BASIC was developed in 1981 as a native programming language for the MOS Technology 6502 based Acorn BBC Micro home/personal computer, mainly by Roger Wilson. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... PL/I (Programming Language One, pronounced pee el one) is an imperative computer programming language designed for scientific, engineering, and business applications. ... Since December, 2001, IBM designates all its mainframes with the name eServer zSeries, with the e depicted in IBMs well-known red trademarked symbol. ... Enterprise class server and the successor to the AS/400. ... Microchip Technology (NASDAQ: MCHP) is a manufacturer of semiconductors, founded in ??. Its products include microcontrollers (PICmicro, dsPIC, PIC24), EEPROM and Flash memory devices, KEELOQ devices, radio frequency (RF) devices, battery management devices, interface devices, analog devices and many others. ... Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... Image File history File links Hexadecimal_multiplication_table. ... Image File history File links Hexadecimal_multiplication_table. ... Times table redirects here. ...

The most commonly used (or encountered) notations are the ones with a prefix "0x" or a subscript-base 16, for hex numbers. For example, both 0x2BAD and 2BAD₁₆ represent the decimal number 11181 (or 11181₁₀). For other uses, see Decimal (disambiguation). ...

The choice of the letters A through F to represent the additional digits was not universal in the early history of computers. During the 1950s, some installations favored using the digits 0 through 5 with a macron to indicate the values 10-15. Users of Bendix G-15 computers used the letters U through Z. A macron, from Greek (makros) meaning large, is a diacritic ¯ placed over a vowel originally to indicate that the vowel is long. ... The Bendix G-15 computer was introduced in 1956 by the Bendix Corporation, Computer Division, Los Angeles, California. ...

One solution how to write hexadecimal numbers distinctively is the use of figures that are made for the hexadecimal system but are not yet representable in Unicode. The Unicode Standard, Version 5. ...

Verbal representations

Not only are there currently no proper digits to represent the quantities from ten to fifteen (so letters are used as a substitute), but English also lacks a proper nomenclature to name hexadecimal numbers. Names such as "thirteen" and "fourteen" are decimal-based, and even though English has a few names for non-decimal powers—pair for the first binary power; score for the first vigesimal power; dozen, gross and great gross for the first three duodecimal powers—no English name currently exists for any of the hexadecimal powers (corresponding to the decimal values 16, 256, 4096, etc.). So people have resorted to reading hexadecimal numbers by naming their digits (or digit-letters) individually in sequence in the same way as reading phone numbers (i.e., 4DA as "four-dee-aye"). However, the letter 'A' sounds similar to '8', 'C' sounds similar to '3', and 'D' can easily be mistaken for the 'ty' suffix as in "forty"; so 4DA could be mistaken for 48. To avoid misunderstandings, some convention must be established when exchanging hexadecimal numbers verbally, at least until a proper hexadecimal nomenclature is developed (if ever). To avoid confusion, the digits A-F are commonly pronounced with the NATO phonetic alphabet ("four-delta-alpha"), the World War II era Joint Army/Navy Phonetic Alphabet ("four-dog-able"), or some approximation of one of those systems. For other uses, see Decimal (disambiguation). ... The word pair, derived via the French words pair/paire from the Latin par equal, can mean: the French equivalent of peer, holder of a French Pairie, French high title roughly equivalent to a member of the British peerage 2 (number), two of something Couple, various senses for two joined... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... 20 (twenty) is the natural number following 19 and preceding 21. ... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... Dozen is another word for the number twelve. ... Categories: | | ... A great gross is equal to a dozen gross, i. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... FAA radiotelephony phonetic alphabet and Morse code chart. ... The Joint Army/Navy Phonetic Alphabet was developed in 1941 and was used by all branches of the United States military until the promulgation of the NATO phonetic alphabet in 1956, which replaced it. ...

Fractions

As with other numeral systems, the hexadecimal system can be used to represent rational numbers, although recurring digits are common since 16 has only a single prime factor: In mathematics, a rational number is a number which can be expressed as a ratio of two integers. ... A recurring or repeating decimal is a number which when expressed as a decimal has a set of final digits which repeat an infinite number of times. ...

Because the radix 16 is a perfect square (4²), fractions expressed in hexadecimal have an odd period much more often than decimal ones, and there are no cyclic numbers (other than trivial single digits). Recurring digits occur when the denominator in lowest terms has a prime factor not found in the radix; thus, when using hexadecimal notation all fractions with denominators that are not a power of two will result in an infinite string of recurring digits (e.g., thirds and fifths). This makes hexadecimal (and binary) less convenient than decimal (not to mention duodecimal and sexagesimal) for the purpose of representing rational numbers, since a larger proportion of them lie outside its range of finite representation. All rational numbers finitely representable in hexadecimal are also finitely representable in decimal, duodecimal and sexagesimal (i.e., any hexadecimal number with a finite number of digits will have a finite number of digits when expressed in those other bases), whereas only a fraction of those finitely representable in the latter ones are finitely representable in the former (e.g., decimal 0.1, that is, the fraction one tenth, corresponds to the infinite recurring representation 0.199999999999... in hexadecimal). Although hexadecimal is more efficient than those other bases for the particular case of representing fractions with powers of two as the denominator (cf. one sixteenth is 0.1 in hexadecimal, 0.09 in duodecimal, 0;3,45 in sexagesimal and 0.0625 in decimal). The term perfect square is used in mathematics in two meanings: an integer which is the square of some other integer, i. ... A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number. ... This article is about the concept in number theory. ... In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. ... For other uses, see Decimal (disambiguation). ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ...

Mapping to binary

Sometimes it is necessary to use binary data when working with computers, but it is difficult for humans to work with the large number of digits in binary. Although most humans are more familiar with the base 10 system, it is much easier to map binary to hexadecimal than to decimal because each hexadecimal digit maps to a whole number of bits (4₁₀). The following is an example of converting 1111₂ to base 10. Since each position in a binary numeral can only contain either a 1 or 0, its value may be easily determined by its position from the right: A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system. ...

• 0001₂ = 1₁₀
• 0010₂ = 2₁₀
• 0100₂ = 4₁₀
• 1000₂ = 8₁₀

Therefore:

This example shows addition of 4 numbers; but with some practice, 1111₂ can be mapped directly to F₁₆ in one step (see table in Representing hexadecimal). The advantage of using hexadecimal rather than decimal increases with the size of the number. When the number becomes large, conversion to decimal becomes much more tedious; however, when mapping to hexadecimal, it is simple to divide the binary string into blocks of 4 positions and map each block of 4 bits to a single position hexadecimal digit. In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. ...

This example shows the conversion of a binary number to decimal, mapping each digit to the decimal value, and adding the results.

Compare this to the conversion to hexadecimal, where each group of four digits can be considered independently, and converted directly:

Conversion from hexadecimal back to binary is just as direct.

The octal system can also be useful as a tool for people who need to deal directly with binary computer data, as in reading and understanding it. Compared to hexadecimal, octal represents data in blocks of 3 bits each, rather than 4. The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ...

One advantage of hexadecimal is that every unique 2-digit pair (or octet) always represents the same byte value. To "translate" a hexadecimal value into bytes, one needs only to separate the value into individual 2-digit groups, translate each group into its respective byte value, and then combine the results together to form an accurate translation of the entire original hexadecimal word. Conversely, bytes can also be easily translated into hexadecimal values by translating each byte individually into its hexadecimal 2-digit value, and then recombining the hexadecimal values into a "word". The resulting "word" will be an accurate hexadecimal representation of the original string of bytes.

Converting from other bases

Division-remainder in source base

As with all bases there is a simple algorithm for converting a representation of a number to hexadecimal by doing integer division and remainder operations in the source base. Theoretically this is possible from any base but for most humans only decimal and for most computers only binary (which can be converted by far more efficient methods) can be easily handled with this method. In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ...

Let d be the number to represent in hexadecimal, and the series h_ih_i-1...h₂h₁ be the hexadecimal digits representing the number.

1. i := 1
2. h_i := d mod 16
3. d := (d-h_i) / 16
4. If d = 0 (return series h_i) else increment i and go to step 2

"16" may be replaced with any other base that may be desired.

The following is a JavaScript implementation of the above algorithm for converting any number to a hexadecimal in String representation. Its purpose is to illustrate the above algorithm. To work with data seriously however, it is much more advisable to work with bitwise operators. JavaScript is a scripting language most often used for client-side web development. ... In computer programming, a bitwise operation operates on one or two bit patterns or binary numerals at the level of their individual bits. ...

 function toHex(d) { var r = d % 16; var result; if(d-r==0) result = toChar(r); else result = toHex( (d-r)/16 )+toChar(r); return result; } function toChar(n) { var alpha = "0123456789ABCDEF"; return alpha.charAt(n); } 

Addition and multiplication in hexadecimal

It is also possible to make the conversion by assigning each place in the source base the hexadecimal representation of its place value and then performing multiplication and addition to get the final representation.

Conversion via binary

As computers generally work in binary the normal way for a computer to make such a conversion would be to convert to binary first (by doing multiplication and addition in binary) and then make use of the direct mapping from binary to hexadecimal.

Etymology

It was IBM that decided on the prefix of "hexa" rather than the proper Latin prefix of "sexa". The word "hexadecimal" is strange in that hexa is derived from the Greek έξ (hex) for "six" and decimal is derived from the Latin for "tenth". It may have been derived from the Latin root, but Greek deka is so similar to the Latin decem that some would not consider this nomenclature inconsistent. An older term was the incorrect Latin-like "sexidecimal" (correct Latin is "sedecim" for 16), but that was changed because some people thought it too risqué, and it also had an alternative meaning of "base 60". However, the word "sexagesimal" (base 60) retains the prefix. The earlier Bendix documentation used the term "sexadecimal". Donald Knuth has pointed out that the etymologically correct term is "senidenary", from the Latin term for "grouped by 16". (The terms "binary", "ternary" and "quaternary" are from the same Latin construction, and the etymologically correct term for "decimal" arithmetic should be "denary".)^[1] Schwartzman notes that the expected purely Latin form would be "sexadecimal", but then computer hackers would be tempted to shorten the word to "sex".^[2] Incidentally, the etymologically proper Greek term would be hexadecadic (although in Modern Greek deca-hexadic (δεκαεξαδικός) is more commonly used). For other uses, see Latin (disambiguation). ... Sexagesimal numbering is a numeral system with number 60 as the base. ... The sexagesimal (base-sixty) is a numeral system with sixty as the base. ... Donald Ervin Knuth ( or Ka-NOOTH[1], Chinese: [2]) (b. ... Etymologies redirects here. ... Main article: Greek language Modern Greek (Νέα Ελληνικά or Νεοελληνική, lit. ...

Humor

Hexadecimal is sometimes used in programmer jokes because certain words can be formed using only hexadecimal digits. Some of these words are "dead", "beef", "babe", and with appropriate substitutions "c0ffee". Since these are quickly recognizable by programmers, debugging setups sometimes initialize memory to them to help programmers see when something has not been initialized. Some people add an H after a number if they want to show that it is written in hexadecimal. In older Intel assembly syntax, this is sometimes the case. "Hexspeak" may be the forerunner of the modern web parlance of "1337speak" See the terminology section, below, regarding inconsistent use of the terms assembly and assembler. ... Hexspeak, like leetspeak, is a novelty form of variant English spelling. ... This article does not adequately cite its references or sources. ...

An example is the magic number in FAT Mach-O files and java programs, which is "CAFEBABE". Single-architecture Mach-O files have the magic number "FEEDFACE" at their beginning. In computer programming, the term magic number has multiple meanings. ... The Java platform is the name for a bundle of related programs, or platform, from Sun Microsystems which allow for developing and running programs written in the Java programming language. ...

A Knuth reward check is one hexadecimal dollar, or $2.56. One of Donald Knuths reward checks In the preface of each of his books and on his website[1], computer scientist Donald Knuth offers to cheerfully pay a reward of $2. ...

The following table shows a joke in hexadecimal:

 3x12=36 2x12=24 1x12=12 0x12=18 

The first three are interpreted as multiplication, while in the last one "0x12" in hex is 18.

0xdeadbeef is sometimes put into uninitialized memory. Wikipedia does not yet have an article with this exact name. ...

Microsoft Windows XP clears its locked index.dat files with the hex codes: "0BADF00D"

Trivia

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• Hexadecimal is used in the Traveller family of role playing games as a form of shorthand for character attributes and world specifications.
• Hexadecimal is a villain in the CGI animated series ReBoot

Image File history File links Broom_icon. ... Traveller is a series of related science fiction role-playing games, first published in 1977 by Game Designers Workshop. ... This article is about the television program ReBoot. ...

See also

Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... In computing, base64 is a data encoding scheme whereby binary-encoded data is converted to printable ASCII characters. ... In computing, Bubble Babble is a binary data encoding designed by Antti Huima. ... A hex editor (or binary file editor or byte editor) is a type of computer program that allows a user to manipulate binary (normally non-plain text) computer files. ... Hexadecimal time is the representation of the time of day as a hexadecimal number in the interval [0,1] or [0,2], regulary multipied by a multiple of 16. ... Hexspeak, like leetspeak, is a novelty form of variant English spelling. ... For other uses, see Nibble (disambiguation). ... This article is about different methods of expressing numbers with symbols. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... HTML, an initialism of Hypertext Markup Language, is the predominant markup language for web pages. ...

References

External links

• Online Converter for Decimal/Hexadecimal Numerals (JavaScript, GPL)
• Intuitor Hex Headquarters - A site dedicated to changing the traditional base 10 (decimal) standard to hexadecimal.
• The hexadecimal metric system  at hexadecimal.florencetime.net
• base42 - A site proposing an alternate symbol set for hexadecimal numbers.
• Leet Key, a Firefox extension that supports ASCII/Hex conversions and typing
• (Hexadecimal) web colors explained

• Hex/ASCII 'translation' service