In mathematics and computing, hexadecimal is a positional system that represents numbers using a base of 16. Unlike the common way of representing numbers with ten symbols, it uses sixteen distinct symbols, most the symbols "0"–"9" to represent values zero to nine, "A"–"F" to represent values ten to fifteen. Hexadecimal numerals are used by computer system designers and programmers, as they provide a human-friendly representation of binary-coded values; each hexadecimal digit represents four binary digits known as a nibble, half a byte. For example, a single byte can have values ranging from 00000000 to 11111111 in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is used to specify the base known as the radix. For example, the decimal value 10,995 would be expressed in hexadecimal as 2AF316. In programming, a number of notations are used to support hexadecimal representation involving a prefix or suffix; the prefix 0x is used in C and related languages, which would denote this value by 0x2AF3.

Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits. All modern use uses the letters A-F to represent the digits with values 10-15. There is no universal convention to use lowercase or uppercase, each is prevalent or preferred in particular environments by community standards or convention, mixed case is used. Seven-segment displays use mixed-case AbCdEF to make digits that can be distinguished from each other. In contexts where the base is not clear, hexadecimal numbers can be ambiguous and confused with numbers expressed in other bases. There are several conventions for expressing values unambiguously. A numerical subscript can give the base explicitly: 15910 is decimal 159; some authors prefer a text subscript, such as 159decimal and 159hex, or 159h. Donald Knuth introduced the use of a particular typeface to represent a particular radix in his book The TeXbook. Hexadecimal representations are written there in a typewriter typeface: 5A3 In linear text systems, such as those used in most computer programming environments, a variety of methods have arisen: Unix shells, AT&T assembly language and the C programming language use the prefix 0x for numeric constants represented in hex: 0x5A3.

Character and string constants may express character codes in hexadecimal with the prefix \x followed by two hex digits:'\x1B' represents the Esc control character. To output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In URIs, character codes are written as hexadecimal pairs prefixed with %: http://www.example.com/name%20with%20spaces where %20 is the code for the space character, ASCII code point 20 in hex, 32 in decimal. In XML and XHTML, characters can be expressed as hexadecimal numeric character references using the notation &#xcode. If there is no x the number is decimal. In the Unicode standard, a character value is represented with U+ followed by the hex value, e.g. U+20AC is the Euro sign. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #: white, for example, is represented as #FFFFFF. CSS allows 3-hexdigit abbreviations with one hexdigit per component: #FA3 abbreviates #FFAA33.

In MIME quoted-printable encoding, character codes are written as hexadecimal pairs prefixed with =: Espa=F1a is "España".) In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h: FFh or 05A3H. Some implementations require a leading zero when the first hexadecimal digit character is not a decimal digit, so one would write 0FFh instead of FFh Other assembly languages, Delphi, some versions of BASIC, GameMaker Language and Forth use $ as a prefix: $5A3; some assembly languages use the notation H'ABCD'. Fortran 95 uses Z'ABCD'. Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. For bit vector constants VHDL uses the notation x"5A3". Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits in the value and FF is the hexadecimal constant; the Smalltalk language uses the prefix 16r: 16r5A3 PostScript and the Bourne shell and its derivatives denote hex with prefix 16#: 16#5A3. For PostScript, binary data can be expressed as unprefixed consecutive hexadecimal pairs: AA213FD51B3801043FBC...

Common Lisp uses the prefixes # 16r. Setting the variables *read-base* and *print-base* to 16 can be used to switch the reader and printer of a Common Lisp system to Hexadecimal number representation for reading and printing numbers, thus Hexadecimal 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 hexadecimal numbers with &H: &H5A3 BBC BASIC and Locomotive BASIC use & for hex. TI-89 and 92 series uses a 0h prefix: 0h5A3 ALGOL 68 uses the prefix 16r to denote hexadecimal numbers: 16r5a3. Binary

Charles Jenkins is a musician based in Melbourne, Australia. He is a member of Icecream Hands, has released eight solo albums and is a member of Charles Jenkins and the Zhivagos. Following his birth in Mildura, Jenkins moved to Adelaide, South Australia. Jenkins started as a solo performer and joined the band The Mad Turks From Istanbul. In 1989, Jenkins relocated to Melbourne, Australia with the band, but the Mad Turks disbanded soon after the move and Jenkins formed a new band called'Icecream Hands'; the band formed in 1992 and was named'Chuck Skatt and His Icecream Hands'. Jenkins revealed in 2007 that the first of the five albums that Icecream Hands recorded, Travelling... Made Easy, sold poorly and he attributed this to "too many chords and too many words". Icecream Hands functioned as a band for 16 years and Jenkins has stated that becoming a father affected the manner in which he wrote songs for the quartet, as he was forced to exercise a greater degree of self-restraint: "I'm fond of that album because of the heartache that went into it.

It was a real struggle." The band's third album Sweeter than the Radio was released in 1999 and the independent label they were signed to had secured an arrangement with major label Bertelsmann Music Group, otherwise known as BMG. Up until that point, the band had never received the backing of a corporate music company and subsequently released five songs from their BMG-backed work, followed by constant touring. Jenkins explained afterwards: "I never saw as a missed opportunity. I thought we were lucky just to have a major label."By the time the third album Sweeter Than The Radio was released, again through independent Melbourne, Australian label Rubber Records, but BMG was no longer involved and Jenkins spoke of "one girl in Melbourne" handling duties by that stage. Prior to the band's fifth and final album, a'best of' compilation, titled The Best of the Ice Cream Hands - You Can Ride My Bike was released by Rubber Records on the first day of 2004. Containing 43 songs, the live performance that coincided with the release of the compilation was described by an Australian music journalist as "strong, poetic songs filled the show with moments of sweet sonic purity.

Melbourne is lucky to have them."During periods of inactivity by the members of Icecream Hands, Jenkins recorded three solo albums, including Bungalow from 2004. As a solo artist, Jenkins released a total of four studio albums between 2004 and 2010, 2010's Blue Atlas, released on Dust Devil Music, introduced the public to a new band called the Zhivagos. Writing for website Mess + Noise, JP Hammond concluded that "There's no better soundtrack of hope to close 2008."Charles Jenkins and the Zhivagos have released three studio albums as of January 2014: Walk This Ocean, Love Your Crooked Neighbour with Your Crooked Heart and Blue Atlas. Released on Silver Stamp Records, Love Your Crooked Neighbour with Your Crooked Heart received a 4-star rating from music journalist Iain Shedden, writing for The Age newspaper, stated: There's a smattering of gospel-tinged singalong, exquisitely crafted balladry and melodic invention in the mix as well, all matched by a sharp tongue and an ear for a killer hook.

Jenkins received a grant from the Australia Council in 2013 to record an album centred upon the theme of water. Along with band members Dave Mine, Davey Lane, Art Starr and Matty Vehl, Jenkins created Too Much Water In the Boat that consists of songs such as "Sweet Mildura", "Seven Creeks" and "The Barrel Song". On 3 January 2014, Jenkins's band previewed the album on "The Inner Sleeve", Paul Gough's program on the ABC's Radio National network. Gough described Jenkins's work as "wry, insightful pop songs that have more to say than most". Too Much Water In the Boat was produced and engineered by Justin Rudge, features backing harmonies from ex-Icecream Hands member Douglas Lee Robertson, described by Jenkins as "extraordinary". Bungalow - Parole Records The City Gates - Parole Records Blue Atlas - Dust Devil Music Walk This Ocean - Dust Devil Music Love Your Crooked Neighbor With Your Crooked Heart - Silver Stamp Records Too Much Water In The Boat - Silver Stamp Records The Last Polaroid - Silver Stamp Records When I Was On The Moon - Silver Stamp Records Charles Jenkins website Dust Devil Music website

Áed mac Neíll, called Áed Findliath to distinguish him from his paternal grandfather Áed Oirdnide, was king of Ailech and High King of Ireland. A member of the northern Uí Néill kindred of the Cenél nEógain, Áed was the son of Niall Caille. From the death of Áed Allán in 743 until the overthrow of Máel Sechnaill mac Domnaill by Brian Boru in 1002, the succession to the High Kingship of Ireland alternated between northern and southern branches of the Uí Néill with the north represented by members of the Cenél nÉogain, Áed's paternal kindred, the south by the Clann Cholmáin, his mother's kin. Francis John Byrne describes this as "a fragile convention, marked by watchful jealousy rather than friendly accord."During the reign of Máel Sechnaill mac Maíl Ruanaid, who succeeded Áed's father as High King, the balance of power between north and south which had ensured the alternating succession appeared to be tipping in favour of the southern Clann Cholmáin kindred. The weakness of the Kings of Munster following the death of the powerful Feidlimid mac Crimthainn in 847 led to repeated attacks on Munster by Máel Sechnaill in the 850s and a submission by the kings of Munster in 858.

In 859, Osraige was made subject to the Uí Néill, this led to open warfare between Máel Sechnaill and Áed. Áed was the son of Niall Gormlaith. His mother, Gormflaith ingen Donncadha, is called "Gormlaith of the dazzling white complexion" by the Banshenchas, his maternal grandfather was his paternal grandfather Áed Oirdnide. His father, his mother's brother, Conchobar mac Donnchada, both of his grandfathers had been counted as High Kings of Ireland; the names of three of Áed's wives are recorded, although the order of his marriages is uncertain. His first wife may have been Gormlaith Rapach, "the harsh", daughter of Muiredach mac Eochada, king of Ulster; the Banshenchas say that Domnall mac Áeda was her son, Eithne, who married Flann Sinna, may have been her daughter. Áed's second wife, Land ingen Dúngaile was the widow of his predecessor as High King, Máel Sechnaill mac Máele Ruanaid, a grandson of Donnchad Midi. His third known wife was Máel Muire the daughter of Cináed mac Ailpín, the king of the Picts in Britain.

She was the mother of Niall Glúndub. On Áed's death she married his successor Flann Sinna. Other children of Áed included Domnall Dabaill. Following the death of Neill Caille in 845, Áed's uncle Máel Dúin mac Áeda assumed the kingship of Ailech; when Áed succeeded him is not recorded, but it might have been in 855. Áed is mentioned for the first time in the annals this year, as the Annals of Ulster records that he made a foray against the Ulaid, he left behind dead Coinnecán son of Colmán and Flaithbertach son of Niall, a large number besides Presumably Flaithbertach was his own brother, this foray was made to secure Áed's position as king of Ailech. Áed came into power at a critical period in the history of Ireland. Raids by Norse Vikings had taken place for half a century, the Norse settlements now seemed to have become permanent establishments more than just bases for raids, they now had an effective leadership under Amlaíb Conung and Ímar. At this time, both the contemporary annalists as well as modern historians refer to them not just as Vikings, foreigners or pagans, but Norse-Irish or Norse-Gaels.

Áed Findliath has been described as one of the Irish high-kings who most fought the Norse expansion in Ireland. He did indeed win some crucial battles against the Norse-gaels; the reigning High-King at the time, Mael Sechnaill, seemed more concerned with the internal Irish power struggle in Munster, than with engaging the Norse. There is however one reference in 856 to him fighting against "pagans" with the support of the Norse-Gaels; this could be interpreted as an alliance between the Norse settlers and the established Irish society against marauders. In 858, Máel Sechnaill managed to establish control over Munster, in 859 he made a peace settlement with Cerball mac Dúnlainge king of Osraige. Máel Sechnaill now turned his attention to the north, where the growing power of Áed Findliath had become a threat against him as head of Uí Néill. In 860 he brought an army consisting of forces from all of the southern part of Ireland to Armagh. While they were camped there, Áed Findliath attacked; the outcome of the battle seem to have been some sort of draw.

By now it was Áed Findliath. In 861 as well as 862 he plundered Míde in co-operation with Norse forces, in 862 he had the support of Flann mac Conaing, king of Brega. Máel Sechnaill mac Máele Ruanaid died 20 November 862, he was on that occasion described in the Annals of Ulster as ri h-Erenn uile, king of all Ireland; that was a title that would never be used about Áed Findliath though he assumed the kingship of Tara following Máel Sechnaill's death, has been counted in the lists of High Kings of Ireland. His kingship was disputed throughout his 17-year-long reign, he did not have support from the southern clans of Uí Néill; the annals show that the Taillten Fair on was not held in six of those 17 years, a strong indication of strife and unrest. The Norse of Dublin had, by the beginning of Áed's reign, become an important, if not trustworthy, ally in the struggle