1.
Roman numerals
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The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers in this system are represented by combinations of letters from the Latin alphabet, Roman numerals, as used today, are based on seven symbols, The use of Roman numerals continued long after the decline of the Roman Empire. The numbers 1 to 10 are usually expressed in Roman numerals as follows, I, II, III, IV, V, VI, VII, VIII, IX, Numbers are formed by combining symbols and adding the values, so II is two and XIII is thirteen. Symbols are placed left to right in order of value. Named after the year of its release,2014 as MMXIV, the year of the games of the XXII Olympic Winter Games The standard forms described above reflect typical modern usage rather than a universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval, Roman inscriptions, especially in official contexts, seem to show a preference for additive forms such as IIII and VIIII instead of subtractive forms such as IV and IX. Both methods appear in documents from the Roman era, even within the same document, double subtractives also occur, such as XIIX or even IIXX instead of XVIII. Sometimes V and L are not used, with such as IIIIII. Such variation and inconsistency continued through the period and into modern times. Clock faces that use Roman numerals normally show IIII for four o’clock but IX for nine o’clock, however, this is far from universal, for example, the clock on the Palace of Westminster in London uses IV. Similarly, at the beginning of the 20th century, different representations of 900 appeared in several inscribed dates. For instance,1910 is shown on Admiralty Arch, London, as MDCCCCX rather than MCMX, although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used
2.
NASCAR
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The National Association for Stock Car Auto Racing is an American family-owned and operated business venture that sanctions and governs multiple auto-racing sports events. Bill France Sr. founded the company in 1948 and his grandson Brian France became its CEO in 2003, NASCAR is motorsports preeminent stock-car racing organization. The three largest racing-series sanctioned by this company are the Monster Energy NASCAR Cup Series, the Xfinity Series, the company also oversees NASCAR Local Racing, the Whelen Modified Tour, the Whelen All-American Series, and the NASCAR iRacing. com Series. NASCAR sanctions over 1,500 races at over 100 tracks in 39 of the 50 US states as well as in Canada. NASCAR has presented exhibition races at the Suzuka and Motegi circuits in Japan, the Autódromo Hermanos Rodríguez in Mexico, NASCAR has its official headquarters in Daytona Beach, Florida, and also maintains offices in the North Carolina cities of Charlotte, Concord, and Conover. Regional offices are located in New York City and Los Angeles, with offices in Mexico City. Owing to NASCARs Southern roots, all but a handful of NASCAR teams are based in North Carolina. NASCAR is second to the National Football League among professional sports franchises in terms of television viewers, internationally, its races are broadcast on television in over 150 countries. In 2004, NASCARs Director of Security stated that the company holds 17 of the Top 20 regularly attended single-day sporting events in the world, fortune 500 companies sponsor NASCAR more than any other motor sport, although this sponsorship has declined since the early-2000s. By the time the Bonneville Salt Flats became the location for pursuit of land speed records. Drivers raced on a 4. 1-mile course, consisting of a 1. 5–2. 0-mile stretch of beach as one straightaway, the two straights were connected by two tight, deeply rutted and sand covered turns at each end. Stock car racing in the United States has its origins in bootlegging during Prohibition, bootleggers needed to distribute their illicit products, and they typically used small, fast vehicles to better evade the police. Many of the drivers would modify their cars for speed and handling, as well as increased cargo capacity, the cars continued to improve, and by the late 1940s, races featuring these cars were being run for pride and profit. These races were popular entertainment in the rural Southern United States, most races in those days were of modified cars. Street vehicles were lightened and reinforced, mechanic William France Sr. moved to Daytona Beach, Florida, from Washington, D. C. in 1935 to escape the Great Depression. He was familiar with the history of the area from the speed record attempts. France entered the 1936 Daytona event, finishing fifth and he took over running the course in 1938. He promoted a few races before World War II, France had the notion that people would enjoy watching stock cars race
3.
Fiat 600
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The Fiat 600 is a city car produced by the Italian manufacturer Fiat from 1955 to 1969. Measuring only 3.22 m long, it was the first rear-engined Fiat, the total number produced from 1955 to 1969 at the Mirafiori plant in Turin was 2,695,197. Codenamed Progetto 100, the Fiat 600 mirrored the layout of the Volkswagen Beetle, a total of 5 prototypes were built between 1952 and 1954, which all differed from one another. Chassis number 000001 with engine number 000002 is believed to be the remaining example. It was powered by an innovative single-cam V2-cylinder engine designed to simplify maintenance, at the official launch in 1955, FIAT engineer, Dante Giacosa declared that the aim had been to create something new, both in the interest of progress and simplification. This prototype, however, did not become the chosen design, the car had hydraulic drum brakes on all four wheels. All 600 models had 3-synchro 4-speed transaxles, all models of the 600 had generators with mechanical external regulators. The top speed ranged from 95 km/h empty with the 633 cc inline-four engine to 110 km/h with the 767 cc version, the car had good ventilation and defrosting systems. A year after its debut, in 1956, a version was introduced. It was a precursor of current multi-purpose vehicles, at the time when the millionth car was produced, the manufacturer reported it was producing the car at the then remarkable rate of 1,000 a day. As of 2011 there are only 65 left in the UK that are road legal, in Spain, the 600 model was made under the make of SEAT, from 1957 to 1973. Up to 797,319 SEAT600 were made, the Spanish car maker exported them to a number of countries worldwide. This car motorised Spain after the Spanish Civil War, the most interesting version produced between 1964 and 1967 by SEAT is the SEAT800, the sole four-door derivative of the 600 model which received a longer wheelbase. It was developed in-house by SEAT and produced exclusively by the Spanish car maker without any equivalent model in Fiats range, the Fiat 600 was also manufactured at Fiat Neckar in Germany between 1956 and 1967. Presented in a first time as Jagst 600, in 1960 with the release of Fiat 600D it became Jagst 770, the model was manufactured until the end of 1967, more than 172,000 copies. It was produced by the Zastava factory in Kragujevac, Serbia, from the early 1960s until 1985, during time it played a major role in motorisation of the country. The 600 was built as the Fiat 600 R by Sevel in Argentina from 1960 to 1982, with operations also taking place in Uruguay by Ayax S. A. At first, Someca S. A. built the 600 with rear-hinged doors, as a new plant was constructed in the Ferreyra, a suburb of Córdoba, the local parts content steadily increased
4.
Phoenix, Arizona
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Phoenix is the capital and most populous city of the U. S. state of Arizona. Phoenix is the anchor of the Phoenix metropolitan area, also known as the Valley of the Sun, the metropolitan area is the 12th largest by population in the United States, with approximately 4.3 million people as of 2010. Settled in 1867 as a community near the confluence of the Salt and Gila Rivers. Located in the reaches of the Sonoran Desert, Phoenix has a subtropical desert climate. Despite this, its canal system led to a farming community, many of the original crops remaining important parts of the Phoenix economy for decades, such as alfalfa, cotton, citrus. The city averaged a four percent annual growth rate over a 40-year period from the mid-1960s to the mid-2000s. This growth rate slowed during the Great Recession of 2007–09, and has rebounded slowly, Phoenix is the cultural center of the Valley of the Sun, as well as the entire state. For more than 2,000 years, the Hohokam people occupied the land that would become Phoenix, the Hohokam created roughly 135 miles of irrigation canals, making the desert land arable. Paths of these canals would later used for the modern Arizona Canal, Central Arizona Project Canal. The Hohokam also carried out trade with the nearby Anasazi, Mogollon and Sinagua. It is believed that between 1300 and 1450, periods of drought and severe floods led to the Hohokam civilizations abandonment of the area. After the departure of the Hohokam, groups of Akimel Oodham, Tohono Oodham and Maricopa tribes began to use the area, as well as segments of the Yavapai and Apache. The Oodham were offshoots of the Sobaipuri tribe, who in turn were thought to be the descendants of the formerly urbanized Hohokam and their crops included corn, beans, and squash for food, while cotton and tobacco were also cultivated. Mostly a peaceful group, they did together with the Maricopa for their mutual protection against incursions by both the Yuma and Apache tribes. The Tohono Oodham lived in the region as well, but their concentration was to the south. Living in small settlements, the Oodham were seasonal farmers who took advantage of the rains and they also hunted local game such as deer, rabbit, and javalina for meat. When the Mexican–American War ended in 1848, Mexico ceded its northern zone to the United States, the Phoenix area became part of the New Mexico Territory. In 1863 the mining town of Wickenburg was the first to be established in what is now Maricopa County, at the time Maricopa County had not yet been incorporated, the land was within Yavapai County, which included the major town of Prescott to the north of Wickenburg
5.
New Hampshire
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New Hampshire is a state in the New England region of the northeastern United States. It is bordered by Massachusetts to the south, Vermont to the west, Maine and the Atlantic Ocean to the east, New Hampshire is the 5th smallest by land area and the 9th least populous of the 50 United States. Concord is the capital, while Manchester is the largest city in the state and in northern New England, including Vermont. It has no sales tax, nor is personal income taxed at either the state or local level. The New Hampshire primary is the first primary in the U. S. presidential election cycle and its license plates carry the state motto, Live Free or Die. The states nickname, The Granite State, refers to its extensive granite formations, the state was named after the southern English county of Hampshire by Captain John Mason. New Hampshire is part of the New England region and it is bounded by Quebec, Canada, to the north and northwest, Maine and the Atlantic Ocean to the east, Massachusetts to the south, and Vermont to the west. New Hampshires major regions are the Great North Woods, the White Mountains, the Lakes Region, the Seacoast, the Merrimack Valley, the Monadnock Region, and the Dartmouth-Lake Sunapee area. New Hampshire has the shortest ocean coastline of any U. S. coastal state, New Hampshire was home to the rock formation called the Old Man of the Mountain, a face-like profile in Franconia Notch, until the formation disintegrated in May 2003. Major rivers include the 110-mile Merrimack River, which bisects the lower half of the state north–south and ends up in Newburyport and its tributaries include the Contoocook River, Pemigewasset River, and Winnipesaukee River. The 410-mile Connecticut River, which starts at New Hampshires Connecticut Lakes and flows south to Connecticut, only one town – Pittsburg – shares a land border with the state of Vermont. The northwesternmost headwaters of the Connecticut also define the Canada–U. S, the Piscataqua River and its several tributaries form the states only significant ocean port where they flow into the Atlantic at Portsmouth. The Salmon Falls River and the Piscataqua define the southern portion of the border with Maine, the U. S. Supreme Court dismissed the case in 2002, leaving ownership of the island with Maine. New Hampshire still claims sovereignty of the base, however, the largest of New Hampshires lakes is Lake Winnipesaukee, which covers 71 square miles in the east-central part of New Hampshire. Umbagog Lake along the Maine border, approximately 12.3 square miles, is a distant second, Squam Lake is the second largest lake entirely in New Hampshire. New Hampshire has the shortest ocean coastline of any state in the United States, Hampton Beach is a popular local summer destination. It is the state with the highest percentage of area in the country. New Hampshire is in the temperate broadleaf and mixed forests biome, much of the state, in particular the White Mountains, is covered by the conifers and northern hardwoods of the New England-Acadian forests
6.
Australia
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Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania and numerous smaller islands. It is the worlds sixth-largest country by total area, the neighbouring countries are Papua New Guinea, Indonesia and East Timor to the north, the Solomon Islands and Vanuatu to the north-east, and New Zealand to the south-east. Australias capital is Canberra, and its largest urban area is Sydney, for about 50,000 years before the first British settlement in the late 18th century, Australia was inhabited by indigenous Australians, who spoke languages classifiable into roughly 250 groups. The population grew steadily in subsequent decades, and by the 1850s most of the continent had been explored, on 1 January 1901, the six colonies federated, forming the Commonwealth of Australia. Australia has since maintained a liberal democratic political system that functions as a federal parliamentary constitutional monarchy comprising six states. The population of 24 million is highly urbanised and heavily concentrated on the eastern seaboard, Australia has the worlds 13th-largest economy and ninth-highest per capita income. With the second-highest human development index globally, the country highly in quality of life, health, education, economic freedom. The name Australia is derived from the Latin Terra Australis a name used for putative lands in the southern hemisphere since ancient times, the Dutch adjectival form Australische was used in a Dutch book in Batavia in 1638, to refer to the newly discovered lands to the south. On 12 December 1817, Macquarie recommended to the Colonial Office that it be formally adopted, in 1824, the Admiralty agreed that the continent should be known officially as Australia. The first official published use of the term Australia came with the 1830 publication of The Australia Directory and these first inhabitants may have been ancestors of modern Indigenous Australians. The Torres Strait Islanders, ethnically Melanesian, were originally horticulturists, the northern coasts and waters of Australia were visited sporadically by fishermen from Maritime Southeast Asia. The first recorded European sighting of the Australian mainland, and the first recorded European landfall on the Australian continent, are attributed to the Dutch. The first ship and crew to chart the Australian coast and meet with Aboriginal people was the Duyfken captained by Dutch navigator, Willem Janszoon. He sighted the coast of Cape York Peninsula in early 1606, the Dutch charted the whole of the western and northern coastlines and named the island continent New Holland during the 17th century, but made no attempt at settlement. William Dampier, an English explorer and privateer, landed on the north-west coast of New Holland in 1688, in 1770, James Cook sailed along and mapped the east coast, which he named New South Wales and claimed for Great Britain. The first settlement led to the foundation of Sydney, and the exploration, a British settlement was established in Van Diemens Land, now known as Tasmania, in 1803, and it became a separate colony in 1825. The United Kingdom formally claimed the part of Western Australia in 1828. Separate colonies were carved from parts of New South Wales, South Australia in 1836, Victoria in 1851, the Northern Territory was founded in 1911 when it was excised from South Australia
7.
Binary number
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The base-2 system is a positional notation with a radix of 2. Because of its implementation in digital electronic circuitry using logic gates. Each digit is referred to as a bit, the modern binary number system was devised by Gottfried Leibniz in 1679 and appears in his article Explication de lArithmétique Binaire. Systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, Leibniz was specifically inspired by the Chinese I Ching. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions and Horus-Eye fractions, the method used for ancient Egyptian multiplication is also closely related to binary numbers. This method can be seen in use, for instance, in the Rhind Mathematical Papyrus, the I Ching dates from the 9th century BC in China. The binary notation in the I Ching is used to interpret its quaternary divination technique and it is based on taoistic duality of yin and yang. Eight trigrams and a set of 64 hexagrams, analogous to the three-bit and six-bit binary numerals, were in use at least as early as the Zhou Dynasty of ancient China. The Song Dynasty scholar Shao Yong rearranged the hexagrams in a format that resembles modern binary numbers, the Indian scholar Pingala developed a binary system for describing prosody. He used binary numbers in the form of short and long syllables, Pingalas Hindu classic titled Chandaḥśāstra describes the formation of a matrix in order to give a unique value to each meter. The binary representations in Pingalas system increases towards the right, the residents of the island of Mangareva in French Polynesia were using a hybrid binary-decimal system before 1450. Slit drums with binary tones are used to encode messages across Africa, sets of binary combinations similar to the I Ching have also been used in traditional African divination systems such as Ifá as well as in medieval Western geomancy. The base-2 system utilized in geomancy had long been applied in sub-Saharan Africa. Leibnizs system uses 0 and 1, like the modern binary numeral system, Leibniz was first introduced to the I Ching through his contact with the French Jesuit Joachim Bouvet, who visited China in 1685 as a missionary. Leibniz saw the I Ching hexagrams as an affirmation of the universality of his own beliefs as a Christian. Binary numerals were central to Leibnizs theology and he believed that binary numbers were symbolic of the Christian idea of creatio ex nihilo or creation out of nothing. Is not easy to impart to the pagans, is the ex nihilo through Gods almighty power. In 1854, British mathematician George Boole published a paper detailing an algebraic system of logic that would become known as Boolean algebra
8.
Senary
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The senary numeral system has six as its base. It has been adopted independently by a number of cultures. Like decimal, it is a semiprime, though being the product of the two consecutive numbers that are both prime it has a high degree of mathematical properties for its size. As six is a highly composite number, many of the arguments made in favor of the duodecimal system also apply to this base-6. Senary may be considered interesting in the study of numbers, since all primes other than 2 and 3. That is, for every number p greater than 3, one has the modular arithmetic relations that either p ≡1 or 5. This property maximizes the probability that the result of an integer multiplication will end in zero, E. g. if three fingers are extended on the left hand and four on the right, 34senary is represented. This is equivalent to 3 ×6 +4 which is 22decimal, flipping the sixes hand around to its backside may help to further disambiguate which hand represents the sixes and which represents the units. While most developed cultures count by fingers up to 5 in very similar ways, beyond 5 non-Western cultures deviate from Western methods, such as with Chinese number gestures. More abstract finger counting systems, such as chisanbop or finger binary, allow counting to 99,1,023, or even higher depending on the method. The English monk and historian Bede, in the first chapter of De temporum ratione, titled Tractatus de computo, vel loquela per gestum digitorum, the Ndom language of Papua New Guinea is reported to have senary numerals. Mer means 6, mer an thef means 6 ×2 =12, nif means 36, another example from Papua New Guinea are the Morehead-Maro languages. In these languages, counting is connected to ritualized yam-counting and these languages count from a base six, employing words for the powers of six, running up to 66 for some of the languages. One example is Kómnzo with the numerals, nimbo, féta, tarumba, ntamno, wärämäkä. Some Niger-Congo languages have been reported to use a number system, usually in addition to another. For some purposes, base 6 might be too small a base for convenience. The choice of 36 as a radix is convenient in that the digits can be represented using the Arabic numerals 0–9 and the Latin letters A–Z, this choice is the basis of the base36 encoding scheme. Base36 encoding scheme Binary Ternary Duodecimal Sexagesimal Shacks Base Six Dialectic Digital base 6 clock Analog Clock Designer capable of rendering a base 6 clock Senary base conversion
9.
Fibonacci number
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The Fibonacci sequence is named after Italian mathematician Leonardo of Pisa, known as Fibonacci. His 1202 book Liber Abaci introduced the sequence to Western European mathematics, the sequence described in Liber Abaci began with F1 =1. Fibonacci numbers are related to Lucas numbers L n in that they form a complementary pair of Lucas sequences U n = F n and V n = L n. They are intimately connected with the ratio, for example. Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is a journal dedicated to their study. The Fibonacci sequence appears in Indian mathematics, in connection with Sanskrit prosody, in the Sanskrit tradition of prosody, there was interest in enumerating all patterns of long syllables that are 2 units of duration, and short syllables that are 1 unit of duration. Counting the different patterns of L and S of a given duration results in the Fibonacci numbers, susantha Goonatilake writes that the development of the Fibonacci sequence is attributed in part to Pingala, later being associated with Virahanka, Gopāla, and Hemachandra. He dates Pingala before 450 BC, however, the clearest exposition of the sequence arises in the work of Virahanka, whose own work is lost, but is available in a quotation by Gopala, Variations of two earlier meters. For example, for four, variations of meters of two three being mixed, five happens, in this way, the process should be followed in all mātrā-vṛttas. The sequence is also discussed by Gopala and by the Jain scholar Hemachandra, outside India, the Fibonacci sequence first appears in the book Liber Abaci by Fibonacci. The puzzle that Fibonacci posed was, how many pairs will there be in one year, at the end of the first month, they mate, but there is still only 1 pair. At the end of the month the female produces a new pair. At the end of the month, the original female produces a second pair. At the end of the month, the original female has produced yet another new pair. At the end of the nth month, the number of pairs of rabbits is equal to the number of new pairs plus the number of pairs alive last month and this is the nth Fibonacci number. The name Fibonacci sequence was first used by the 19th-century number theorist Édouard Lucas, the most common such problem is that of counting the number of compositions of 1s and 2s that sum to a given total n, there are Fn+1 ways to do this. For example, if n =5, then Fn+1 = F6 =8 counts the eight compositions, 1+1+1+1+1 = 1+1+1+2 = 1+1+2+1 = 1+2+1+1 = 2+1+1+1 = 2+2+1 = 2+1+2 = 1+2+2, all of which sum to 5. The Fibonacci numbers can be found in different ways among the set of strings, or equivalently
10.
Greek numerals
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Greek numerals are a system of writing numbers using the letters of the Greek alphabet. These alphabetic numerals are known as Ionic or Ionian numerals, Milesian numerals. In modern Greece, they are used for ordinal numbers. For ordinary cardinal numbers, however, Greece uses Arabic numerals, attic numerals, which were later adopted as the basis for Roman numerals, were the first alphabetic set. They were acrophonic, derived from the first letters of the names of the numbers represented and they ran =1, =5, =10, =100, =1000, and =10000. 50,500,5000, and 50000 were represented by the letter with minuscule powers of ten written in the top right corner, the same system was used outside of Attica, but the symbols varied with the local alphabets, in Boeotia, was 1000. The present system probably developed around Miletus in Ionia, 19th-century classicists placed its development in the 3rd century BC, the occasion of its first widespread use. The present system uses the 24 letters adopted by Euclid as well as three Phoenician and Ionic ones that were not carried over, digamma, koppa, and sampi. The position of characters within the numbering system imply that the first two were still in use while the third was not. Greek numerals are decimal, based on powers of 10, the units from 1 to 9 are assigned to the first nine letters of the old Ionic alphabet from alpha to theta. Each multiple of one hundred from 100 to 900 was then assigned its own separate letter as well and this alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example,241 was represented as, in ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars, α, β, γ, etc. In medieval manuscripts of the Book of Revelation, the number of the Beast 666 is written as χξϛ, although the Greek alphabet began with only majuscule forms, surviving papyrus manuscripts from Egypt show that uncial and cursive minuscule forms began early. These new letter forms sometimes replaced the ones, especially in the case of the obscure numerals. The old Q-shaped koppa began to be broken up and simplified, the numeral for 6 changed several times. During antiquity, the letter form of digamma came to be avoided in favor of a special numerical one. By the Byzantine era, the letter was known as episemon and this eventually merged with the sigma-tau ligature stigma. In modern Greek, a number of changes have been made
11.
Hexadecimal
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In mathematics and computing, hexadecimal 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, Hexadecimal numerals are widely used by computer system designers and programmers. As each hexadecimal digit represents four binary digits, it allows a more human-friendly representation of binary-coded values, one hexadecimal digit represents a nibble, which is half of an octet or byte. For example, a byte can have values ranging from 00000000 to 11111111 in binary form. In a non-programming context, a subscript is typically used to give the radix, several notations are used to support hexadecimal representation of constants in programming languages, usually involving a prefix or suffix. The prefix 0x is used in C and related languages, where this value might be denoted as 0x2AF3, 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 159,15916 is hexadecimal 159, which is equal to 34510. Some authors prefer a text subscript, such as 159decimal and 159hex, or 159d and 159h. example. com/name%20with%20spaces where %20 is the space character, thus ’, represents the right single quotation mark, Unicode code point number 2019 in hex,8217. In the Unicode standard, a value is represented with U+ followed by the hex value. Color references in HTML, CSS and X Window can be expressed with six hexadecimal digits prefixed with #, white, CSS allows 3-hexdigit abbreviations with one hexdigit per component, #FA3 abbreviates #FFAA33. *nix shells, AT&T assembly language and likewise the C programming language, to output an integer as hexadecimal with the printf function family, the format conversion code %X or %x is used. In Intel-derived assembly languages and Modula-2, hexadecimal is denoted with a suffixed H or h, some assembly languages use the notation HABCD. Ada and VHDL enclose hexadecimal numerals in based numeric quotes, 16#5A3#, for bit vector constants VHDL uses the notation x5A3. Verilog represents hexadecimal constants in the form 8hFF, where 8 is the number of bits in the value, 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, in early systems when a Macintosh crashed, one or two lines of hexadecimal code would be displayed under the Sad Mac to tell the user what went wrong. Common Lisp uses the prefixes #x and #16r, setting the variables *read-base* and *print-base* to 16 can also 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, 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 ALGOL68 uses the prefix 16r to denote hexadecimal numbers, binary, quaternary and octal numbers can be specified similarly
12.
Negative number
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In mathematics, a negative number is a real number that is less than zero. If positive represents movement to the right, negative represents movement to the left, if positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal and they are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, if a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage, negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common idea of an opposite is reflected in arithmetic. For example, − −3 =3 because the opposite of an opposite is the original thing, negative numbers are usually written with a minus sign in front. For example, −3 represents a quantity with a magnitude of three, and is pronounced minus three or negative three. To help tell the difference between a subtraction operation and a number, occasionally the negative sign is placed slightly higher than the minus sign. Conversely, a number that is greater than zero is called positive, the positivity of a number may be emphasized by placing a plus sign before it, e. g. +3. In general, the negativity or positivity of a number is referred to as its sign, every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative numbers are referred to as integers. In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, Liu Hui established rules for adding and subtracting negative numbers. By the 7th century, Indian mathematicians such as Brahmagupta were describing the use of negative numbers, islamic mathematicians further developed the rules of subtracting and multiplying negative numbers and solved problems with negative coefficients. Western mathematicians accepted the idea of numbers by the 17th century. Prior to the concept of numbers, mathematicians such as Diophantus considered negative solutions to problems false. Negative numbers can be thought of as resulting from the subtraction of a number from a smaller. For example, negative three is the result of subtracting three from zero,0 −3 = −3, in general, the subtraction of a larger number from a smaller yields a negative result, with the magnitude of the result being the difference between the two numbers
