In Euclidean geometry, an arc is a closed segment of a differentiable curve. A common example in the plane, is a segment of a circle called a circular arc. In space, if the arc is part of a great circle, it is called a great arc; every pair of distinct points on a circle determines two arcs. If the two points are not directly opposite each other, one of these arcs, the minor arc, will subtend an angle at the centre of the circle, less than π radians, the other arc, the major arc, will subtend an angle greater than π radians; the length of an arc of a circle with radius r and subtending an angle θ with the circle center — i.e. the central angle — is L = θ r. This is because L c i r c u m f e r e n c e = θ 2 π. Substituting in the circumference L 2 π r = θ 2 π, with α being the same angle measured in degrees, since θ = α/180π, the arc length equals L = α π r 180. A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center solve for L by cross-multiplying the statement: measure of angle in degrees/360° = L/circumference.
For example, if the measure of the angle is 60 degrees and the circumference is 24 inches 60 360 = L 24 360 L = 1440 L = 4. This is so because the circumference of a circle and the degrees of a circle, of which there are always 360, are directly proportional; the area of the sector formed by an arc and the center of a circle is A = r 2 θ 2. The area A has the same proportion to the circle area as the angle θ to a full circle: A π r 2 = θ 2 π. We can cancel π on both sides: A r 2 = θ 2. By multiplying both sides by r2, we get the final result: A = 1 2 r 2 θ. Using the conversion described above, we find that the area of the sector for a central angle measured in degrees is A = α 360 π r 2; the area of the shape bounded by the arc and the straight line between its two end points is 1 2 r 2. To get the area of the arc segment, we need to subtract the area of the triangle, determined by the circle's center and the two end points of the arc, from the area A. See Circular segment for details. Using the intersecting chords theorem it is possible to calculate the radius r of a circle given the height H and the width W of an arc: Consider the chord with the same endpoints as the arc.
Its perpendicular bisector is another chord, a diameter of the circle. The length of the first chord is W, it is divided by the bisector into two equal halves, each with length W/2; the total length of the diameter is 2r, it is divided into two parts by the first chord. The length of one part is the sagitta of the arc, H, the other part is the remainder of the diameter, with length 2r − H. Applying the intersecting chords theorem to these two chords produces H = 2, whence 2 r − H = W 2 4 H, so r = W 2 8 H + H 2. Biarc Circular-arc graph Meridian arc Circumference Perimeter Table of contents for Math Open Reference Circle pages Math Open Reference page on circular arcs With interactive animation Math Open Reference page on Radius of a circular arc
Inkjet printing is a type of computer printing that recreates a digital image by propelling droplets of ink onto paper, plastic, or other substrates. Inkjet printers are the most used type of printer, range from small inexpensive consumer models to expensive professional machines; the concept of inkjet printing originated in the 20th century, the technology was first extensively developed in the early 1950s. Starting in the late 1970s, inkjet printers that could reproduce digital images generated by computers were developed by Epson, Hewlett-Packard and Canon. In the worldwide consumer market, four manufacturers account for the majority of inkjet printer sales: Canon, HP, Epson and Brother; the emerging ink jet material deposition market uses inkjet technologies printheads using piezoelectric crystals, to deposit materials directly on substrates. The technology has been extended and the'ink' can now comprise solder paste in PCB assembly, or living cells, for creating biosensors and for tissue engineering.
Images produced on inkjet printers are sometime sold under other names since the term is associated with words like "digital", "computers", "everyday printing", which can have negative connotations in some contexts. These trade names or coined terms are used in the fine arts reproduction field, they include Digigraph, Iris prints, Cromalin. There are two main technologies in use in contemporary inkjet printers: continuous and drop-on-demand; the continuous inkjet method is used commercially for coding of products and packages. In 1867, Lord Kelvin patented the syphon recorder, which recorded telegraph signals as a continuous trace on paper using an ink jet nozzle deflected by a magnetic coil; the first commercial devices were introduced in 1951 by Siemens. In CIJ technology, a high-pressure pump directs liquid ink from a reservoir through a gunbody and a microscopic nozzle, creating a continuous stream of ink droplets via the Plateau-Rayleigh instability. A piezoelectric crystal creates an acoustic wave as it vibrates within the gunbody and causes the stream of liquid to break into droplets at regular intervals: 64,000 to 165,000 droplets per second may be achieved.
The ink droplets are subjected to an electrostatic field created by a charging electrode as they form. This results in a variable electrostatic charge on each droplet. Charged droplets are separated by one or more uncharged "guard droplets" to minimize electrostatic repulsion between neighbouring droplets; the charged droplets pass through another electrostatic field and are directed by electrostatic deflection plates to print on the receptor material, or allowed to continue on undeflected to a collection gutter for re-use. The more charged droplets are deflected to a greater degree. Only a small fraction of the droplets is used to the majority being recycled. CIJ is one of the oldest ink jet technologies in use and is mature; the major advantages are the high velocity of the ink droplets, which allows for a long distance between print head and substrate, the high drop ejection frequency, allowing for high speed printing. Another advantage is freedom from nozzle clogging as the jet is always in use, therefore allowing volatile solvents such as ketones and alcohols to be employed, giving the ink the ability to "bite" into the substrate and dry quickly.
The ink system requires active solvent regulation to counter solvent evaporation during the time of flight, from the venting process whereby air, drawn into the gutter along with the unused drops is vented from the reservoir. Viscosity is monitored and a solvent is added to counteract solvent loss. Drop-on-demand is divided into thermal DOD and piezoelectric DOD. Most consumer inkjet printers, including those from Canon, Hewlett-Packard, Lexmark, use the thermal inkjet process; the idea of using thermal excitation to move tiny drops of ink was developed independently by two groups at the same time: John Vaught and a team at Hewlett-Packard's Corvallis Division, Canon engineer Ichiro Endo. In 1977, Endo's team was trying to use the piezoelectric effect to move ink out of the nozzle but noticed that ink shot out of a syringe when it was accidentally heated with a soldering iron. Vaught's work started in late 1978 with a project to develop low-cost printing; the team at HP found. Two years the HP and Canon teams found out about each other's work.
In the thermal inkjet process, the print cartridges consist of a series of tiny chambers, each containing a heater, all of which are constructed by photolithography. To eject a droplet from each chamber, a pulse of current is passed through the heating element causing a rapid vaporization of the ink in the chamber and forming a bubble, which causes a large pressure increase, propelling a droplet of ink onto the paper; the ink's surface tension, as well as the condensation and resultant contraction of the vapor bubble, pulls a further charge of ink into the chamber through a narrow channel attached to an ink reservoir. The inks involved are water-based and use either pigments or dyes as the colorant; the inks must have a volatile component to form the vapor bubble. As no special materials are required, the print head is cheaper to produce than in other inkjet technologies. Most commercial and industrial inkjet printers and
The Hewlett-Packard Company or Hewlett-Packard was an American multinational information technology company headquartered in Palo Alto, California. It developed and provided a wide variety of hardware components as well as software and related services to consumers, small- and medium-sized businesses and large enterprises, including customers in the government and education sectors; the company was founded in a one-car garage in Palo Alto by Bill Hewlett and David Packard, produced a line of electronic test equipment. HP was the world's leading PC manufacturer from 2007 to Q2 2013, at which time Lenovo ranked ahead of HP. HP specialized in developing and manufacturing computing, data storage, networking hardware, designing software and delivering services. Major product lines included personal computing devices and industry standard servers, related storage devices, networking products, software and a diverse range of printers and other imaging products. HP directly marketed its products to households, small- to medium-sized businesses and enterprises as well as via online distribution, consumer-electronics and office-supply retailers, software partners and major technology vendors.
HP had services and consulting business around its products and partner products. Hewlett-Packard company events included the spin-off of its electronic and bio-analytical measurement instruments part of its business as Agilent Technologies in 1999, its merger with Compaq in 2002, the acquisition of EDS in 2008, which led to combined revenues of $118.4 billion in 2008 and a Fortune 500 ranking of 9 in 2009. In November 2009, HP announced the acquisition of 3Com, with the deal closing on April 12, 2010. On April 28, 2010, HP announced the buyout of Inc. for $1.2 billion. On September 2, 2010, HP won its bidding war for 3PAR with a $33 a share offer, which Dell declined to match. Hewlett-Packard spun off its enterprise products and services business as Hewlett Packard Enterprise on November 1, 2015. Hewlett-Packard held onto the PC and printer businesses, was renamed to HP Inc. Bill Hewlett and David Packard graduated with degrees in electrical engineering from Stanford University in 1935; the company originated in a garage in nearby Palo Alto during a fellowship they had with a past professor, Frederick Terman at Stanford during the Great Depression.
They considered Terman a mentor in forming Hewlett-Packard. In 1938, Packard and Hewlett begin part-time work in a rented garage with an initial capital investment of US$538. In 1939 Hewlett and Packard decided to formalize their partnership, they tossed a coin to decide whether the company they founded would be called Hewlett-Packard or Packard-Hewlett. HP incorporated on August 18, 1947, went public on November 6, 1957. Of the many projects they worked on, their first financially successful product, was a precision audio oscillator, the Model HP200A, their innovation was the use of a small incandescent light bulb as a temperature dependent resistor in a critical portion of the circuit, the negative feedback loop which stabilized the amplitude of the output sinusoidal waveform. This allowed them to sell the Model 200A for $89.40 when competitors were selling less stable oscillators for over $200. The Model 200 series of generators continued production until at least 1972 as the 200AB, still tube-based but improved in design through the years.
One of the company's earliest customers was Walt Disney Productions, which bought eight Model 200B oscillators for use in certifying the Fantasound surround sound systems installed in theaters for the movie Fantasia. They worked on counter-radar technology and artillery shell fuses during World War II, which allowed Packard to be exempt from the draft. HP is recognized as the symbolic founder of Silicon Valley, although it did not investigate semiconductor devices until a few years after the "traitorous eight" had abandoned William Shockley to create Fairchild Semiconductor in 1957. Hewlett-Packard's HP Associates division, established around 1960, developed semiconductor devices for internal use. Instruments and calculators were some of the products using these devices. During the 1960s, HP partnered with Sony and the Yokogawa Electric companies in Japan to develop several high-quality products; the products were not a huge success, as there were high costs in building HP-looking products in Japan.
HP and Yokogawa formed a joint venture in 1963 to market HP products in Japan. HP bought Yokogawa Electric's share of Hewlett-Packard Japan in 1999. HP spun off Dynac, to specialize in digital equipment; the name was picked so that the HP logo "hp" could be turned upside down to be a reverse reflect image of the logo "dy" of the new company. Dynac changed to Dymec, was folded back into HP in 1959. HP experimented with using Digital Equipment Corporation minicomputers with its instruments, but after deciding that it would be easier to build another small design team than deal with DEC, HP entered the computer market in 1966 with the HP 2100 / HP 1000 series of minicomputers; these had a simple accumulator-based design, with two accumulator registers and, in the HP 1000 models, two index registers. The series was produced for 20 years, in spite of several attempts to replace it, was a forerunner of the HP 9800 and HP 250 series of desktop and business computers; the HP 3000 was an advanced stack-based design for a business computing server redesigned with RISC technology.
The HP 2640 series of smart and intelligent terminals introduced forms-based interfaces to ASCII terminals, introduced screen labeled functio
In computing, a printer is a peripheral device which makes a persistent representation of graphics or text on paper. While most output is human-readable, bar code printers are an example of an expanded use for printers; the first computer printer designed was a mechanically driven apparatus by Charles Babbage for his difference engine in the 19th century. The first electronic printer was the EP-101, invented by Japanese company Epson and released in 1968; the first commercial printers used mechanisms from electric typewriters and Teletype machines. The demand for higher speed led to the development of new systems for computer use. In the 1980s were daisy wheel systems similar to typewriters, line printers that produced similar output but at much higher speed, dot matrix systems that could mix text and graphics but produced low-quality output; the plotter was used for those requiring high quality line art like blueprints. The introduction of the low-cost laser printer in 1984 with the first HP LaserJet, the addition of PostScript in next year's Apple LaserWriter, set off a revolution in printing known as desktop publishing.
Laser printers using PostScript mixed text and graphics, like dot-matrix printers, but at quality levels available only from commercial typesetting systems. By 1990, most simple printing tasks like fliers and brochures were now created on personal computers and laser printed; the HP Deskjet of 1988 offered the same advantages as laser printer in terms of flexibility, but produced somewhat lower quality output from much less expensive mechanisms. Inkjet systems displaced dot matrix and daisy wheel printers from the market. By the 2000s high-quality printers of this sort had fallen under the $100 price point and became commonplace; the rapid update of internet email through the 1990s and into the 2000s has displaced the need for printing as a means of moving documents, a wide variety of reliable storage systems means that a "physical backup" is of little benefit today. The desire for printed output for "offline reading" while on mass transit or aircraft has been displaced by e-book readers and tablet computers.
Today, traditional printers are being used more for special purposes, like printing photographs or artwork, are no longer a must-have peripheral. Starting around 2010, 3D printing became an area of intense interest, allowing the creation of physical objects with the same sort of effort as an early laser printer required to produce a brochure; these devices have not yet become commonplace. Personal printers are designed to support individual users, may be connected to only a single computer; these printers are designed for low-volume, short-turnaround print jobs, requiring minimal setup time to produce a hard copy of a given document. However, they are slow devices ranging from 6 to around 25 pages per minute, the cost per page is high. However, this is offset by the on-demand convenience; some printers can print documents stored from digital cameras and scanners. Networked or shared printers are "designed for high-volume, high-speed printing", they are shared by many users on a network and can print at speeds of 45 to around 100 ppm.
The Xerox 9700 could achieve 120 ppm. A virtual printer is a piece of computer software whose user interface and API resembles that of a printer driver, but, not connected with a physical computer printer. A virtual printer can be used to create a file, an image of the data which would be printed, for archival purposes or as input to another program, for example to create a PDF or to transmit to another system or user. A barcode printer is a computer peripheral for printing barcode labels or tags that can be attached to, or printed directly on, physical objects. Barcode printers are used to label cartons before shipment, or to label retail items with UPCs or EANs. A 3D printer is a device for making a three-dimensional object from a 3D model or other electronic data source through additive processes in which successive layers of material are laid down under computer control, it is called a printer by analogy with an inkjet printer which produces a two-dimensional document by a similar process of depositing a layer of ink on paper.
The choice of print technology has a great effect on the cost of the printer and cost of operation, speed and permanence of documents, noise. Some printer technologies do not work with certain types of physical media, such as carbon paper or transparencies. A second aspect of printer technology, forgotten is resistance to alteration: liquid ink, such as from an inkjet head or fabric ribbon, becomes absorbed by the paper fibers, so documents printed with liquid ink are more difficult to alter than documents printed with toner or solid inks, which do not penetrate below the paper surface. Cheques can be printed with liquid ink or on special cheque paper with toner anchorage so that alterations may be detected; the machine-readable lower portion of a cheque must be printed using MICR ink. Banks and other clearing houses employ automation equipment that relies on the magnetic flux from these specially printed characters to function properly; the following printing technologies are found in modern printers: A laser printer produces high quality text and graphics.
As with digital photocopiers and multifunction printers, laser printers employ a xerographic printing process but differ from analog photocopiers in
The plotter is a computer printer for printing vector graphics. Plotters draw pictures on paper using a pen. In the past, plotters were used in applications such as computer-aided design, as they were able to produce line drawings much faster and of a higher quality than contemporary conventional printers, small desktop plotters were used for business graphics. Although they retained a niche for producing large drawings for many years, plotters have now been replaced by wide-format conventional printers. Digitally controlled plotters evolved from earlier analog XY-writers used as output devices for measurement instruments and analog computers. Pen plotters print by moving a pen or other instrument across the surface of a piece of paper; this means that plotters are vector graphics devices, rather than raster graphics as with other printers. Pen plotters can draw complex line art, including text, but do so because of the mechanical movement of the pens, they are incapable of efficiently creating a solid region of color, but can hatch an area by drawing a number of close, regular lines.
Plotters offered the fastest way to efficiently produce large drawings or color high-resolution vector-based artwork when computer memory was expensive and processor power was limited, other types of printers had limited graphic output capabilities. Pen plotters have become obsolete, have been replaced by large-format inkjet printers and LED toner based printers; such devices may still understand vector languages designed for plotter use, because in many uses, they offer a more efficient alternative to raster data. Electrostatic plotters used a dry toner transfer process similar to that in many photocopiers, they were faster than pen plotters and were available in large formats, suitable for reproducing engineering drawings. The quality of image was not as good as contemporary pen plotters. Electrostatic plotters were made in both drum types. Cutting plotters use knives to cut into a piece of material, lying on the flat surface area of the plotter, it is achieved because the cutting plotter is connected to a computer, equipped with specialized cutting design or drawing computer software programs.
Those computer software programs are responsible for sending the necessary cutting dimensions or designs in order to command the cutting knife to produce the correct project cutting needs. In recent years the use of cutting plotters has become popular with home enthusiasts of paper crafts such as cardmaking and scrapbooking; such tools allow desired card shapes to be cut out precisely, repeated identically. A number of printer control languages were created to operate pen plotters, transmit commands like "lift pen from paper", "place pen on paper", or "draw a line from here to here". Three common ASCII-based plotter control languages are Hewlett-Packard's HP-GL, its successor HP-GL/2 and Houston Instruments DMPL. Here is a simple HP-GL script drawing a line: SP1. Programmers using FORTRAN or BASIC did not program these directly, but used software packages, such as the Calcomp library, or device independent graphics packages, such as Hewlett-Packard's AGL libraries or BASIC extensions or high end packages such as DISSPLA.
These would establish scaling factors from world coordinates to device coordinates, translate to the low level device commands. For example, to plot X*X in HP 9830 BASIC, the program would be 10 SCALE -1,1,1,1 20 FOR X =-1 to 1 STEP 0.1 30 PLOT X, X*X 40 NEXT X 50 PEN 60 END Early pen plotters, e.g. the Calcomp 565 of 1959, worked by placing the paper over a roller that moved the paper back and forth for X motion, while the pen moved back and forth on a track for Y motion. The paper was supplied in roll form and had perforations along both edges that were engaged by sprockets on the rollers. Another approach, e.g. Computervision's Interact I, involved attaching ball-point pens to drafting pantographs and driving the machines with stepper motors controlled by the computer; this had the disadvantage of being somewhat slow to move, as well as requiring floor space equal to the size of the paper, but could double as a digitizer. A change was the addition of an electrically controlled clamp to hold the pens, which allowed them to be changed, thus create multi-colored output.
Hewlett Packard and Tektronix produced small, desktop-sized flatbed plotters in the late 1960s and 1970s. The pens were mounted on a traveling bar, whereby the y-axis was represented by motion up and down the length of the bar and the x-axis was represented by motion of the bar back and forth across the plotting table. Due to the mass of the bar, these plotters operated slowly. In the 1980s, the small and lightweight HP 7470 introduced the "grit wheel" mechanism, eliminating the need for perforations along the edges, unlike the Calcomp plotters two decades earlier; the grit wheels at opposite edges of the sheet press against resilient polyurethane-coated rollers and form tiny indentations in the sheet. As the sheet is moved back and forth, the grit wheels keep the sheet in proper registration due to the grit particles falling into the earlier indentations, much like the teeth of two gears meshing; the pen is mounted on a carriage that moves back and forth in a line between the gri
A mnemonic device, or memory device, is any learning technique that aids information retention or retrieval in the human memory. Mnemonics make use of elaborative encoding, retrieval cues, imagery as specific tools to encode any given information in a way that allows for efficient storage and retrieval. Mnemonics aid original information in becoming associated with something more accessible or meaningful—which, in turn, provides better retention of the information. Encountered mnemonics are used for lists and in auditory form, such as short poems, acronyms, or memorable phrases, but mnemonics can be used for other types of information and in visual or kinesthetic forms, their use is based on the observation that the human mind more remembers spatial, surprising, sexual, humorous, or otherwise "relatable" information, rather than more abstract or impersonal forms of information. The word "mnemonic" is derived from the Ancient Greek word μνημονικός, meaning "of memory, or relating to memory" and is related to Mnemosyne, the name of the goddess of memory in Greek mythology.
Both of these words are derived from μνήμη, "remembrance, memory". Mnemonics in antiquity were most considered in the context of what is today known as the art of memory. Ancient Greeks and Romans distinguished between two types of memory: the "natural" memory and the "artificial" memory; the former is inborn, is the one that everyone uses instinctively. The latter in contrast has to be trained and developed through the learning and practice of a variety of mnemonic techniques. Mnemonic systems are strategies consciously used to improve memory, they help use information stored in long-term memory to make memorisation an easier task. The general name of mnemonics, or memoria technica, was the name applied to devices for aiding the memory, to enable the mind to reproduce a unfamiliar idea, a series of dissociated ideas, by connecting it, or them, in some artificial whole, the parts of which are mutually suggestive. Mnemonic devices were much cultivated by Greek sophists and philosophers and are referred to by Plato and Aristotle.
In times the poet Simonides was credited for development of these techniques for no reason other than that the power of his memory was famous. Cicero, who attaches considerable importance to the art, but more to the principle of order as the best help to memory, speaks of Carneades of Athens and Metrodorus of Scepsis as distinguished examples of people who used well-ordered images to aid the memory; the Romans valued. The Greek and the Roman system of mnemonics was founded on the use of mental places and signs or pictures, known as "topical" mnemonics; the most usual method was to choose a large house, of which the apartments, windows, furniture, etc. were each associated with certain names, events or ideas, by means of symbolic pictures. To recall these, an individual had only to search over the apartments of the house until discovering the places where images had been placed by the imagination. In accordance with said system, if it were desired to fix a historic date in memory, it was localised in an imaginary town divided into a certain number of districts, each of with ten houses, each house with ten rooms, each room with a hundred quadrates or memory-places on the floor on the four walls on the roof.
Therefore, if it were desired to fix in the memory the date of the invention of printing, an imaginary book, or some other symbol of printing, would be placed in the thirty-sixth quadrate or memory-place of the fourth room of the first house of the historic district of the town. Except that the rules of mnemonics are referred to by Martianus Capella, nothing further is known regarding the practice until the 13th century. Among the voluminous writings of Roger Bacon is a tractate De arte memorativa. Ramon Llull devoted special attention to mnemonics in connection with his ars generalis; the first important modification of the method of the Romans was that invented by the German poet Konrad Celtes, who, in his Epitoma in utramque Ciceronis rhetoricam cum arte memorativa nova, used letters of the alphabet for associations, rather than places. About the end of the 15th century, Petrus de Ravenna provoked such astonishment in Italy by his mnemonic feats that he was believed by many to be a necromancer.
His Phoenix artis memoriae went through as many as nine editions, the seventh being published at Cologne in 1608. About the end of the 16th century, Lambert Schenkel, who taught mnemonics in France and Germany surprised people with his memory, he was denounced as a sorcerer by the University of Louvain, but in 1593 he published his tractate De memoria at Douai with the sanction of that celebrated theological faculty. The most complete account of his system is given in two works by his pupil Martin Sommer, published in Venice in 1619. In 1618 John Willis published Mnemonica. Giordano Bruno included a memoria technica in his treatise De umbris idearum, as part of his study of the ars generalis of Llull. Other writers of this period are the Florentine Publicius. Porta, Ars reminiscendi. In 1648 Stanislaus Mink von Wennsshein revealed what he called the "most fertile secret" in mnemonics — using consonants for figures, thus expressing numbers by words, i
In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision. For this reason, floating-point computation is found in systems which include small and large real numbers, which require fast processing times. A number is, in general, represented to a fixed number of significant digits and scaled using an exponent in some fixed base. A number that can be represented is of the following form: significand × base exponent, where significand is an integer, base is an integer greater than or equal to two, exponent is an integer. For example: 1.2345 = 12345 ⏟ significand × 10 ⏟ base − 4 ⏞ exponent. The term floating point refers to the fact that a number's radix point can "float"; this position is indicated as the exponent component, thus the floating-point representation can be thought of as a kind of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of different orders of magnitude: e.g. the distance between galaxies or the diameter of an atomic nucleus can be expressed with the same unit of length.
The result of this dynamic range is that the numbers that can be represented are not uniformly spaced. Over the years, a variety of floating-point representations have been used in computers. In 1985, the IEEE 754 Standard for Floating-Point Arithmetic was established, since the 1990s, the most encountered representations are those defined by the IEEE; the speed of floating-point operations measured in terms of FLOPS, is an important characteristic of a computer system for applications that involve intensive mathematical calculations. A floating-point unit is a part of a computer system specially designed to carry out operations on floating-point numbers. A number representation specifies some way of encoding a number as a string of digits. There are several mechanisms. In common mathematical notation, the digit string can be of any length, the location of the radix point is indicated by placing an explicit "point" character there. If the radix point is not specified the string implicitly represents an integer and the unstated radix point would be off the right-hand end of the string, next to the least significant digit.
In fixed-point systems, a position in the string is specified for the radix point. So a fixed-point scheme might be to use a string of 8 decimal digits with the decimal point in the middle, whereby "00012345" would represent 0001.2345. In scientific notation, the given number is scaled by a power of 10, so that it lies within a certain range—typically between 1 and 10, with the radix point appearing after the first digit; the scaling factor, as a power of ten, is indicated separately at the end of the number. For example, the orbital period of Jupiter's moon Io is 152,853.5047 seconds, a value that would be represented in standard-form scientific notation as 1.528535047×105 seconds. Floating-point representation is similar in concept to scientific notation. Logically, a floating-point number consists of: A signed digit string of a given length in a given base; this digit string is referred to mantissa, or coefficient. The length of the significand determines the precision; the radix point position is assumed always to be somewhere within the significand—often just after or just before the most significant digit, or to the right of the rightmost digit.
This article follows the convention that the radix point is set just after the most significant digit. A signed integer exponent. To derive the value of the floating-point number, the significand is multiplied by the base raised to the power of the exponent, equivalent to shifting the radix point from its implied position by a number of places equal to the value of the exponent—to the right if the exponent is positive or to the left if the exponent is negative. Using base-10 as an example, the number 152,853.5047, which has ten decimal digits of precision, is represented as the significand 1,528,535,047 together with 5 as the exponent. To determine the actual value, a decimal point is placed after the first digit of the significand and the result is multiplied by 105 to give 1.528535047×105, or 152,853.5047. In storing such a number, the base need not be stored, since it will be the same for the entire range of supported numbers, can thus be inferred. Symbolically, this final value is: s b p − 1 × b e, where s is the