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An electronic calculator is a small, portable, often inexpensive electronic device used to perform both basic and complex operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs or mobile phones are comparable in size to handheld calculators and may soon replace them.
The first solid state electronic calculator was created in the 1960s, building on the extensive history of tools such as the abacus, developed around 2000 BC; and the mechanical calculator, developed in the 17th century. It was developed in parallel with the analog computers of the day.
Modern electronic calculators vary from cheap, give-away, credit-card sized models to sturdy desktop models with built-in printers. They became popular in the mid-1970s as integrated circuits made their size and cost small. By the end of that decade, calculator prices had reduced to a point where a basic calculator was affordable to most and they became common in schools.
Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, and calculator functions are included in almost all PDA-type devices (save a few dedicated address book and dictionary devices).
In addition to general purpose calculators, there are those designed for specific markets; for example, there are scientific calculators which include trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher dimensional Euclidean space.
In 1986, calculators still represented an estimated 41% of the world's general-purpose hardware capacity to compute information. This diminished to less than 0.05% by 2007.
Modern electronic calculators contain a keyboard with buttons for digits and arithmetical operations. Some even contain 00 and 000 buttons to make large numbers easier to enter. Most basic calculators assign only one digit or operation on each button. However, in more specific calculators, a button can perform multi-function working with key combination or current reckoning mode.
Calculators usually have liquid crystal displays as output in place of historical vacuum fluorescent displays. See more details in technical improvements. Fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions such as 1⁄7 which is 0.14285714285714 (to 14 significant figures) can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions or mixed numbers.
Calculators also have the ability to store numbers into memory. Basic types of these store only one number at a time. More specific types are able to store many numbers represented in variables. The variables can also be used for constructing formulae. Some models have the ability to extend memory capacity to store more numbers; the extended address is referred to as an array index.
Power sources of calculators are batteries, solar cells or electricity (for old models) turning on with a switch or button. Some models even have no turn-off button but they provide some way to put off, for example, leaving no operation for a moment, covering solar cell exposure, or closing their lid. Crank-powered calculators were also common in the early computer era.
In most countries, students use calculators for schoolwork. There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. There remains disagreement about the importance of the ability to perform calculations "in the head", with some curricula restricting calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation techniques and problem-solving. Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in. Others have argued[by whom?] that calculator use can even cause core mathematical skills to atrophy, or that such use can prevent understanding of advanced algebraic concepts. In December 2011 the UK's Minister of State for Schools, Nick Gibb, voiced concern that children can become "too dependent" on the use of calculators. As a result, the use of calculators is to be included as part of a review of the National Curriculum. Scratch papers are new alternatives when calculator sales decreased in 2007.
Exams are generally not allowed to use calculators including other computable devices. However, some of which may be too difficult to do in mind so such exams may clearly specify that calculators can be used.
In general, a basic electronic calculator consists of the following components:
A basic explanation as to how calculations are performed in a simple 4-function calculator: To perform the calculation 25 + 9, one presses keys in the following sequence on most calculators: 2 5 + 9 =.
All other functions are usually carried out using repeated additions. Where calculators have additional functions such as square root, or trigonometric functions, software algorithms are required to produce high precision results. Sometimes significant design effort is required to fit all the desired functions in the limited memory space available in the calculator chip, with acceptable calculation time.
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The fundamental difference between a calculator and computer is that a computer can be programmed in a way that allows the program to take different branches according to intermediate results, while calculators are pre-designed with specific functions such as addition, multiplication, and logarithms built in. The distinction is not clear-cut: some devices classed as programmable calculators have programming functionality, sometimes with support for programming languages such as RPL or TI-BASIC.
Typically the user buys the least expensive model having a specific feature set, but does not care much about speed (since speed is constrained by how fast the user can press the buttons). Thus designers of calculators strive to minimize the number of logic elements on the chip, not the number of clock cycles needed to do a computation.
For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in ROM, and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require hardware floating-point. Bit serial logic designs are more common in calculators whereas bit parallel designs dominate general-purpose computers, because a bit serial design minimizes chip complexity, but takes many more clock cycles. (Again, the line blurs with high-end calculators, which use processor chips associated with computer and embedded systems design, particularly the Z80, MC68000, and ARM architectures, as well as some custom designs specifically made for the calculator market.)
The first known tool used to aid arithmetic calculations was the Abacus, devised by Sumerians and Egyptians before 2000 BC. Except for the Antikythera mechanism, an "out of the time" astronomical device, development of computing tools arrived in the beginning of the 17th century: Geometric-military compass by Galileo, Logarithms and Napier Bones by Napier, slide rule by Edmund Gunter.
In 1642, the Renaissance saw the invention of the mechanical calculator by the famous intellectual Blaise Pascal, a device that will eventually perform all four arithmetic operations without relying on human intelligence. Pascal's Calculator could add and subtract two numbers directly and multiply and divide by repetition. He was followed by Gottfried Leibniz who spent forty years designing a four-operation mechanical calculator, inventing in the process his leibniz wheel, but who couldn't design a fully operational machine. There were also five unsuccessful attempts to design a calculating clock in the 17th century.
The 18th century saw the arrival of some interesting improvements, first by Poleni with the first fully functional calculating clock and four-operation machine, but these machines were almost always one of the kind. It was not until the 19th century and the Industrial Revolution that real developments began to occur. Although machines capable of performing all four arithmetic functions existed prior to the 19th century, the refinement of manufacturing and fabrication processes during the eve of the industrial revolution made large scale production of more compact and modern units possible. The Arithmometer, invented in 1820 as a four-operation mechanical calculator, was released to production in 1851 as an adding machine and became the first commercially successful unit; forty years later, by 1890, about 2,500 arithmometers had been sold plus a few hundreds more from two arithmometer clone makers (Burkhardt, Germany, 1878 and Layton, UK, 1883) and Felt and Tarrant, the only other competitor in true commercial production, had sold 100 comptometers.
It wasn't until 1902 that the familiar push-button user interface was developed, with the introduction of the Dalton Adding Machine, developed by James L. Dalton in the United States.
The Curta calculator was developed in 1948 and, although costly, became popular for its portability. This purely mechanical hand-held device could do addition, subtraction, multiplication and division. By the early 1970s electronic pocket calculators ended manufacture of mechanical calculators, although the Curta remains a popular collectable item.
The first mainframe computers, using firstly vacuum tubes and later transistors in the logic circuits, appeared in the 1940s and 1950s. This technology was to provide a stepping stone to the development of electronic calculators.
The Casio Computer Company, in Japan, released the Model 14-A calculator in 1957, which was the world's first all-electric (relatively) "compact" calculator. It did not use electronic logic but was based on relay technology, and was built into a desk.
In October 1961 the world's first all-electronic desktop calculator, the British Bell Punch/Sumlock Comptometer ANITA (A New Inspiration To Arithmetic/Accounting) was announced. This machine used vacuum tubes, cold-cathode tubes and Dekatrons in its circuits, with 12 cold-cathode "Nixie" tubes for its display. Two models were displayed, the Mk VII for continental Europe and the Mk VIII for Britain and the rest of the world, both for delivery from early 1962. The Mk VII was a slightly earlier design with a more complicated mode of multiplication, and was soon dropped in favour of the simpler Mark VIII. The ANITA had a full keyboard, similar to mechanical comptometers of the time, a feature that was unique to it and the later Sharp CS-10A among electronic calculators. Bell Punch had been producing key-driven mechanical calculators of the comptometer type under the names "Plus" and "Sumlock", and had realised in the mid-1950s that the future of calculators lay in electronics. They employed the young graduate Norbert Kitz, who had worked on the early British Pilot ACE computer project, to lead the development. The ANITA sold well since it was the only electronic desktop calculator available, and was silent and quick.
The tube technology of the ANITA was superseded in June 1963 by the U.S. manufactured Friden EC-130, which had an all-transistor design, a stack of four 13-digit numbers displayed on a 5-inch (13 cm) CRT, and introduced reverse Polish notation (RPN) to the calculator market for a price of $2200, which was about three times the cost of an electromechanical calculator of the time. Like Bell Punch, Friden was a manufacturer of mechanical calculators that had decided that the future lay in electronics. In 1964 more all-transistor electronic calculators were introduced: Sharp introduced the CS-10A, which weighed 25 kg (55 lb) and cost 500,000 yen (~US$2500), and Industria Macchine Elettroniche of Italy introduced the IME 84, to which several extra keyboard and display units could be connected so that several people could make use of it (but apparently not at the same time).
There followed a series of electronic calculator models from these and other manufacturers, including Canon, Mathatronics, Olivetti, SCM (Smith-Corona-Marchant), Sony, Toshiba, and Wang. The early calculators used hundreds of germanium transistors, which were cheaper than silicon transistors, on multiple circuit boards. Display types used were CRT, cold-cathode Nixie tubes, and filament lamps. Memory technology was usually based on the delay line memory or the magnetic core memory, though the Toshiba "Toscal" BC-1411 appears to have used an early form of dynamic RAM built from discrete components. Already there was a desire for smaller and less power-hungry machines.
The Olivetti Programma 101 was introduced in late 1965; it was a stored program machine which could read and write magnetic cards and displayed results on its built-in printer. Memory, implemented by an acoustic delay line, could be partitioned between program steps, constants, and data registers. Programming allowed conditional testing and programs could also be overlaid by reading from magnetic cards. It is regarded as the first personal computer produced by a company (that is, a desktop electronic calculating machine programmable by non-specialists for personal use). The Olivetti Programma 101 won many industrial design awards.
The Monroe Epic programmable calculator came on the market in 1967. A large, printing, desk-top unit, with an attached floor-standing logic tower, it could be programmed to perform many computer-like functions. However, the only branch instruction was an implied unconditional branch (GOTO) at the end of the operation stack, returning the program to its starting instruction. Thus, it was not possible to include any conditional branch (IF-THEN-ELSE) logic. During this era, the absence of the conditional branch was sometimes used to distinguish a programmable calculator from a computer.
The electronic calculators of the mid-1960s were large and heavy desktop machines due to their use of hundreds of transistors on several circuit boards with a large power consumption that required an AC power supply. There were great efforts to put the logic required for a calculator into fewer and fewer integrated circuits (chips) and calculator electronics was one of the leading edges of semiconductor development. U.S. semiconductor manufacturers led the world in Large Scale Integration (LSI) semiconductor development, squeezing more and more functions into individual integrated circuits. This led to alliances between Japanese calculator manufacturers and U.S. semiconductor companies: Canon Inc. with Texas Instruments, Hayakawa Electric (later known as Sharp Corporation) with North-American Rockwell Microelectronics, Busicom with Mostek and Intel, and General Instrument with Sanyo.
By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first portable calculators appeared in Japan in 1970, and were soon marketed around the world. These included the Sanyo ICC-0081 "Mini Calculator", the Canon Pocketronic, and the Sharp QT-8B "micro Compet". The Canon Pocketronic was a development of the "Cal-Tech" project which had been started at Texas Instruments in 1965 as a research project to produce a portable calculator. The Pocketronic has no traditional display; numerical output is on thermal paper tape. As a result of the "Cal-Tech" project, Texas Instruments was granted master patents on portable calculators.
Sharp put in great efforts in size and power reduction and introduced in January 1971 the Sharp EL-8, also marketed as the Facit 1111, which was close to being a pocket calculator. It weighed about 455 grams or one pound, had a vacuum fluorescent display, rechargeable NiCad batteries, and initially sold for $395.
However, the efforts in integrated circuit development culminated in the introduction in early 1971 of the first "calculator on a chip", the MK6010 by Mostek, followed by Texas Instruments later in the year. Although these early hand-held calculators were very expensive, these advances in electronics, together with developments in display technology (such as the vacuum fluorescent display, LED, and LCD), lead within a few years to the cheap pocket calculator available to all.
In 1971 Pico Electronics. and General Instrument also introduced their first collaboration in ICs, a complete single chip calculator IC for the Monroe Royal Digital III calculator. Pico was a spinout by five GI design engineers whose vision was to create single chip calculator ICs. Pico and GI went on to have significant success in the burgeoning handheld calculator market.
The first truly pocket-sized electronic calculator was the Busicom LE-120A "HANDY", which was marketed early in 1971. Made in Japan, this was also the first calculator to use an LED display, the first hand-held calculator to use a single integrated circuit (then proclaimed as a "calculator on a chip"), the Mostek MK6010, and the first electronic calculator to run off replaceable batteries. Using four AA-size cells the LE-120A measures 4.9x2.8x0.9 in (124x72x24 mm).
The first American-made pocket-sized calculator, the Bowmar 901B (popularly referred to as The Bowmar Brain), measuring 5.2 × 3.0 × 1.5 in (131 × 77 × 37 mm), came out in the Autumn of 1971, with four functions and an eight-digit red LED display, for $240, while in August 1972 the four-function Sinclair Executive became the first slimline pocket calculator measuring 5.4 × 2.2 × 0.35 in (138 × 56 × 9 mm) and weighing 2.5 oz (70g). It retailed for around $150 (£79). By the end of the decade, similar calculators were priced less than $10 (£5).
The first Soviet-made pocket-sized calculator, the "Elektronika B3-04" was developed by the end of 1973 and sold at the beginning of 1974.
One of the first low-cost calculators was the Sinclair Cambridge, launched in August 1973. It retailed for £29.95, or £5 less in kit form. The Sinclair calculators were successful because they were far cheaper than the competition; however, their design was flawed and their accuracy in some functions was questionable. The scientific programmable models were particularly poor in this respect, with the programmability comings at a heavy price in Transcendental function accuracy.[original research?]
Meanwhile Hewlett Packard (HP) had been developing a pocket calculator. Launched in early 1972 it was unlike the other basic four-function pocket calculators then available in that it was the first pocket calculator with scientific functions that could replace a slide rule. The $395 HP-35, along with nearly all later HP engineering calculators, used reverse Polish notation (RPN), also called postfix notation. A calculation like "8 plus 5" is, using RPN, performed by pressing "8", "Enter↑", "5", and "+"; instead of the algebraic infix notation: "8", "+", "5", "=").
The first Soviet scientific pocket-sized calculator the "B3-18" was completed by the end of 1975.
In 1973, Texas Instruments(TI) introduced the SR-10, (SR signifying slide rule) an algebraic entry pocket calculator using scientific notation for $150. Shortly after the SR-11 featured an additional key for entering "π". It was followed the next year by the SR-50 which added log and trig functions to compete with the HP-35, and in 1977 the mass-marketed TI-30 line which is still produced.
In 1978 a new company, Calculated Industries, came onto the scene, focusing on specific markets. Their first calculator, the Loan Arranger  (1978) was a pocket calculator marketed to the Real Estate industry with preprogrammed functions to simplify the process of calculating payments and future values. In 1985, CI launched a calculator for the construction industry called the Construction Master  which came preprogrammed with common construction calculations (such as angles, stairs, roofing math, pitch, rise, run, and feet-inch fraction conversions). This would be the first in a line of construction related calculators.
The first desktop programmable calculators were produced in the mid-1960s by Mathatronics and Casio (AL-1000). These machines were, however, very heavy and expensive. The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader. Two years later the HP-25C introduced continuous memory, i.e. programs and data were retained in CMOS memory during power-off. In 1979, HP released the first alphanumeric, programmable, expandable calculator, the HP-41C. It could be expanded with RAM (memory) and ROM (software) modules, as well as peripherals like bar code readers, microcassette and floppy disk drives, paper-roll thermal printers, and miscellaneous communication interfaces (RS-232, HP-IL, HP-IB).
The first Soviet programmable desktop calculator ISKRA 123, powered by the power grid, was released at the beginning of the 1970s. The first Soviet pocket battery-powered programmable calculator, Elektronika "B3-21", was developed by the end of 1977 and released at the beginning of 1978. The successor of B3-21, the Elektronika B3-34 wasn't backward compatible with B3-21, even if it kept the reverse Polish notation (RPN). Thus B3-34 defined a new command set, which later was used in a series of later programmable Soviet calculators. Despite very limited capabilities (98 bytes of instruction memory and about 19 stack and addressable registers), people managed to write all kinds of programs for them, including adventure games and libraries of calculus-related functions for engineers. Hundreds, perhaps thousands, of programs were written for these machines, from practical scientific and business software, which were used in real-life offices and labs, to fun games for children. The Elektronika MK-52 calculator (using the extended B3-34 command set, and featuring internal EEPROM memory for storing programs and external interface for EEPROM cards and other periphery) was used in Soviet spacecraft program (for Soyuz TM-7 flight) as a backup of the board computer.
This series of calculators was also noted for a large number of highly counter-intuitive mysterious undocumented features, somewhat similar to "synthetic programming" of the American HP-41, which were exploited by applying normal arithmetic operations to error messages, jumping to non-existent addresses and other techniques. A number of respected monthly publications, including the popular science magazine "Наука и жизнь" ("Science and Life"), featured special columns, dedicated to optimization techniques for calculator programmers and updates on undocumented features for hackers, which grew into a whole esoteric science with many branches, known as "yeggogology" ("еггогология"). The error messages on those calculators appear as a Russian word "YEGGOG" ("ЕГГОГ") which, unsurprisingly, is translated to "Error".
Through the 1970s the hand-held electronic calculator underwent rapid development. The red LED and blue/green vacuum fluorescent displays consumed a lot of power and the calculators either had a short battery life (often measured in hours, so rechargeable nickel-cadmium batteries were common) or were large so that they could take larger, higher capacity batteries. In the early 1970s liquid crystal displays (LCDs) were in their infancy and there was a great deal of concern that they only had a short operating lifetime. Busicom introduced the Busicom LE-120A "HANDY" calculator, the first pocket-sized calculator and the first with an LED display, and announced the Busicom LC with LCD display. However, there were problems with this display and the calculator never went on sale. The first successful calculators with LCDs were manufactured by Rockwell International and sold from 1972 by other companies under such names as: Dataking LC-800, Harden DT/12, Ibico 086, Lloyds 40, Lloyds 100, Prismatic 500 (aka P500), Rapid Data Rapidman 1208LC. The LCDs were an early form using the Dynamic Scattering Mode DSM with the numbers appearing as bright against a dark background. To present a high-contrast display these models illuminated the LCD using a filament lamp and solid plastic light guide, which negated the low power consumption of the display. These models appear to have been sold only for a year or two.
A more successful series of calculators using a reflective DSM-LCD was launched in 1972 by Sharp Inc with the Sharp EL-805, which was a slim pocket calculator. This, and another few similar models, used Sharp's "COS" (Calculator On Substrate) technology. An extension of one glass plate needed for the Liquid Crystal Display was used as a substrate to mount the required chips based on a new hybrid technology. The "COS" technology may have been too expensive since it was only used in a few models before Sharp reverted to conventional circuit boards.
In the mid-1970s the first calculators appeared with field-effect, Twisted Nematic TN LCDs with dark numerals against a grey background, though the early ones often had a yellow filter over them to cut out damaging ultraviolet rays. The advantage of LCDs is that they are passive light modulators reflecting light, which require much less power than light-emitting displays such as LEDs or VFDs. This led the way to the first credit-card-sized calculators, such as the Casio Mini Card LC-78 of 1978, which could run for months of normal use on button cells.
There were also improvements to the electronics inside the calculators. All of the logic functions of a calculator had been squeezed into the first "Calculator on a chip" integrated circuits in 1971, but this was leading edge technology of the time and yields were low and costs were high. Many calculators continued to use two or more integrated circuits (ICs), especially the scientific and the programmable ones, into the late 1970s.
The power consumption of the integrated circuits was also reduced, especially with the introduction of CMOS technology. Appearing in the Sharp "EL-801" in 1972, the transistors in the logic cells of CMOS ICs only used any appreciable power when they changed state. The LED and VFD displays often required additional driver transistors or ICs, whereas the LCD displays were more amenable to being driven directly by the calculator IC itself.
With this low power consumption came the possibility of using solar cells as the power source, realised around 1978 by such calculators as the Royal Solar 1, Sharp EL-8026, and Teal Photon.
At the beginning of the 1970s hand-held electronic calculators were very expensive, costing two or three weeks' wages, and so were a luxury item. The high price was due to their construction requiring many mechanical and electronic components which were expensive to produce, and production runs were not very large. Many companies saw that there were good profits to be made in the calculator business with the margin on these high prices. However, the cost of calculators fell as components and their production techniques improved, and the effect of economies of scale were felt.
By 1976 the cost of the cheapest 4-function pocket calculator had dropped to a few dollars, about one 20th of the cost five years earlier. The consequences of this were that the pocket calculator was affordable, and that it was now difficult for the manufacturers to make a profit out of calculators, leading to many companies dropping out of the business or closing down altogether. The companies that survived making calculators tended to be those with high outputs of higher quality calculators, or producing high-specification scientific and programmable calculators.
The first calculator capable of symbolic computation was the HP-28C, released in 1987. It was able to, for example, solve quadratic equations symbolically. The first graphing calculator was the Casio FX-7000G released in 1985.
The two leading manufacturers, HP and TI, released increasingly feature-laden calculators during the 1980s and 1990s. At the turn of the millennium, the line between a graphing calculator and a handheld computer was not always clear, as some very advanced calculators such as the TI-89, the Voyage 200 and HP-49G could differentiate and integrate functions, solve differential equations, run word processing and PIM software, and connect by wire or IR to other calculators/computers.
The HP 12c financial calculator is still produced. It was introduced in 1981 and is still being made with few changes. The HP 12c featured the reverse Polish notation mode of data entry. In 2003 several new models were released, including an improved version of the HP 12c, the "HP 12c platinum edition" which added more memory, more built-in functions, and the addition of the algebraic mode of data entry.
Calculated Industries competed with the HP 12c in the mortgage and real estate markets by differentiating the key labeling; changing the “I”, “PV”, “FV” to easier labeling terms such as "Int", "Term", "Pmt", and not using the reverse Polish notation. However, CI's more successful calculators involved a line of construction calculators, which evolved and expanded in the 1990s to present. According to Mark Bollman, a mathematics and calculator historian and associate professor of mathematics at Albion College, the "Construction Master is the first in a long and profitable line of CI construction calculators" which carried them through the 1980s, 1990s, and to the present.
Personal computers often come with a calculator utility program that emulates the appearance and functionality of a calculator, using the graphical user interface to portray a calculator. One such example is Windows Calculator. Most personal data assistants (PDA) and smartphones also have such a feature.
These are some of the manufacturers which made a notable contribution to calculator development:
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