An electronic calculator is typically a portable Electronics device used to perform , ranging from basic arithmetic to complex mathematics.
The first solid-state electronic calculator was created in the early 1960s. Pocket-sized devices became available in the 1970s, especially after the Intel 4004, the first microprocessor, was developed by Intel for the Japanese calculator company Busicom. 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 the incorporation of integrated circuits reduced their size and cost. By the end of that decade, prices had dropped to the point where a basic calculator was affordable to most and they became common in schools.
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. , basic calculators cost little, but scientific and graphing models tend to cost more.
Computer as far back as Ancient UNIX have included interactive calculator Computer program such as dc and hoc, and interactive BASIC could be used to do calculations on most 1970s and 1980s home computers. Calculator functions are included in most , tablet computer, and personal digital assistant (PDA) type devices. With the very wide availability of smartphones and the like, dedicated hardware calculators, while still widely used, are less common than they once were. In 1986, calculators still represented an estimated 41% of the world's general-purpose hardware capacity to compute information. By 2007, this had diminished to less than 0.05%.
Large-sized Number are often used to improve readability; while using decimal separator (usually a point rather than a comma) instead of or in addition to . Various symbols for function commands may also be shown on the display. Fractions such as are displayed as decimal , for example rounded to . Also, some fractions (such as , which is ; 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 .
+ Calculator buttons and their meanings | |
Memory Clear | |
Memory Recall | |
Memory Subtraction | |
Memory Addition | |
All Clear | |
Clear (last) Entry; sometimes called CE/C: a first press clears the last entry (CE), a second press clears all (C) | |
Toggle positive/negative number aka CHange Sign | |
Percent | |
Division | |
Multiplication | |
Subtraction | |
Addition | |
Decimal point | |
Square root | |
Result |
The arrangement of digits on calculator and other with the -- keys two rows above the -- keys is derived from calculators and . It is notably different from the layout of Telephone keypad which have the -- keys on top and -- keys on the third row.
+Processor chip's contents ! width=160px; | Unit !Function |
Scanning (Polling) unit | When a calculator is powered on, it scans the keypad waiting to pick up an electrical signal when a key is pressed. |
Encoder unit | Converts the and functions into binary code. |
X register and Y register | They are number stores where numbers are stored temporarily while doing calculations. All numbers go into the X register first; the number in the X register is shown on the display. |
Flag register | The function for the calculation is stored here until the calculator needs it. |
Permanent Computer memory (ROM) | The instructions for in-built functions (arithmetic operations, , , trigonometry, etc.) are stored here in Binary number form. These instructions are Computer program, stored permanently, and cannot be erased. |
User memory (RAM) | The store where numbers can be stored by the user. User memory contents can be changed or erased by the user. |
Arithmetic logic unit (ALU) | The ALU executes all arithmetic and Boolean algebra instructions, and provides the results in binary coded form. |
Binary decoder unit | Converts binary code into decimal numbers which can be displayed on the display unit. |
Clock rate of a processor Chipset refers to the frequency at which the central processing unit (CPU) is running. It is used as an indicator of the processor's speed, and is measured in clock cycles per second or Hertz. For basic calculators, the speed can vary from a few hundred hertz to the kilohertz range.
To perform the calculation , one presses keys in the following sequence on most calculators: .
Other functions are usually performed using repeated additions or subtractions.
The same argument applies when hardware of this type uses an embedded microcontroller or other small processor. Often, smaller code results when representing numbers internally in BCD format, since a conversion from or to binary representation can be expensive on such limited processors. For these applications, some small processors feature BCD arithmetic modes, which assist when writing routines that manipulate BCD quantities.
Where calculators have added functions (such as square root, or trigonometric functions), software are required to produce high precision results. Sometimes significant design effort is needed to fit all the desired functions in the limited memory space available in the calculator Chipset, with acceptable calculation time.
The Renaissance saw the invention of the mechanical calculator by Wilhelm Schickard in 1623, and later by Blaise Pascal in 1642.; "Pascal's invention of the calculating machine. Pascal invented his machine just four hundred years ago, as a youth of nineteen. He was spurred to it by sharing the burden of arithmetical labor involved in his father's official work as supervisor of taxes at Rouen. He conceived the idea of doing the work mechanically, and developed a design appropriate for this purpose; showing herein the same combination of pure science and mechanical genius that characterized his whole life. But it was one thing to conceive and design the machine, and another to get it made and put into use. Here were needed those practical gifts that he displayed later in his inventions....
In a sense, Pascal's invention was premature, in that the mechanical arts in his time were not sufficiently advanced to enable his machine to be made at an economic price, with the accuracy and strength needed for reasonably long use. This difficulty was not overcome until well on into the nineteenth century, by which time also a renewed stimulus to invention was given by the need for many kinds of calculation more intricate than those considered by Pascal." A device that was at times somewhat over-promoted as being able to perform all four arithmetic operations with minimal human intervention. Pascal's calculator could add and subtract two numbers directly and thus, if the tedium could be borne, multiply and divide by repetition. Schickard's machine, constructed several decades earlier, used a clever set of mechanised multiplication tables to ease the process of multiplication and division with the adding machine as a means of completing this operation. There is a debate about whether Pascal or Shickard should be credited as the known inventor of a calculating machine due to the differences (like the different aims) of both inventions. Schickard and Pascal were followed by Gottfried Leibniz who spent forty years designing a four-operation mechanical calculator, the stepped reckoner, 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.see Mechanical calculator#Other calculating machines
The 18th century saw the arrival of some notable improvements, first by Giovanni Poleni with the first fully functional calculating clock and four-operation machine, but these machines were almost always one of a kind. Luigi Torchi invented the first direct multiplication machine in 1834: this was also the second key-driven machine in the world, following that of James White (1822). 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 . 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.
In 1921, Edith Clarke invented the "Clarke calculator", a simple graph-based calculator for solving line equations involving hyperbolic functions. This allowed electrical engineers to simplify calculations for inductance and capacitance in power transmission lines.
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 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. The IBM 608 plugboard programmable calculator was IBM's first all-transistor product, released in 1957; this was a console type system, with input and output on punched cards, and replaced the earlier, larger, vacuum-tube IBM 603.
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 , cold-cathode tubes and in its circuits, with 12 cold-cathode Nixie tube 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 of the time, a feature that was unique to it and the later Sharp CS-10A among electronic calculators. The ANITA weighed roughly due to its large tube system. 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 cathode-ray tube (CRT), and introduced Reverse Polish Notation (RPN) to the calculator market for a price of $2200, which was about three times the cost of an electromechanical calculator of the time. Like Bell Punch, Friden was a manufacturer of mechanical calculators that had decided that the future lay in electronics. In 1964 more all-transistor electronic calculators were introduced: Sharp introduced the CS-10A, which weighed and cost 500,000 yen ($), 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). The Victor 3900 was the first to use integrated circuits in place of individual , but production problems delayed sales until 1966.
There followed a series of electronic calculator models from these and other manufacturers, including Canon, Mathatronics, Olivetti, SCM Corporation (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 , and . 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.
Bulgaria's ELKA 6521, introduced in 1965, was developed by the Central Institute for Calculation Technologies and built at the Elektronika factory in Sofia. The name derives from ELektronen KAlkulator, and it weighed around . It is the first calculator in the world which includes the square root function. Later that same year were released the ELKA 22 (with a luminescent display) and the ELKA 25, with an built-in printer. Several other models were developed until the first pocket model, the ELKA 101, was released in 1974. The writing on it was in Roman script, and it was exported to western countries.
Another early programmable desktop calculator (and maybe the first Japanese one) was the Casio (AL-1000) produced in 1967. It featured a display and had transistor electronics and ferrite core memory.
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 first Soviet programmable desktop calculator ISKRA 123, powered by the power grid, was released at the start of the 1970s.
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 handheld calculator was a 1967 prototype called Cal Tech, whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator. It could add, multiply, subtract, and divide, and its output device was a paper tape. Audio interview with one of the inventors. As a result of the "Cal-Tech" project, Texas Instruments was granted master patents on portable calculators.
The first commercially produced 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 from the "Cal-Tech" project. It had no traditional display; numerical output was on thermal paper tape.
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 1.59 pounds (721 grams), had a vacuum fluorescent display, rechargeable NiCad batteries, and initially sold for US$395.
However, integrated circuit development efforts culminated in early 1971 with the introduction of the first "calculator on a chip", the MK6010 by Mostek,"Single Chip Calculator Hits the Finish Line", Electronics, February 1, 1971, p. 19. followed by Texas Instruments later in the year. Although these early hand-held calculators were very costly, these advances in electronics, together with developments in display technology (such as the vacuum fluorescent display, LED, and LCD), led 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 full 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 .
The first European-made pocket-sized calculator, DB 800 was made in May 1971 by Digitron in Buje, Croatia (former Yugoslavia) with four functions and an eight-digit display and special characters for a negative number and a warning that the calculation has too many digits to display.
The first American-made pocket-sized calculator, the Bowmar 901B (popularly termed The Bowmar Brain), measuring , came out in the Autumn of 1971, with four functions and an eight-digit red LED display, for , while in August 1972 the four-function Sinclair Executive became the first slimline pocket calculator measuring and weighing . It retailed for around £79 ( at the time). By the end of the decade, similar calculators were priced less than £5 ($). Following protracted development over the course of two years including a botched partnership with Texas Instruments, Eldorado Electrodata released five pocket calculators in 1972. One called the Touch Magic was "no bigger than a pack of cigarettes" according to Administrative Management.
The first Soviet Union made pocket-sized calculator, the Elektronika B3-04 was developed by the end of 1973 and sold at the start 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, and later models included some scientific functions. The Sinclair calculators were successful because they were far cheaper than the competition; however, their design led to slow and less accurate computations of transcendental functions (maximum three decimal places of accuracy). See in particular the section "Limited performance and accuracy". For more coverage of Shirriff's results, see
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 added key for entering pi (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 arose which focused on specialized 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.
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 nonexistent addresses and other methods. A number of respected monthly publications, including the popular science magazine Nauka i Zhizn ( Наука и жизнь, Science and Life), featured special columns, dedicated to optimization methods for calculator programmers and updates on undocumented features for hackers, which grew into a whole esoteric science with many branches, named "yeggogology" ("еггогология"). The error messages on those calculators appear as a Russian word "YEGGOG" ("ЕГГОГ") which, unsurprisingly, is translated to "Error".
A similar hacker culture in the US revolved around the HP-41, which was also noted for a large number of undocumented features and was much more powerful than B3-34.
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 Calculator On Substrate (COS) technology. An extension of one glass plate needed for the liquid crystal display was used as a substrate to mount the needed chips based on a new hybrid technology. The COS technology may have been too costly 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 (ICs) 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 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 in the logic cells of CMOS ICs only used any appreciable power when they changed state. The LED and VFD displays often required added driver transistors or ICs, whereas the LCDs were more amenable to being driven directly by the calculator IC itself.
With this low power consumption came the possibility of using as the power source, realised around 1978 by calculators such as the Royal Solar 1, Sharp EL-8026, and Teal Photon.
By 1976, the cost of the cheapest four-function pocket calculator had dropped to a few dollars, about 1/20 of the cost five years before. The results of this were that the pocket calculator was affordable, and that it was now difficult for the manufacturers to make a profit from calculators, leading to many firms dropping out of the business or closing. The firms that survived making calculators tended to be those with high outputs of higher quality calculators, or producing high-specification scientific and programmable calculators.
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 derivative and integral functions, solve differential equations, run word processing and PIM software, and connect by wire or infrared 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.
Calculators may in some circumstances be used within school and college examinations. In the United Kingdom there are limitations on the type of calculator which may be used in an examination to avoid malpractice. Some calculators which offer additional functionality have an "exam mode" setting which makes them compliant with examination regulations.Joint Council for Qualifications, Instructions for conducting examinations, section 10.9, September 2024, accessed on 27 December 2024
For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in read-only memory (ROM), and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require much multiplication. Bit serial logic designs are more common in calculators whereas bit parallel designs dominate general-purpose computers, because a bit serial design minimizes chipset complexity, but takes many more clock cycles. This distinction blurs with high-end calculators, which use processor chips associated with computer and embedded systems design, more so the Z80, MC68000, and ARM architectures, and some custom designs specialized for the calculator market.
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