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An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
to complex
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
. 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 A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, a ...
, was developed by
Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, and Delaware General Corporation Law, incorporated in Delaware. Intel designs, manufactures, and sells computer compo ...
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 circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
s 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 Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
calculations. Some calculators even have the ability to do
computer algebra In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating expression (mathematics), ...
.
Graphing calculator Graphing Calculator may refer to: * Graphing calculators, calculators that are able to display and/or analyze mathematical function graphs * NuCalc, a computer software program able to perform many graphing calculator functions * Grapher, th ...
s can be used to graph functions defined on the real line, or higher-dimensional
Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces ...
. , basic calculators cost little, but scientific and graphing models tend to cost more. Computer
operating system An operating system (OS) is system software that manages computer hardware and software resources, and provides common daemon (computing), services for computer programs. Time-sharing operating systems scheduler (computing), schedule tasks for ...
s as far back as early Unix have included interactive calculator programs such as dc and hoc, and interactive
BASIC Basic or BASIC may refer to: Science and technology * BASIC, a computer programming language * Basic (chemistry), having the properties of a base * Basic access authentication, in HTTP Entertainment * Basic (film), ''Basic'' (film), a 2003 film ...
could be used to do calculations on most 1970s and 1980s home computers. Calculator functions are included in most
smartphone A smartphone is a mobile phone with advanced computing capabilities. It typically has a touchscreen interface, allowing users to access a wide range of applications and services, such as web browsing, email, and social media, as well as multi ...
s, tablets, and
personal digital assistant A personal digital assistant (PDA) is a multi-purpose mobile device which functions as a personal information manager. Following a boom in the 1990s and 2000s, PDAs were mostly displaced by the widespread adoption of more highly capable smar ...
(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%.


Design


Input

Electronic calculators contain a keyboard with buttons for digits and
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
al operations; some even contain "00" and "000" buttons to make larger or smaller
number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
s 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 combinations.


Display output

Calculators usually have
liquid-crystal display A liquid-crystal display (LCD) is a flat-panel display or other Electro-optic modulator, electronically modulated optical device that uses the light-modulating properties of liquid crystals combined with polarizers to display information. Liq ...
s (LCD) as output in place of historical
light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corre ...
(LED) displays and vacuum fluorescent displays (VFD); details are provided in the section '' Technical improvements''. Large-sized figures are often used to improve readability; while using
decimal separator FIle:Decimal separators.svg, alt=Four types of separating decimals: a) 1,234.56. b) 1.234,56. c) 1'234,56. d) ١٬٢٣٤٫٥٦., Both a comma and a full stop (or period) are generally accepted decimal separators for international use. The apost ...
(usually a point rather than a
comma The comma is a punctuation mark that appears in several variants in different languages. Some typefaces render it as a small line, slightly curved or straight, but inclined from the vertical; others give it the appearance of a miniature fille ...
) instead of or in addition to vulgar fractions. Various symbols for function commands may also be shown on the display. Fractions such as are displayed as decimal approximations, for example rounded to . Also, some fractions (such as , which is ; to 14
significant figures Significant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcom ...
) can be difficult to recognize in
decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of th ...
form; as a result, many
scientific Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
calculators are able to work in vulgar fractions or mixed numbers.


Memory

Calculators also have the ability to save numbers into
computer memory Computer memory stores information, such as data and programs, for immediate use in the computer. The term ''memory'' is often synonymous with the terms ''RAM,'' ''main memory,'' or ''primary storage.'' Archaic synonyms for main memory include ...
. Basic calculators usually store only one number at a time; more specific types are able to store many numbers represented in variables. Usually these variables are named ans or ans(0). The variables can also be used for constructing
formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwe ...
s. Some models have the ability to extend
memory Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembe ...
capacity to store more numbers; the extended memory address is termed an array index.


Power source

Power sources of calculators are batteries,
solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
s or
mains electricity Mains electricity, utility power, grid power, domestic power, wall power, household current, or, in some parts of Canada, hydro, is a general-purpose Alternating current, alternating-current (AC) electric power supply. It is the form of electri ...
(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 A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
exposure, or closing their lid). Crank-powered calculators were also common in the early computer era.


Key layout

The following keys are common to most pocket calculators. While the arrangement of the digits is standard, the positions of other keys vary from model to model; the illustration is an example. The arrangement of digits on calculator and other numeric keypads with the -- keys two rows above the -- keys is derived from calculators and
cash register A cash register, sometimes called a till or automated money handling system, is a mechanical or electronic device for registering and calculating transactions at a point of sale. It is usually attached to a Cash register#Cash drawer, drawer fo ...
s. It is notably different from the layout of telephone Touch-Tone keypads which have the -- keys on top and -- keys on the third row.


Internal workings

In general, a basic electronic calculator consists of the following components: * Power source (
mains electricity Mains electricity, utility power, grid power, domestic power, wall power, household current, or, in some parts of Canada, hydro, is a general-purpose Alternating current, alternating-current (AC) electric power supply. It is the form of electri ...
, battery and/or
solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
) * Keypad (input device) – consists of keys used to input numbers and function commands (
addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...
,
multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
,
square root In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...
, etc.) * Display panel (output device) – displays input numbers, commands and results.
Liquid-crystal display A liquid-crystal display (LCD) is a flat-panel display or other Electro-optic modulator, electronically modulated optical device that uses the light-modulating properties of liquid crystals combined with polarizers to display information. Liq ...
s (LCDs), vacuum fluorescent displays (VFDs), and
light-emitting diode A light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corre ...
(LED) displays use seven segments to represent each digit in a basic calculator. Advanced calculators may use
dot matrix A dot matrix is a 2-dimensional patterned Array data structure, array, used to represent characters, symbols and images. Most types of modern technology use dot matrices for display of information, including mobile phones, televisions, and pri ...
displays. ** A printing calculator, in addition to a display panel, has a printing unit that prints results in ink onto a roll of paper, using a printing mechanism. * Processor chip (
microprocessor A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, a ...
or
central processing unit A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions ...
).
Clock rate Clock rate or clock speed in computing typically refers to the frequency at which the clock generator of a processor can generate pulses used to synchronize the operations of its components. It is used as an indicator of the processor's s ...
of a processor chip refers to the frequency at which the
central processing unit A central processing unit (CPU), also called a central processor, main processor, or just processor, is the primary Processor (computing), processor in a given computer. Its electronic circuitry executes Instruction (computing), instructions ...
(CPU) is running. It is used as an indicator of the processor's speed, and is measured in ''clock cycles per second'' or hertz (Hz). For basic calculators, the speed can vary from a few hundred
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in ter ...
to the
kilohertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base ...
range.


Example

A basic explanation as to how calculations are performed in a simple four-function calculator: To perform the calculation , one presses keys in the following sequence on most calculators:     . :* When   is entered, it is picked up by the scanning unit; the number 25 is encoded and sent to the X register; :* Next, when the key is pressed, the "
addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...
" instruction is also encoded and sent to the flag or the status register; :* The second number is encoded and sent to the X register. This "pushes" (shifts) the first number out into the Y register; :* When the key is pressed, a "message" (signal) from the flag or status register tells the permanent or non-volatile memory that the operation to be done is "
addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...
"; :* The numbers in the X and Y registers are then loaded into the ALU and the calculation is carried out following instructions from the permanent or non-volatile memory; :* The answer, 34 is sent (shifted) back to the X register. From there, it is converted by the binary decoder unit into a decimal number (usually binary-coded decimal), and then shown on the display panel. Other functions are usually performed using repeated additions or subtractions.


Numeric representation

Most pocket calculators do all their calculations in binary-coded decimal (BCD) rather than binary. BCD is common in electronic systems where a numeric value is to be displayed, especially in systems consisting solely of digital logic, and not containing a microprocessor. By employing BCD, the manipulation of numerical data for display can be greatly simplified by treating each digit as a separate single sub-circuit. This matches much more closely the physical reality of display hardware—a designer might choose to use a series of separate identical seven-segment displays to build a metering circuit, for example. If the numeric quantity were stored and manipulated as pure binary, interfacing to such a display would require complex circuitry. Therefore, in cases where the calculations are relatively simple, working throughout with BCD can lead to a simpler overall system than converting to and from binary. (For example, CDs keep the track number in BCD, limiting them to 99 tracks.) 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 In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...
), software
algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...
s 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 chip, with acceptable calculation time.


History


Precursors to the electronic calculator

The first known tools used to aid arithmetic calculations were: bones (used to tally items), pebbles, and counting boards, and the
abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. A ...
, known to have been used by
Sumer Sumer () is the earliest known civilization, located in the historical region of southern Mesopotamia (now south-central Iraq), emerging during the Chalcolithic and Early Bronze Age, early Bronze Ages between the sixth and fifth millennium BC. ...
ians and
Egyptians Egyptians (, ; , ; ) are an ethnic group native to the Nile, Nile Valley in Egypt. Egyptian identity is closely tied to Geography of Egypt, geography. The population is concentrated in the Nile Valley, a small strip of cultivable land stretchi ...
before 2000 BC. Except for the Antikythera mechanism (an "out of the time"
astronomical Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include ...
device), development of computing tools arrived near the start of the 17th century: the geometric-military compass (by
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...
),
logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
s and Napier bones (by Napier), and the slide rule (by Edmund Gunter). The
Renaissance The Renaissance ( , ) is a Periodization, period of history and a European cultural movement covering the 15th and 16th centuries. It marked the transition from the Middle Ages to modernity and was characterized by an effort to revive and sur ...
saw the invention of the mechanical calculator by Wilhelm Schickard in 1623, and later by
Blaise Pascal Blaise Pascal (19June 162319August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. Pascal was a child prodigy who was educated by his father, a tax collector in Rouen. His earliest ...
in 1642. A device that was at times somewhat over-promoted as being able to perform all four
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
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 Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in ad ...
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. The 18th century saw the arrival of some notable improvements, first by 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 The Industrial Revolution, sometimes divided into the First Industrial Revolution and Second Industrial Revolution, was a transitional period of the global economy toward more widespread, efficient and stable manufacturing processes, succee ...
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 United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
. 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 Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
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.


Development of electronic calculators

The first
mainframe computer A mainframe computer, informally called a mainframe or big iron, is a computer used primarily by large organizations for critical applications like bulk data processing for tasks such as censuses, industry and consumer statistics, enterprise ...
s, initially using
vacuum tube A vacuum tube, electron tube, thermionic valve (British usage), or tube (North America) is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. It ...
s and later
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s in the logic circuits, appeared in the 1940s and 1950s. Electronic circuits developed for computers also had application to electronic calculators. The Casio Computer Company, in
Japan Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...
, 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
vacuum tube A vacuum tube, electron tube, thermionic valve (British usage), or tube (North America) is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. It ...
s, 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. 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 A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a phosphorescent screen. The images may represent electrical waveforms on an oscilloscope, a ...
(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 circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
s in place of individual
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s, 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 (Smith-Corona-Marchant),
Sony is a Japanese multinational conglomerate (company), conglomerate headquartered at Sony City in Minato, Tokyo, Japan. The Sony Group encompasses various businesses, including Sony Corporation (electronics), Sony Semiconductor Solutions (i ...
,
Toshiba is a Japanese multinational electronics company headquartered in Minato, Tokyo. Its diversified products and services include power, industrial and social infrastructure systems, elevators and escalators, electronic components, semiconductors ...
, and
Wang Wang may refer to: Names * Wang (surname) Wang () is the pinyin romanization of Chinese, romanization of the common Chinese surname (''Wáng''). It has a mixture of various origin with uncertain lineage of family history, however it is c ...
. 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. Bulgaria's ELKA 6521, introduced in 1965, was developed by the Central Institute for Calculation Technologies and built at the Elektronika factory in
Sofia Sofia is the Capital city, capital and List of cities and towns in Bulgaria, largest city of Bulgaria. It is situated in the Sofia Valley at the foot of the Vitosha mountain, in the western part of the country. The city is built west of the Is ...
. The name derives from ''ELektronen KAlkulator'', and it weighed around . It is the first calculator in the world which includes the
square root In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...
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.


Programmable calculators

The first desktop ''programmable calculators'' were produced in the mid-1960s. They included the Mathatronics Mathatron (1964) and the Olivetti Programma 101 (late 1965) which were solid-state, desktop, printing, floating point, algebraic entry, programmable, stored-program electronic calculators. Both could be programmed by the end user and print out their results. The Programma 101 saw much wider distribution and had the added feature of offline storage of programs via magnetic cards. Another early programmable desktop calculator (and maybe the first Japanese one) was the Casio (AL-1000) produced in 1967. It featured a nixie tubes 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 A branch, jump or transfer is an instruction in a computer program that can cause a computer to begin executing a different instruction sequence and thus deviate from its default behavior of executing instructions in order. ''Branch'' (or ''br ...
(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.


1970s to mid-1980s

The electronic calculators of the mid-1960s were large and heavy desktop machines due to their use of hundreds of
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s 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 circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
s (chips) and calculator electronics was one of the leading edges of
semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
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 renamed
Sharp Corporation is a Japanese electronics company. It is headquartered in Sakai, Osaka, and was founded by Tokuji Hayakawa in 1912 in Honjo, Tokyo, and established as the Hayakawa Metal Works Institute in Abeno-ku, Osaka, in 1924. Since 2016, it is majority o ...
) with North-American Rockwell Microelectronics (later renamed Rockwell International), Busicom with Mostek and
Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, and Delaware General Corporation Law, incorporated in Delaware. Intel designs, manufactures, and sells computer compo ...
, and General Instrument with
Sanyo is a former Japanese electronics manufacturer founded in 1947 by Toshio Iue, the brother-in-law of Kōnosuke Matsushita, the founder of Matsushita Electric Industrial, now known as Panasonic. Iue left Matsushita Electric to start his own bu ...
.


Pocket calculators

Released in 1947, the first pocket calculator which could perform the four basic arithmetic functions with digital precision was the Curta, a mechanical device operated by a crank, bearing “an uncanny resemblance to a pepper grinder”. The readout was digital with eleven digits of precision. For comparison, the contemporaneous ten inch slide rule used analog calculation to approximate answers to only four digits of precision. The Curta remained the finest pocket calculator available for a quarter of a century. 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. 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 is a former Japanese electronics manufacturer founded in 1947 by Toshio Iue, the brother-in-law of Kōnosuke Matsushita, the founder of Matsushita Electric Industrial, now known as Panasonic. Iue left Matsushita Electric to start his own bu ...
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, 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 Croatia, officially the Republic of Croatia, is a country in Central Europe, Central and Southeast Europe, on the coast of the Adriatic Sea. It borders Slovenia to the northwest, Hungary to the northeast, Serbia to the east, Bosnia and Herze ...
(former
Yugoslavia , common_name = Yugoslavia , life_span = 1918–19921941–1945: World War II in Yugoslavia#Axis invasion and dismemberment of Yugoslavia, Axis occupation , p1 = Kingdom of SerbiaSerbia , flag_p ...
) 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 The Sinclair Executive was the world's first "slimline" pocket calculator, and the first to be produced by Clive Sinclair's company Sinclair Radionics. Introduced in 1972, the calculator was produced in at least two versions with different ke ...
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 The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
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).


Scientific pocket calculators

Meanwhile,
Hewlett-Packard The Hewlett-Packard Company, commonly shortened to Hewlett-Packard ( ) or HP, was an American multinational information technology company. It was founded by Bill Hewlett and David Packard in 1939 in a one-car garage in Palo Alto, California ...
(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, uses reverse Polish notation (RPN), also called postfix notation. A calculation like "8 plus 5" is, using RPN, performed by pressing , , , and ; instead of the algebraic infix notation: , , , . It had 35 buttons and was based on Mostek Mk6020 chip. 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 Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to as scientif ...
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. File:Calculator Adler 81S.jpg, Adler 81S pocket calculator with vacuum fluorescent display (VFD) from the mid-1970s. File:Casio cm602.jpg, The Casio CM-602 Mini electronic calculator provided basic functions in the 1970s. File:SinclairExecutive-01.jpg, The 1972
Sinclair Executive The Sinclair Executive was the world's first "slimline" pocket calculator, and the first to be produced by Clive Sinclair's company Sinclair Radionics. Introduced in 1972, the calculator was produced in at least two versions with different ke ...
pocket calculator. File:Hewlett-Packard Model 35 Calculator with case - DPLA - a04795d0729a4900d2f641331ecba723 (page 1).jpg, The HP-35, the world's first scientific pocket calculator by Hewlett Packard (1972). File:Canon Pocketronic.jpg, Canon Pocketronic calculator prints output using paper tape (1971).


Programmable pocket calculators

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 Alphanumericals or alphanumeric characters are any collection of number characters and letters in a certain language. Sometimes such characters may be mistaken one for the other. Merriam-Webster suggests that the term "alphanumeric" may often ...
'', programmable, ''expandable'' calculator, the HP-41C. It could be expanded with
random-access memory Random-access memory (RAM; ) is a form of Computer memory, electronic computer memory that can be read and changed in any order, typically used to store working Data (computing), data and machine code. A random-access memory device allows ...
(RAM, for memory) and read-only memory (ROM, for software) modules, and peripherals like bar code readers, microcassette and
floppy disk A floppy disk or floppy diskette (casually referred to as a floppy, a diskette, or a disk) is a type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined with a ...
drives, paper-roll thermal printers, and miscellaneous communication interfaces ( RS-232, HP-IL, HP-IB). The first Soviet pocket battery-powered programmable calculator, Elektronika '' B3-21'', was developed by the end of 1976 and released at the start of 1977. 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 abilities (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 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.


Technical improvements

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 display A liquid-crystal display (LCD) is a flat-panel display or other Electro-optic modulator, electronically modulated optical device that uses the light-modulating properties of liquid crystals combined with polarizers to display information. Liq ...
s (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. 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'' (a.k.a. ''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 ''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 Ultraviolet radiation, also known as simply UV, is electromagnetic radiation of wavelengths of 10–400 nanometers, shorter than that of visible light, but longer than X-rays. UV radiation is present in sunlight and constitutes about 10% of ...
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 circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
s (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
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s 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
solar cell A solar cell, also known as a photovoltaic cell (PV cell), is an electronic device that converts the energy of light directly into electricity by means of the photovoltaic effect.
s as the power source, realised around 1978 by calculators such as the Royal ''Solar 1'', Sharp ''EL-8026'', and Teal ''Photon''. File:CasioFX20-inside.jpg, The interior of a Casio fx-20 scientific calculator from the mid-1970s, using a VFD. The processor integrated circuit (IC) is made by NEC (marked μPD978C). Discrete electronic components like
capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
s and resistors and the IC are mounted on a
printed circuit board A printed circuit board (PCB), also called printed wiring board (PWB), is a Lamination, laminated sandwich structure of electrical conduction, conductive and Insulator (electricity), insulating layers, each with a pattern of traces, planes ...
(PCB). This calculator uses a battery pack as a power source. File:Sharp el-323 ic 1ae.jpg, The processor chip (integrated circuit package) inside a 1980s Sharp pocket calculator, marked SC6762 1•H. An LCD is directly under the chip. This was a PCB-less design. No discrete components are used. The battery compartment at the top can hold two button cells. File:Casio fx-992VB interior both aa1.JPG, Inside a Casio scientific calculator from the mid-1990s, showing the processor chip (small square; top-middle; left), keypad contacts, right (with matching contacts on the left), the back of the LCD (top; marked 4L102E), battery compartment, and other components. The solar cell assembly is under the chip. File:Citizen se-733 int 1ac.jpg, The interior of a newer () pocket calculator. It uses a button battery in combination with a solar cell. The processor is a "Chip on Board" type, covered with dark epoxy.


Mass-market phase

At the start of the 1970s, hand-held electronic calculators were very costly, at 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 costly to produce, and production runs that were too small to exploit
economies of scale In microeconomics, economies of scale are the cost advantages that enterprises obtain due to their scale of operation, and are typically measured by the amount of Productivity, output produced per unit of cost (production cost). A decrease in ...
. Many firms saw that there were good profits to be made in the calculator business with the margin on such high prices. However, the cost of calculators fell as components and their production methods improved, and the effect of economies of scale was felt. 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.


Mid-1980s to present

The first calculator capable of symbolic computing was the HP-28C, released in 1987. It could, for example, solve quadratic equations symbolically. The first
graphing calculator Graphing Calculator may refer to: * Graphing calculators, calculators that are able to display and/or analyze mathematical function graphs * NuCalc, a computer software program able to perform many graphing calculator functions * Grapher, th ...
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 A word processor (WP) is a device or computer program that provides for input, editing, formatting, and output of text, often with some additional features. Word processor (electronic device), Early word processors were stand-alone devices dedicate ...
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.


Use in education

In most countries,
student A student is a person enrolled in a school or other educational institution, or more generally, a person who takes a special interest in a subject. In the United Kingdom and most The Commonwealth, commonwealth countries, a "student" attends ...
s use calculators for schoolwork. There was some initial resistance to the idea out of fear that basic or
elementary arithmetic Elementary arithmetic is a branch of mathematics involving addition, subtraction, multiplication, and Division (mathematics), division. Due to its low level of abstraction, broad range of application, and position as the foundation of all mathema ...
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 methods 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 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
Curriculum In education, a curriculum (; : curriculums or curricula ) is the totality of student experiences that occur in an educational process. The term often refers specifically to a planned sequence of instruction, or to a view of the student's experi ...
. In the United States, many math educators and boards of education have enthusiastically endorsed the
National Council of Teachers of Mathematics Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds an ...
(NCTM) standards and actively promoted the use of classroom calculators from kindergarten through high school. 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


Personal computers

Personal computers often come with a calculator utility program that emulates the appearance and functions of a calculator, using the
graphical user interface A graphical user interface, or GUI, is a form of user interface that allows user (computing), users to human–computer interaction, interact with electronic devices through Graphics, graphical icon (computing), icons and visual indicators such ...
to portray a calculator. Examples include the Windows Calculator, Apple's Calculator, and KDE's KCalc. Most personal data assistants (PDAs) and
smartphone A smartphone is a mobile phone with advanced computing capabilities. It typically has a touchscreen interface, allowing users to access a wide range of applications and services, such as web browsing, email, and social media, as well as multi ...
s also have such a feature.


Calculators compared to computers

The fundamental difference between a calculator and
computer A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
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 Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...
,
multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
, and
logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
s) built in. The distinction is not clear-cut: some devices classed as programmable calculators have programming functions, sometimes with support for
programming language A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...
s (such as RPL or TI-BASIC). 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 chip 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.


See also

* Calculator spelling * Comparison of HP graphing calculators *
Comparison of Texas Instruments graphing calculators A graphing calculator is a class of hand-held calculator that is capable of plotting graphs and solving complex functions. There are several companies that manufacture models of graphing calculators. Texas Instruments is a major manufacturer. Th ...
* Formula calculator * HP calculators *
History of computing hardware The history of computing hardware spans the developments from early devices used for simple calculations to today's complex computers, encompassing advancements in both analog and digital technology. The first aids to computation were purely mec ...
* Scientific calculator * Software calculator * Solar-powered calculator * Photomath


Notes


References


Sources

* * * * * *


Further reading

* – ''Complex computer'' – G. R. Stibitz, Bell Laboratories, 1954 (filed 1941, refiled 1944), electromechanical (relay) device that could calculate complex numbers, record, and print results. * – ''Miniature electronic calculator'' – J. S. Kilby, Texas Instruments, 1974 (originally filed 1967), handheld () battery operated electronic device with thermal printer * – ''Floating Point Calculator With RAM Shift Register'' – 1977 (originally filed GB March 1971, US July 1971), very early single chip calculator claim. * – ''Extended Numerical Keyboard with Structured Data-Entry Capability'' – J. H. Redin, 1997 (originally filed 1996), Usage of Verbal Numerals as a way to enter a number.
European Patent Office Database
– Many patents about mechanical calculators are in classifications G06C15/04, G06C15/06, G06G3/02, G06G3/04 * ''Collectors Guide to Pocket Calculators''. by Guy Ball and Bruce Flamm, 1997, – includes an extensive history of early pocket calculators and highlights over 1,500 different models from the early 1970s. Book still in print. * (64 pages)


External links


30th Anniversary of the Calculator
– From Sharp's web presentation of its history; including a picture of the CS-10A desktop calculator
The Museum of HP calculators

Microprocessor and single chip calculator history; foundations in Glenrothes, Scotland


– A thorough analysis of the HP-35 firmware including the Cordic algorithms and the bugs in the early ROM
Bell Punch Company and the development of the Anita calculator
– The story of the first electronic desktop calculator
Dentaku-Museum
– Shows mainly Japanese calculators but also others. {{Authority control American inventions Mathematical tools Office equipment 20th-century inventions Electronic calculators