Citizendia

For other uses, see Calculator (disambiguation).

A calculator is an electronic device for performing mathematical calculations, distinguished from a computer by a limited problem solving ability and an interface optimized for interactive calculation rather than programming. Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical A computer is a Machine that manipulates data according to a list of instructions. Calculators can be hardware or software, and mechanical or electronic, and are often built into devices such as PDAs or mobile phones.

A basic calculator
A basic calculator
An old mechanical calculator.
An old mechanical calculator.
A scientific calculator.
A scientific calculator.

Modern electronic calculators are generally small, digital, (often pocket-sized) and usually inexpensive. In addition to general purpose calculators, there are those designed for specific markets; for example, there are scientific calculators which focus on advanced math like trigonometry and statistics. A scientific calculator is a type of electronic Calculator, usually but not always handheld designed to calculate problems in science (especially Physics Circle-trig6svg|300px|thumb|right|All of the Trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.

Contents

Overview

In the past, mechanical clerical aids such as abaci, comptometers, Napier's bones, books of mathematical tables, slide rules, or mechanical adding machines were used for numeric work. An abacus, also called a counting frame, is a calculating tool used primarily by Asians for performing arithmetic processes A Comptometer is a type of mechanical (or electro-mechanical Adding machine. Napier's bones is an Abacus created by John Napier for Calculation of products and quotients of numbers that was based on Arab mathematics and Before Calculators were cheap and plentiful people would use mathematical tables &mdashlists of numbers showing the results of calculation with varying arguments&mdash to simplify The slide rule, also known as a slipstick, is a mechanical Analog computer. See Adding machine (disambiguation for other uses of this term This semi-manual process of calculation was tedious and error-prone.

Modern calculators are electrically powered (usually by battery and/or solar cell) and vary from cheap, give-away, credit-card sized models to sturdy adding machine-like models with built-in printers. A solar cell or photovoltaic cell is a device that converts Solar energy into Electricity by the photovoltaic effect. They first became popular in the late 1960s as decreasing size and cost of electronics made possible devices for calculations, avoiding the use of scarce and expensive computer resources. By the 1980s, calculator prices had reduced to a point where a basic calculator was affordable to most. By the 1990s they had become common in math classes in schools, with the idea that students could be freed from basic calculations and focus on the concepts.

Computer operating systems as far back as early Unix have included interactive calculator programs such as dc and hoc, and calculator functions are included in almost all PDA-type devices (save a few dedicated address book and dictionary devices). Ancient UNIX is a term coined by Santa Cruz Operation (now SCO) to describe early releases of the Unix code base released prior to Unix System III dc is a reverse-polish desk calculator which supports unlimited precision arithmetics. hoc, an acronym for High Order Calculator, is an interpreted Programming language that was used in the 1984 book The Unix Programming Environment

Electronic calculators

In the past, some calculators were as large as today's computers. A computer is a Machine that manipulates data according to a list of instructions. The first mechanical calculators were mechanical desktop devices which were replaced by electromechanical desktop calculators, and then by electronic devices using first thermionic valves, then transistors, then hard-wired integrated circuit logic. The history of computer hardware encompasses the hardware, its architecture, and its impact on software. This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside By the mid-1970s, pocket-sized calculators based on ICs were routinely available, often at prices less than $100, and by the early 1980s the LED displays of 1970s units had been replaced by power-saving liquid crystal displays. Modern electronic calculators range in size from keychain-sized units only a couple of centimeters long all the way up to desktop calculators the size of a textbook, and in complexity from very basic up to graphing calculators capable of video display and sometimes extensive general-purpose programming capability. A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld Calculators that are capable of

Basic configuration

A simple modern calculator (usually known colloquially as a "four function" calculator, even with the presence of a square root button) might consist of the following parts:

Since the late-1980s, calculators have been installed in other small devices, such as mobile phones, pagers or wrist watches. A pager (sometimes called a beeper) is a simple personal Telecommunications device for short messages

Scientific and financial calculators

A TI-89 calculator can produce 3D wire frame graphs such as this graph of z(x,y) = x3y − y3x.
A TI-89 calculator can produce 3D wire frame graphs such as this graph of z(x,y) = x3y − y3x. The TI-89 and the TI-89 Titanium are Graphing calculators developed by Texas Instruments.

More complex scientific calculators support trigonometric, statistical and other mathematical functions. A scientific calculator is a type of electronic Calculator, usually but not always handheld designed to calculate problems in science (especially Physics Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. In Mathematics, several functions or groups of functions are important enough to deserve their own names The most advanced modern calculators can display graphics, and include features of computer algebra systems. A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld Calculators that are capable of A computer algebra system ( CAS) is a software program that facilitates Symbolic mathematics. They are also programmable; calculator applications include algebraic equation solvers, financial models and even games. Most calculators of this type can print numbers up to ten digits or decimal places in full on the screen. Scientific notation is used to notate numbers up to a limit chosen by the calculator designer, such as 9. Scientific notation, also sometimes known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be 999999999×1099. If a larger number or a mathematical expression yielding a larger number than this is entered (a common example comes from typing "100!", read as "100 factorial") then the calculator might simply display "Error". Definition The factorial function is formally defined by n!=\prod_{k=1}^n k

"Error" might also be displayed if a function or an operation is undefined mathematically; for example, division by zero or even roots of negative numbers (most scientific calculators do not allow complex numbers, though a few do have a special function for working with them). In In Mathematics, an n th root of a Number a is a number b such that bn = a. Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted Some, but not most, calculators do distinguish between these two types of "error", though when they do, it is not always easy for the user to understand because they are often given as "Error 1" or "Error 2".

Financial calculators are similar in overall design to scientific calculators, but specialize in time value of money calculations and are used in the accounting and real estate professions. The time value of money is based on the premise that an Investor prefers to receive a payment of a fixed amount of money today rather than an equal amount in the future Accountancy or accounting is the measurement statement or provision of assurance about financial information primarily used by Lenders managers, Real estate is a legal term (in some jurisdictions notably in the USA, United Kingdom

Only a few companies make professional engineering and finance calculators. They include Casio, Sharp, Hewlett-Packard (HP), Victor and Texas Instruments (TI), as well as Chinese manufacturer Karce, who provides OEM calculators for the private label market. ( is a Japanese electronic devices manufacturing company founded in 1946 with its Headquarters in Tokyo. () is a Japanese Electronics manufacturer founded in 1912 It takes its name from one of its founder's first inventions the Ever-Sharp Mechanical pencil, which Victor Technology LLC (also known as Victor Calculator is a supplier of printing Calculators scientific calculators financial calculators basic calculators and desktop accessories Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA Private label products or services are typically those manufactured or provided by one company for offer under another company's Brand. Such calculators are examples of embedded systems. An embedded system is a special-purpose Computer system designed to perform one or a few dedicated functions often with Real-time computing constraints

Use in education

In most countries, students use calculators for schoolwork. The word student is etymologically derived through Middle English from the Latin second-type conjugation Verb "studēre" There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. Elementary arithmetic is the most basic kind of Mathematics: it concerns the operations of Addition, Subtraction, Multiplication, and division There remains disagreement about the importance of the ability to perform calculations by hand or "in the head", with some curricula restricting calculator use until a certain level of proficiency has been obtained, while others concentrate more on teaching estimation techniques and problem-solving. Estimation is the calculated Approximation of a result which is usable even if Input data may be incomplete or uncertain. Research suggests that inadequate guidance in the use of calculating tools can restrict the kind of mathematical thinking that students engage in. [1] 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.

There are other concerns - for example, that a pupil could use the calculator in the wrong fashion but believe the answer because that was the result given. Teachers try to combat this by encouraging the student to make an estimate of the result manually and ensuring it roughly agrees with the calculated result. Also, it is possible for a child to type in −1 × −1 and obtain the correct answer '1' without realizing the principle involved. In this sense, the calculator becomes a crutch rather than a learning tool, and it can slow down students in exam conditions as they check even the most trivial result on a calculator. Crutches are Medical Tools used when a patient is injured usually anywhere below the waist

Other concerns on usage

Errors are not restricted to school pupils. Any user could carelessly rely on the calculator's output without double-checking the magnitude of the result — i. An order of magnitude is the class of scale or magnitude of any amount where each class contains values of a fixed ratio to the class preceding it e. , where the decimal point is positioned. In a positional Numeral system, the decimal separator is a Symbol used to mark the boundary between the integral and the fractional This problem was all but nonexistent in the era of slide rules and pencil-and-paper calculations, when the task of establishing the magnitudes of results had to be done by the user. The slide rule, also known as a slipstick, is a mechanical Analog computer. In addition, algorithmic flaws and rounding techniques can sometimes lead to minor precision errors. [2]

Some fractions such as 2/3 are awkward to display on a calculator display as they are usually rounded to 0. 66666667. Also, some fractions such as 1/7 which is 0. 14285714285714 can be difficult to recognize in decimal form; as a result, many scientific calculators are able to work in vulgar fractions and/or mixed numbers. In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object

Calculating vs. computing

The fundamental difference between calculators and computers is that computers can be programmed to perform different tasks while calculators are pre-designed with specific functions built in, for example addition, multiplication, logarithms, etc. While computers may be used to handle numbers, they can also manipulate words, images or sounds and other tasks they have been programmed to handle. However, the distinction between the two is quite blurred; some calculators have built-in programming functions, ranging from simple formula entry to full programming languages such as RPL or TI-BASIC. TI-BASIC is the unofficial name of a BASIC -like language built into Texas Instruments (TI 's Graphing calculators TI-89 series TI-89 TI-89 Titanium| Graphing calculators in particular can, along with PDAs, be viewed as direct descendants of the 1980s pocket computers, essentially calculators with full keyboards and programming capability. A pocket computer is a small Calculator -sized Handheld computer programmable in BASIC.

The market for calculators is extremely price-sensitive, to an even greater extent than the personal computer market; typically the user desires the least expensive model having a specific feature set, but does not care much about speed (since speed is constrained by how fast the user can press the buttons). Thus designers of calculators strive to minimize the number of logic elements on the chip, not the number of clock cycles needed to do a computation.

For instance, instead of a hardware multiplier, a calculator might implement floating point mathematics with code in ROM, and compute trigonometric functions with the CORDIC algorithm because CORDIC does not require hardware floating-point. In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number. CORDIC (digit-by-digit method Volder's algorithm (for CO ordinate R otation DI gital C omputer is a simple and efficient Algorithm Bit serial logic designs are more common in calculators whereas bit parallel designs dominate general-purpose computers, because a bit serial design minimizes the chip complexity, but takes many more clock cycles. In Telecommunications serial transmission is the sequential transmission of Signal elements of a group representing a character or other entity In Telecommunication, parallel transmission is The simultaneous transmission of the signal elements of a character or other (Again, the line blurs with high-end calculators, which use processor chips associated with computer and embedded systems design, particularly the Z80, MC68000, and ARM architectures, as well as some custom designs specifically made for the calculator market. The Zilog Z80 is an 8-bit Microprocessor designed and sold by Zilog from July 1976 onwards The Motorola 68000 is a 16/32-bit CISC Microprocessor core designed and marketed by Freescale Semiconductor (formerly Motorola Semiconductor The ARM architecture (previously the Advanced RISC Machine, and prior to that Acorn RISC Machine) is a 32-bit RISC processor architecture )

Personal computers and personal digital assistants can perform general calculations in a variety of ways:

History

Origin: the abacus

Chinese abacus.
Chinese abacus.
Main article: Abacus

The first calculators were abaci, and were often constructed as a wooden frame with beads sliding on wires. An abacus, also called a counting frame, is a calculating tool used primarily by Asians for performing arithmetic processes Abacuses were in use centuries before the adoption of the written Arabic numerals system and are still used by some merchants, fishermen and clerks in China and elsewhere.

The 17th century

William Oughtred invents the slide rule in 1622 and is revealed by his student Richard Delamain in 1630. William Oughtred ( March 5, 1575 – June 30, 1660) was an English Mathematician. [3] Wilhelm Schickard built the first automatic calculator called the "Calculating Clock" in 1623. Wilhelm Schickard ( April 22 1592 &ndash October 24 1635) was a German Polymath who built one of the first Calculating machines [4]Some 20 years later, in 1643, French philosopher Blaise Pascal invented the calculation device later known as the Pascaline, which was used for taxes in France until 1799. Blaise Pascal (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher The German philosopher G. W. v. Leibniz also produced a calculating machine. The Calculus Ratiocinator is a theoretical universal logical calculation framework a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently

The 19th century

The London Science Museum's working difference engine, built from Charles Babbage's design.
The London Science Museum's working difference engine, built from Charles Babbage's design.

1900s to 1960s

Mechanical calculators reach their zenith

Mechanical calculator from 1914
Mechanical calculator from 1914

The first half of the 20th century saw the gradual development of the mechanical calculator mechanism.

The Dalton adding-listing machine introduced in 1902 was the first of its type to use only ten keys, and became the first of many different models of "10-key add-listers" manufactured by many companies.

An Addiator could be used for addition and subtraction.
An Addiator could be used for addition and subtraction. The Addiator was a mechanical add/subtract Calculator, made by Addiator Gesellschaft, Berlin.

In 1948 the miniature Curta calculator, that was held in one hand for operation, was introduced after being developed by Curt Herzstark in a Nazi concentration camp. The Curta was a small hand-cranked mechanical Calculator introduced in 1948 Curt Herzstark was born in July 26, 1902 in Vienna, and died October 27, 1988 in Nendeln, Liechtenstein. This was an extreme development of the stepped-gear calculating mechanism.

From the early 1900s through the 1960s, mechanical calculators dominated the desktop computing market (see History of computing hardware). The history of computer hardware encompasses the hardware, its architecture, and its impact on software. Major suppliers in the USA included Friden, Monroe, and SCM/Marchant. Friden Calculating Machine Company (Friden Inc was an American manufacturer of typewriters and electronic calculators The Monroe Calculator Company was a leading maker of Adding machines and Calculators founded in 1912 by Jay R (Some comments about European calculators follow below. ) These devices were motor-driven, and had movable carriages where results of calculations were displayed by dials. Nearly all keyboards were full — each digit that could be entered had its own column of nine keys, 1. . 9, plus a column-clear key, permitting entry of several digits at once. (See the illustration of a 1914 mechanical calculator. ) One could call this parallel entry, by way of contrast with ten-key serial entry that was commonplace in mechanical adding machines, and is now universal in electronic calculators. (Nearly all Friden calculators had a ten-key auxiliary keyboard for entering the multiplier when doing multiplication. ) Full keyboards generally had ten columns, although some lower-cost machines had eight. Most machines made by the three companies mentioned did not print their results, although other companies, such as Olivetti, did make printing calculators.

In these machines, Addition and subtraction were performed in a single operation, as on a conventional adding machine, but multiplication and division were accomplished by repeated mechanical additions and subtractions. Addition is the mathematical process of putting things together Subtraction is one of the four basic Arithmetic operations it is the inverse of Addition, meaning that if we start with any number and add any number and then subtract In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. Friden made a calculator that also provided square roots, basically by doing division, but with added mechanism that automatically incremented the number in the keyboard in a systematic fashion. Friden Calculating Machine Company (Friden Inc was an American manufacturer of typewriters and electronic calculators In Mathematics, a square root of a number x is a number r such that r 2 = x, or in words a number r whose Friden and Marchant (Model SKA) made calculators with square root. Handheld mechanical calculators such as the 1948 Curta continued to be used until they were displaced by electronic calculators in the 1970s. The Curta was a small hand-cranked mechanical Calculator introduced in 1948

Facit NTK (1954)
Facit NTK (1954)
Triumphator CRN1 (1958)
Triumphator CRN1 (1958)
Walther WSR160 (1960)
Walther WSR160 (1960)
Olivetti Divisumma 24 (1964)
Olivetti Divisumma 24 (1964)

The Facit, Triumphator, and Walther calculators are typical European machines. Similar-looking machines included the Odhner and Brunsviga. Although these are operated by handcranks, there were motor-driven versions. Most machines that look like these use the Odhner mechanism, or variations of it. The Olivetti Divisumma did all four basic operations of arithmetic, and has a printer. Full-keyboard machines, including motor-driven ones, were also used in Europe for many decades. Some European machines had as many as 20 columns in their full keyboards.

The development of electronic calculators

The first main-frame computers, using firstly vacuum tubes and later transistors in the logic circuits, appeared in the late 1940s and 1950s. Mainframes (often colloquially referred to as Big Iron) are Computers used mainly by large organizations for critical applications typically bulk data This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals This technology was to provide a stepping stone to the development of electronic calculators.

In 1954, IBM, in the U.S.A., demonstrated a large all-transistor calculator and, in 1957, the company released the first commercial all-transistor calculator, the IBM 608, though it was housed in several cabinets and cost about $80,000[1]. International Business Machines Corporation abbreviated IBM and nicknamed "Big Blue", is a multinational Computer Technology The United States of America —commonly referred to as the In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals

The Casio Computer Co., in Japan, released the Model 14-A calculator in 1957, which was the world's first all-electric "compact" calculator. ( is a Japanese electronic devices manufacturing company founded in 1946 with its Headquarters in Tokyo. For a topic outline on this subject see List of basic Japan topics. It did not use electronic logic but was based on relay technology, and was built into a desk. A relay is an electrical Switch that opens and closes under the control of another Electrical circuit.

In October 1961, the world's first all-electronic desktop calculator, the Bell Punch/Sumlock Comptometer ANITA (A New Inspiration To Arithmetic/Accounting) was announced. The ANITA Mark VII and ANITA Mark VIII Calculators were launched simultaneously in late 1961 as the world's first all- electronic desktop [5][6] This British designed-and-built machine used vacuum tubes, cold-cathode tubes and Dekatrons in its circuits, with 12 cold-cathode "Nixie"-type tubes for its display. This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. In Electronics, a Dekatron (or Decatron, or generically three-phase gas counting tube or glow-transfer counting tube or cold cathode A nixie tube is an electronic device for displaying numerals or other information. 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 version. 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. A Comptometer is a type of mechanical (or electro-mechanical Adding machine. () is a Japanese Electronics manufacturer founded in 1912 It takes its name from one of its founder's first inventions the Ever-Sharp Mechanical pencil, which 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. A Comptometer is a type of mechanical (or electro-mechanical Adding machine. They employed the young graduate Norbert Kitz, who had worked on the early British Pilot ACE computer project, to lead the development. The Pilot ACE was one of the first Computers built in the United Kingdom, at the National Physical Laboratory (NPL in the early 1950s The ANITA sold well since it was the only electronic desktop calculator available, and was silent and quick. The ANITA Mark VII and ANITA Mark VIII Calculators were launched simultaneously in late 1961 as the world's first all- electronic desktop

The tube technology of the ANITA was superseded in June 1963, by the U. The ANITA Mark VII and ANITA Mark VIII Calculators were launched simultaneously in late 1961 as the world's first all- electronic desktop S. manufactured Friden EC-130, which had an all-transistor design, 13-digit capacity on a 5-inch CRT, and introduced reverse Polish notation (RPN) to the calculator market for a price of $2200, which was about triple the cost of an electromechanical calculator of the time. The Lockheed EC-130 Commando Solo is a modified C-130 Hercules used to conduct psychological operations (PSYOP and civil affairs broadcast missions The cathode ray tube (CRT is a Vacuum tube containing an Electron gun (a source of electrons and a Fluorescent screen with internal or Reverse Polish notation (or just RPN) by analogy with the related Polish notation, a prefix notation introduced in 1920 by the Polish mathematician Like Bell Punch, Friden was a manufacturer of mechanical calculators that had decided that the future lay in electronics. In 1964 more all-transistor elctronic calculators were introduced: Sharp introduced the CS-10A, which weighed 25 kg (55 lb) and cost 500,000 yen (~US$2500), and Industria Macchine Elettroniche of Italy introduced the IME 84, to which several extra keyboard and display units could be connected so that several people could make use of it (but apparently not at the same time). () is a Japanese Electronics manufacturer founded in 1912 It takes its name from one of its founder's first inventions the Ever-Sharp Mechanical pencil, which

There followed a series of electronic calculator models from these and other manufacturers, including Canon, Mathatronics, Olivetti, SCM (Smith-Corona-Marchant), Sony, Toshiba, and Wang. The early calculators used hundreds of Germanium transistors, since these were then cheaper than Silicon transistors, on multiple circuit boards. Germanium (dʒɚˈmeɪniəm is a Chemical element with the symbol Ge and Atomic number 32 Silicon (ˈsɪlɪkən or /ˈsɪlɪkɒn/ silicium is the Chemical element that has the symbol Si and Atomic number 14 Display types used were CRT, cold-cathode Nixie tubes, and filament lamps. The cathode ray tube (CRT is a Vacuum tube containing an Electron gun (a source of electrons and a Fluorescent screen with internal or A nixie tube is an electronic device for displaying numerals or other information. The incandescent light bulb, incandescent lamp or incandescent light globe is a source of electric Light that works by Incandescence, (a general Memory technology was usually based on the delay line memory or the magnetic core memory, though the Toshiba "Toscal" BC-1411 appears to use an early form of dynamic RAM built from discrete components. Genesis in radar The basic concept of the delay line originated with World War II Radar research as a system to reduce clutter from reflections from the ground Magnetic core memory, or ferrite-core memory, is an early form of Random access Computer memory. Already there was a desire for smaller and less power-hungry machines.

The Olivetti Programma 101 was introduced in late 1965; it was a stored program machine which could read and write magnetic cards and displayed results on its built-in printer. Ing C Olivetti & Co SpA, known as Olivetti, is an Italian manufacturer of Computers printers and other business machines The Programma 101 was a printing Programmable calculator manufactured by Olivetti in 1965 Memory, implemented by an acoustic delay line, could be partitioned between program steps, constants, and data registers. Programming allowed conditional testing and programs could also be overlaid by reading from magnetic cards. It is regarded as the first personal computer produced by a company (that is, a desktop electronic calculating machine programmable by non-specialists for personal use). The Olivetti Programma 101 won many industrial design awards.

The Monroe Epic programmable calculator came on the market in 1967. The Monroe EPIC was a programmable Calculator come on the market in the 1960s A large, printing, desk-top unit, with an attached floor-standing logic tower, it was capable of being 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. A branch (or jump on some Computer architectures, such as the PDP-8 and Intel x86) is a point in a Computer program where the During this era, the absence of the conditional branch was sometimes used to distinguish a programmable calculator from a computer.

The first handheld calculator was developed by Texas Instruments in 1967. Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA It could add, multiply, subtract, and divide, and its output device was a paper tape. [7][8]

1970s to mid-1980s

Old calculator LED display.
Old calculator LED display.

The electronic calculators of the mid-1960s were large and heavy desktop machines due to their use of hundreds of transistors on several circuit boards with a large power consumption that required an AC power supply. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals There were great efforts to put the logic required for a calculator into fewer and fewer integrated circuits (chips) and calculator electronics was one of the leading edges of semiconductor development. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that U. S. semiconductor manufacturers led the world in Large Scale Integration (LSI) semiconductor development, squeezing more and more functions into individual integrated circuits. This led to alliances between Japanese calculator manufacturers and U. S. semiconductor companies: Canon Inc. with Texas Instruments, Hayakawa Electric (later known as Sharp Corporation) with North-American Rockwell Microelectronics, Busicom with Mostek and Intel, and General Instrument with Sanyo. is a Japanese Multinational corporation that specializes in imaging and optical products including Cameras photocopiers and Computer printers Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA () is a Japanese Electronics manufacturer founded in 1912 It takes its name from one of its founder's first inventions the Ever-Sharp Mechanical pencil, which Rockwell International was the ultimate incarnation of a series of companies under the sphere of influence of Willard Rockwell, who had made his fortune after the invention and Busicom ( Nippon Calculating Machine Corp changed its name to Business Computer Corporation) was a Japanese company that owned the rights to the first Mostek Podlaskie Voivodeship Mostek was an Integrated circuit manufacturer founded in 1969 by ex-employees of Texas Instruments. General Instrument (GI was an Electronics Manufacturer based in Chicago, IL specializing in Semiconductors and Cable television () is a major Japanese electronics company and member of the Fortune 500 whose headquarters is located in Moriguchi, Osaka prefecture, Japan

Pocket calculators

By 1970 a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first portable calculators appeared in Japan in 1970, and were soon marketed around the world. These included the Sanyo ICC-0081 "Mini Calculator", the Canon Pocketronic, and the Sharp QT-8B "micro Compet". The Canon Pocketronic was a development of the "Cal-Tech" project which had been started at Texas Instruments in 1965 as a research project to produce a portable calculator. Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA The Pocketronic has no traditional display; numerical output is on thermal paper tape. As a result of the "Cal-Tech" project Texas instruments was granted master patents on portable calculators.

Sharp put in great efforts in size and power reduction and introduced in January 1971 the Sharp EL-8, also marketed as the Facit 1111, which was close to being a pocket calculator. The Sharp EL-8, introduced in January 1971 was the first 'portable' electronic Calculator. It weighed about one pound, had a vacuum fluorescent display, rechargeable NiCad batteries, and initially sold for $395. The nickel-cadmium battery (commonly abbreviated NiCd and ˈnɑɪˌkæd "nye-cad" is a type of Rechargeable battery using Nickel oxide hydroxide

However, the efforts in integrated circuit development culminated in the introduction in early 1971 of the first "calculator on a chip", the MK6010 by Mostek,[9] followed by Texas Instruments later in the year. Mostek Podlaskie Voivodeship Mostek was an Integrated circuit manufacturer founded in 1969 by ex-employees of Texas Instruments. Although these early hand-held calculators were very expensive, these advances in electronics, together with developments in display technology (such as the vacuum fluorescent display, LED, and LCD), lead within a few years to the cheap pocket calculator available to all. A vacuum fluorescent display (VFD is a Display device used commonly on consumer-electronics equipment such as Video cassette recorders Car radios

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. Mostek Podlaskie Voivodeship Mostek was an Integrated circuit manufacturer founded in 1969 by ex-employees of Texas Instruments. Using four AA-size cells the LE-120A measures 4. 9x2. 8x0. 9 in (124x72x24 mm).

The first American-made pocket-sized calculator, the Bowmar 901B (popularly referred to as The Bowmar Brain), measuring 5. 2×3. 0×1. 5 in (131×77×37 mm), came out in the fall of 1971, with four functions and an eight-digit red LED display, for $240, while in August 1972 the four-function Sinclair Executive became the first slimline pocket calculator measuring 5. The Sinclair Executive was Clive Sinclair &rsquos first venture into the Pocket calculator market 4×2. 2×0. 35 in (138×56×9 mm) and weighing 2. 5 oz (70g). It retailed for around $150 (GB£79). The Pound Sterling ( symbol £; ISO code: GBP) subdivided into 100 pence (singular penny) is the Currency By the end of the decade, similar calculators were priced less than $10 (GB£5).

The first Soviet-made pocket-sized calculator, the "Elektronika B3-04" was developed by the end of 1973 and sold at the beginning of 1974.

One of the first low-cost calculators was the Sinclair Cambridge, launched in August 1973. The Sinclair Cambridge Calculator was a 4-function pocket-sized calculator manufactured by Sinclair Research Ltd It retailed for £29. The Pound Sterling ( symbol £; ISO code: GBP) subdivided into 100 pence (singular penny) is the Currency 95, or some £5 less in kit form. The Sinclair calculators were successful because they were far cheaper than the competition; however, their design was flawed and their accuracy in some functions was questionable. The scientific programmable models were particularly poor in this respect, with the programmability coming at a heavy price in transcendental accuracy.

Meanwhile Hewlett Packard (HP) had been developing its own 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 slide rule, also known as a slipstick, is a mechanical Analog computer. The $395 HP-35, along with all later HP engineering calculators, used reverse Polish notation (RPN), also called postfix notation. The HP-35 was Hewlett-Packard 's first Pocket calculator and the world's first scientific pocket calculator (a calculator with trigonometric Reverse Polish notation (or just RPN) by analogy with the related Polish notation, a prefix notation introduced in 1920 by the Polish mathematician A calculation like "8 plus 5" is, using RPN, performed by pressing "8", "Enter↑", "5", and "+"; instead of the algebraic infix notation: "8", "+", "5", "="). Infix notation is the common arithmetic and logical formula notation in which Operators are written Infix -style between the Operands they act on (e

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 for $150. Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA The SR-50 was Texas Instruments ' first scientific pocket Calculator with Trigonometric and Logarithm functions The slide rule, also known as a slipstick, is a mechanical Analog computer. 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. The TI-30 is a series of scientific Calculators manufactured by Texas Instruments, the first of which was introduced in 1976.

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. The HP-65 was the first magnetic card-programmable handheld calculator A year later the HP-25C introduced continuous memory, i. The HP-25 was a hand-held programmable scientific/engineering calculator made by Hewlett-Packard between 1975 and 1978 e. programs and data were retained in CMOS memory during power-off. Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology In 1979, HP released the first alphanumeric, programmable, expandable calculator, the HP-41C. Alphanumeric is a is Portmanteau of Alphabetic and Numeric and is used to describe the collection of Latin letters and Arabic digits The HP-41 series are programmable expandable handheld RPN Calculators made by Hewlett-Packard from 1979 to 1990. It could be expanded with RAM (memory) and ROM (software) modules, as well as peripherals like bar code readers, microcassette and floppy disk drives, paper-roll thermal printers, and miscellaneous communication interfaces (RS-232, HP-IL, HP-IB). A bar code (also barcode) is an optical Machine-readable representation of data A Microcassette (often written generically as microcassette) is an Audio storage medium introduced by Olympus in 1969. A floppy disk is an increasingly Obsolete data storage medium that is composed of a disk of thin flexible ("floppy" Magnetic storage medium encased For the type of printer which uses sparks and aluminised paper (and is sometimes referred to as a "thermal printer" see Spark printer. In Telecommunications, RS-232 (Recommended Standard 232 is a standard for serial binary data signals connecting between a DTE ( Data Terminal Equipment The HP-IL ( Hewlett-Packard Interface Loop) was a short-range interconnection bus or network introduced by Hewlett-Packard in the early 1980s IEEE-488 is a short-range digital communications bus specification that has been in use for over 30 years

The first Soviet programmable calculator Elektronika "B3-21" was developed by the end of 1977 and sold at the beginning of 1978. Elektronika (Russian Электроника) is the Brand name used for many different electronic products such as calculators electronic watches portable 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). Reverse Polish notation (or just RPN) by analogy with the related Polish notation, a prefix notation introduced in 1920 by the Polish mathematician Thus B3-34 defined a new command set, which later was used in all programmable soviet calculators. There are hundreds of developed programs for science, business and even games for these machines. 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. The Elektronika MK-52 (Электро́ника МК-52 is a non- BASIC, RPN -programmable calculator which was manufactured in the Soviet Union and Ukraine during EEPROM (also written E2PROM and pronounced e-e-prom or simply e-squared which stands for E lectrically E rasable P rogrammable Soyuz TM-7 was the seventh expedition to the Russian Space Station Mir.

Mechanical calculators continued to be sold, though in rapidly decreasing numbers, into the early 1970s, with many of the manufacturers closing down or being taken over. Comptometer type calculators were often retained for much longer to be used for adding and listing duties, especially in accounting, since a trained and skilled operator could enter all the digits of a number in one movement of the hands on a Comptometer quicker than was possible serially with a 10-key electronic calculator. A Comptometer is a type of mechanical (or electro-mechanical Adding machine. A Comptometer is a type of mechanical (or electro-mechanical Adding machine. The spread of the computer rather than the simple electronic calculator put an end to the Comptometer. A Comptometer is a type of mechanical (or electro-mechanical Adding machine. Also, by the end of the 1970s, the slide rule had become obsolete. The slide rule, also known as a slipstick, is a mechanical Analog computer.

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 displays (LCDs) were in their infancy and there was a great deal of concern that they only had a short operating lifetime. Busicom introduced the Busicom LE-120A "HANDY" calculator, the first pocket-sized calculator and the first with an LED display, and announced the Busicom LC with LCD display. However, there were problems with this display and the calculator never went on sale. The first successful calculators with LCDs were manufactured by Rockwell International and sold from 1972 by other companies under such names as: Dataking LC-800, Harden DT/12, Ibico 086, Lloyds 40, Lloyds 100, Prismatic 500 (aka P500), Rapid Data Rapidman 1208LC. Rockwell International was the ultimate incarnation of a series of companies under the sphere of influence of Willard Rockwell, who had made his fortune after the invention and The LCDs were an early form with the numbers appearing as silver 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 the reflective LCD display was launched in 1972 by Sharp Inc with the Sharp EL-805, which was a slim pocket calculator. () is a Japanese Electronics manufacturer founded in 1912 It takes its name from one of its founder's first inventions the Ever-Sharp Mechanical pencil, which This, and another few similar models, used Sharp's "COS" (Crystal on Substrate) technology. This used a glass-like circuit board which was also an integral part of the LCD. In operation the user looked through this "circuit board" at the numbers being displayed. The "COS" technology may have been too expensive since it was only used in a few models before Sharp reverted to conventional circuit boards, though all the models with the reflective LCD displays are often referred to as "COS".

In the mid-1970s the first calculators appeared with the now "normal" LCDs with dark numerals against a grey background, though the early ones often had a yellow filter over them to cut out damaging UV rays. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays The big advantage of the LCD is that it is passive and reflects light, which requires much less power than generating light. 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 a couple of button cells. ( is a Japanese electronic devices manufacturing company founded in 1946 with its Headquarters in Tokyo.

There were also improvements to the electronics inside the calculators. All of the logic functions of a calculator had been squeezed into the first "Calculator on a chip" integrated circuits in 1971, but this was leading edge technology of the time and yields were low and costs were high. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside Many calculators continued to use two or more integrated circuits (ICs), especially the scientific and the programmable ones, into the late 1970s. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside

The power consumption of the integrated circuits was also reduced, especially with the introduction of CMOS technology. Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology Appearing in the Sharp "EL-801" in 1972, the transistors in the logic cells of CMOS ICs only used any apreciable power when they changed state. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology The LED and VFD displays had often required additional driver transistors or ICs, whereas the LCD displays were more amenable to being driven directly by the calculator IC itself.

With this low power consumption came the possibility of using solar cells as the power source, realised around 1978 by such calculators as the Royal Solar 1, Sharp EL-8026, and Teal Photon. A solar cell or photovoltaic cell is a device that converts Solar energy into Electricity by the photovoltaic effect.

A pocket calculator for everyone

At the beginning of the 1970s hand-held electronic calculators were very expensive, costing two or three weeks' wages, and so were a luxury item. The high price was due to their construction requiring many mechanical and electronic components which were expensive to produce, and production runs were not very large. Many companies saw that there were good profits to be made in the calculator business with the margin on these high prices. However, the cost of calculators fell as components and their production techniques improved, and the effect of economies of scale were felt.

By 1976 the cost of the cheapest 4-function pocket calculator had dropped to a few dollars, about one twentieth of the cost five years earlier. The consequences of this were that the pocket calculator was affordable, and that it was now difficult for the manufacturers to make a profit out of calculators, leading to many companies dropping out of the business or closing down altogether. The companies that survived making calculators tended to be those with high outputs of higher quality calculators, or producing high-specification scientific and programmable calculators.

Mid-1980s to present

The first calculator capable of symbolic computation was the HP-28, released in 1987. The HP-28C and HP-28S were two Graphing calculators produced by Hewlett-Packard from 1987 to 1992 It was able to, for example, solve quadratic equations symbolically. The first graphing calculator was the Casio fx7000G released in 1985. A graphing calculator (also known as a graphic calculator or graphical calculator) typically refers to a class of handheld Calculators that are capable of ( is a Japanese electronic devices manufacturing company founded in 1946 with its Headquarters in Tokyo.

The two leading manufacturers, HP and TI, released increasingly feature-laden calculators during the 1980s and 1990s. At the turn of the millennium, the line between a graphing calculator and a handheld computer was not always clear, as some very advanced calculators such as the TI-89, the Voyage 200 and HP-49G could differentiate and integrate functions, solve differential equations, run word processing and PIM software, and connect by wire or IR to other calculators/computers. A mobile device (also known as cellphone device, handheld device, handheld computer, "Palmtop" or simply handheld) is a pocket-sized The TI-89 and the TI-89 Titanium are Graphing calculators developed by Texas Instruments. The Texas Instruments TI-92 Calculator, originally released in 1995, was a large calculator with a QWERTY keyboard The HP 49G series are Hewlett-Packard (HP manufactured Graphing calculators They are the successors of the HP-48 series, one of the best-selling calculator In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the Word processing is the creation of documents using a Word processor. Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of

The CASIO CM-602 Mini Electronic Calculator provided basic functions in the 1970s
The CASIO CM-602 Mini Electronic Calculator provided basic functions in the 1970s

The HP 12c financial calculator is still produced. The HP-10C series Calculators were introduced by Hewlett-Packard in 1981. 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. Reverse Polish notation (or just RPN) by analogy with the related Polish notation, a prefix notation introduced in 1920 by the Polish mathematician 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.

Online calculators are programs designed to work just like a normal calculator does. Usually the keyboard (or the mouse clicking a virtual numpad) is used, but other means of input (e. g. slide bars) are possible.

Thanks to the Internet, many new types of calculators are possible for calculations that would otherwise be much more difficult or impossible, such as for real time currency exchange rates, loan rates and statistics.

See also

General interest
Mechanical calculators


Electronic calculators

References

  1. ^ Thomas J. The history of computer hardware encompasses the hardware, its architecture, and its impact on software. Calculator spelling (also known as beghilos; see Description below is a technique of spelling words by reading characters upside-down from Calculators equipped A formula calculator is a software calculator that can perform a calculation in two steps 1 An abacus, also called a counting frame, is a calculating tool used primarily by Asians for performing arithmetic processes Napier's bones is an Abacus created by John Napier for Calculation of products and quotients of numbers that was based on Arab mathematics and A Comptometer is a type of mechanical (or electro-mechanical Adding machine. The Mercedes-Euklid is a German -invented Calculator from the early twentieth century See Adding machine (disambiguation for other uses of this term The Addiator was a mechanical add/subtract Calculator, made by Addiator Gesellschaft, Berlin. The Curta was a small hand-cranked mechanical Calculator introduced in 1948 The slide rule, also known as a slipstick, is a mechanical Analog computer. The Difference Engine was an automatic mechanical calculator designed to tabulate polynomial functions. Volvelles, also called wheel charts are a type of Slide chart, Paper constructions with rotating parts The ANITA Mark VII and ANITA Mark VIII Calculators were launched simultaneously in late 1961 as the world's first all- electronic desktop A Machinist Calculator is a hand-held Calculator programmed with built-in formulas making it easy and quick for Machinists to establish speeds feeds and time without A scientific calculator is a type of electronic Calculator, usually but not always handheld designed to calculate problems in science (especially Physics Programmable calculators are Calculators capable of being programmed much like a Computer. HP calculators refer to various Calculators manufactured by the Hewlett-Packard company over the years Eigenmath is a free easy to use no installation multiplatform Computer algebra system by George Weigt written in the C programming language. Bing, Edward F. Redish, Symbolic Manipulators Affect Mathematical Mindsets, December 2007
  2. ^ Mike Sebastian's calculator forensics algorithm is an example of such rounding errors -- the algorithm's arcsin(arccos(arctan(tan(cos(sin(9)))))) should come out 9 on standard floating point hardware, but for CORDIC it's a pathological case that produces different rounding errors on each chip that it is implemented on. The algorithm is primarily used to identify the manufacturer of a particular calculator's CPU, since it is usually reproducible between chips of the same model.
  3. ^ Slide Rules
  4. ^ Smart Computing Article - Calculating Clock to Carnegie Mellon University
  5. ^ "Simple and Silent", Office Magazine, Dec. 1961, p1244
  6. ^ "'Anita' der erste tragbare elektonische Rechenautomat" [trans: "the first portable electronic computer"], Buromaschinen Mechaniker, Nov. 1961, p207
  7. ^ Texas Instruments Celebrates the 35th Anniversary of Its Invention of the Calculator Texas Instruments press release, 15 Aug 2002. Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA
  8. ^ Electronic Calculator Invented 40 Years Ago All Things Considered, NPR, 30 Sept 2007. Audio interview with one of the inventors.
  9. ^ "Single Chip Calculator Hits the Finish Line", Electronics's', Feb. 1 1971, p19

Patents

External links

History
Virtual

Dictionary

calculator

-noun

  1. (dated) A person who performs mathematical calculation
  2. A person who calculates (in the sense of scheming).
  3. A mechanical or electronic device that performs mathematical calculations.
  4. (obsolete) A set of mathematical tables.
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