Calculator

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File:Calculator.kodabar.jpg
A modern basic arithmetic calculator

A calculator is a device for performing numerical calculations. The type is considered distinct from both a calculating machine and a computer in that the calculator is a special-purpose device that may not qualify as a Turing machine. Although modern calculators often incorporate a general purpose computer, the device as a whole is designed for ease of use to perform specific operations, rather than for flexibility.

The complexity of calculators varies with the intended purpose. A simple one with only four functions (addition, subtraction, multiplication and division and perhaps a single-number memory) may be useful for everyday activities such as shopping or checking a bill. More complex ones may include complex mathematical functions suitable to engineering or accounting as well as a substantial memory and the ability to execute moderately complex programs. Since the late-1980's, it has become common to incorporate simple calculators in other small devices, such as mobile phones, pagers or wrist watches.

In most developed countries, students use calculators for schoolwork. There was some initial resistance to the idea out of fear that basic arithmetic skills would suffer. There remains disagreement about the importance of the ability to perform calculations 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.

Overview

Modern calculators are electrically powered, most often by battery, and are made by numerous manufacturers, in countless shapes and sizes varying from cheap, give-away, credit-card sized models to more sturdy adding machine-like models with built-in printers. Only a very few companies develop and make modern professional engineering and finance calculators: The most well-known are Casio, Sharp, Hewlett-Packard (HP) and Texas Instruments (TI). Such calculators are good examples of embedded systems. They are also often complex enough to be programmed; calculator applications include algebraic equation solvers, financial models and even games.

In the near past, mechanical and clerical aids such as abacuses, comptometers, Napier's bones, books of mathematical tables, slide rules, adding machines, were used for serious numeric work, and the word "calculator" denoted a person (most often male) who did such work for a living using such aids as well as pen and paper. This semi-manual process of calculation was tedious and error-prone.

Electronic calculators

Today most calculators are handheld microelectronic devices, but in the past some calculators were as large as today's computers. The first mechanical calculators were mechanical desktop devices, which were soon replaced by electromechanical desktop calculators, and then by electronic devices using first thermionic valves, then transistors, then hard-wired integrated circuit logic.

A pocket calculator is a small battery-powered or solar powered electronic digital computer made possible by integrated circuit and semiconductor technology. Typically they are limited to an 8–10 digit single-number display and a few basic functions of arithmetic, but some modern calculators have more of the features of a general-purpose computer. Pocket calculators rendered the slide rule obsolete.

Calculators vary in their capabilities. Some are limited to only basic arithmetic; others support trigonometric, statistical and other mathematical functions. The most advanced modern calculators are programmable, can display graphics, and include features of computer algebra systems.

Personal computing

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

History

Origin: The Abacus

File:Abacus 6.png
Chinese abacus.
Main article: Abacus

The first calculators were abacuses, and were often constructed as a wooden frame with beads sliding on wires. Abacuses were in use centuries before the adoption of the written Arabic numerals system and are still widely used by merchants and clerks in China and elsewhere.

The 17th century

Wilhelm Schickard built the first automatic calculator called the "Calculating Clock" in 1623. Some 20 years later, in 1645, French philosopher Blaise Pascal invented the calculation device later known as Pascal's calculator, which was used for taxes in France until 1799.

1930s to 1960s

File:Monroecalculator.jpg
Monroe mechanical digital calculator.

From approximately the 1930s through the 1960s, mechanical calculators were often used (see Mechanical Calculator under History of computing hardware). These desktop devices were motor-driven and had multiple columns of keys for each digit. 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. Handheld mechanical calculators such as the Curta continued to be used until they were displaced by electronic calculators in the 1970s.

In 1954, IBM demonstrated a large all-transistor calculator and, in 1957, they released the first commercial all-transistor calculator (the IBM 608). In October 1961, the world's first all-electronic desktop calculator, the Bell Punch/Sumlock Comptometer ANITA Mk.VII was released. This British designed-and-built machine used vacuum tubes in its circuits and cold-cathode nixie tubes for its display. It was superseded, technologically, in 1964 when Sharp introduced the CS-10A—the world's first all-transistor desktop calculator—which weighed 25 kg (55 lb) and cost 500,000 yen (~US$2500). The first handheld electronic calculators went on sale in 1970 with models from Japanese manufacturers Sharp and Canon weighing around 770 g (1.7 lb).

1970s to mid-1980s

In the early 1970s, the Monroe EPIC programmable calculator came on the market. A large 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. During this era, the absence of the conditional branch was sometimes used to distinguish a programmable calculator from a computer.

The first 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 5.4×2.2×0.35 in (138×56×9 mm) and weighing 2.5 oz (70g). It retailed for around $150 (GB£79). By the end of the decade, similar calculators were priced less than $10 (GB£5).

The first pocket calculator with scientific functions, i.e. the first slide rule-replacing model, was the 1972 HP-35 from Hewlett Packard (HP); it, along with all later HP engineering calculators, used reverse Polish notation (RPN) (where a calculation like "6 – 2" is performed by pressing "6", "Enter↑", "2", and "–"; instead of algebraically: "6", "–", "2", "=").

In 1973, Texas Instruments (TI) introduced the SL-10, (SL signifying slide rule) a hand-held algebraic notation calculator, which was later followed by the SL-11 and eventually the TI-30.

The first programmable hand-held 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. A year later the HP-25C introduced continuous memory, i.e. programs and data were retained in memory during power-off. In 1979, HP released the first alphanumeric, programmable, expandable calculator, the HP-41C. It could be expanded with RAM (memory) and ROM (software) modules, as well as peripherals like bar code readers, microcassette and floppy disk drives, paper-roll thermal printers, and miscellaneous communication interfaces (RS-232, HP-IL, HP-IB).

Mid-1980s to present

File:TI-84 Plus.jpg
A TI-84 Plus graphing calculator from Texas Instruments.
File:CRAZY copy.gif
A screenshot of a 3D wire frame graph on a TI-89 calculator.

The two leading manufacturers, HP and TI, released steadily more feature-laden calculators during the 1980s and 90s. At the turn of the millennium, the line between a graphing calculator and a PDA/ handheld computer was not always clear (forgetting the keyboard for the sake of the argument), as some very advanced calculators such as the TI-89 and HP-49G could differentiate and integrate functions, run word processing and PIM software, and connect by wire or IR to other calculators/computers.

In March 2002, HP announced that the company would no longer produce calculators, which was hard to fathom for some fans of the company's products; the HP-48 range in particular had an extremely loyal customer base. Nevertheless, HP restarted their production of calculators in late 2003. The new models, however, reportedly didn't have the mechanical quality and sober design HP's earlier calculators were famous for (instead featuring the more "youthful" look and feel of contemporary competing designs from TI).

The business calculator HP-12C is still produced. It was introduced in 1981 and is still being made with nearly no changes. In 2003 several new models were released, including an improved version of the HP-12C, the "HP-12C platinum edition".

Drawbacks

  • Built-in inaccuracy commonly due to arithmetic underflow is a drawback occurring in many ordinary digital calculators. To obtain an example of this potential problem, the following exercise may be performed: enter the number one, divide by three, to reach 0.333 (recurring, i.e. followed by a theoretically infinite number of 3s), and then multiply by three to get back to one. On some calculators this operation will not work correctly, in that the result is given as 0.999 (recurring)—roughly speaking, this anomaly happens because the calculator works with only a finite number of decimals.
  • Another kind of "drawback" resulting from the use, rather than the construction, of calculators, is the tendency of users to carelessly rely on the calculator's output without double-checking the magnitude (in practice, the placement of the decimal separator) of the result. 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 (sufficiently meticulous) user.

Trivia

  • The word "calculator" is occasionally used as a pejorative term to describe an inadequately capable general-purpose microcomputer. The synonym of this meaning is "bitty box", as discussed in the Jargon file.
  • A curious episode of the mid 1970s involved the Melcor 635, a scientific calculator with a bug in its trigonometric functions. Because the CORDIC algorithms used in most calculators cannot compute the inverse trigonometric functions of zero, these need to be hardcoded — and some engineer at Melcor got it wrong. For any input other than exactly zero, even for instance 1.0E-99, the calculator worked correctly; the user simply had to remember not to compute the arc-cosine of zero. The company discovered this after making 50,000 calculators. The upshot was an advertisement in Scientific American headlined 'Somebody Goofed', offering these calculators for sale at half-price.
  • As many schoolchildren and students know, some words and simple phrases can be written using an ordinary seven-segment display calculator; this involves entering certain numbers and then viewing the resulting words by turning the calculator display upside-down.

See also

General interest:

Mechanical calculators:

Electronic calculators:

Patents

External links

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