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calculating machine,

device for performing numerical computations; it may be mechanical, electromechanical, or electronic. The electronic computercomputer,
device capable of performing a series of arithmetic or logical operations. A computer is distinguished from a calculating machine, such as an electronic calculator, by being able to store a computer program (so that it can repeat its operations and make logical
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 is also a calculator but performs other functions as well.

Mechanical and Electromechanical Calculators

Early devices used to aid in calculation include the abacusabacus
, in mathematics, simple device for performing arithmetic calculations. The type of abacus now best known is represented by a frame with sliding counters. An elementary abacus might have ten parallel wires strung between two boards on a frame, with nine beads on each wire.
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 (still common in E Asia) and the counting rods, or "bones," of the Scottish mathematician John NapierNapier, John
, 1550–1617, Scottish mathematician and theologian. He invented logarithms and wrote Mirifici logarithmorum canonis descriptio (1614), containing the first logarithmic table and the first use of the word logarithm.
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. The slide ruleslide rule,
instrument for making numerical computations and readings, the results of which may be read easily and quickly after performing simple mechanical manipulations.
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, invented in 1622 by William Oughtred, an English mathematician, was widely used to make approximate calculations, but it has been replaced by the electronic calculator. In 1642, Blaise PascalPascal, Blaise
, 1623–62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science.
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 devised what was probably the first simple adding machine using geared wheels.

In 1671 an improved mechanism for performing multiplication by the process of repeated addition was designed by Gottfried W. von LeibnizLeibniz or Leibnitz, Gottfried Wilhelm, Baron von
, 1646–1716, German philosopher and mathematician, b. Leipzig.
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. A machine using the Leibniz mechanism was the first to be produced successfully on a commercial scale; devised in 1820 by the Frenchman Charles X. Thomas, it could be used for adding, subtracting, multiplying, or dividing. A mechanism permitting the construction of a more compact machine than the Leibniz mechanism was incorporated into a machine devised late in the 19th cent. by the American inventor Frank S. Baldwin. Later the machine was redesigned by Baldwin and another American inventor, Jay R. Monroe. At about the same time, W. T. Odhner of Russia constructed a machine using the same device as Baldwin's. Charles BabbageBabbage, Charles
, 1792–1871, English mathematician and inventor. He devoted most of his life and expended much of his private fortune and a government subsidy in an attempt to perfect a mechanical calculating machine that foreshadowed present-day machines.
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, an English mathematician, and William S. Burroughs, an American inventor, also made important contributions to the development of the calculating machine.

Early mechanical adding machines were equipped with a keyboard on which numbers to be added were entered, a lever to actuate the addition process, and an accumulator to display the results. A full keyboard consisted of 10 columns of keys with 9 keys in each column, numbered 1 through 9. Each column could be used to enter a figure in a particular decimal place so that a number up to 10 digits long could be entered; if no key was pressed in a given column, a zero was entered in that decimal place. The lever was pulled in one direction when a number was to be added and in the opposite direction when it was to be subtracted. The accumulator was a set of geared wheels, each corresponding to a decimal place and having the digits 0 through 9 printed on its circumference. When a given wheel made a complete rotation, the next wheel was advanced by one digit. The mechanical adding machine remained essentially the same until the mid-1960s, with improvements consisting of motors to actuate additions and subtractions and mechanisms to print out results on a paper tape.

Electronic Calculators

Electronic calculators, which became available in the early 1960s, at first were merely faster and quieter adding machines. The invention of the microprocessor and advances in integrated-circuit technology made small, but highly sophisticated, calculators possible, and by the mid-1970s they were in wide use. Simple calculators perform only the basic four functions of addition, subtraction, multiplication, and division. More sophisticated calculators can perform trigonometric, statistical, logarithmic, and other advanced calculations.

Some electronic calculators are actually small computers with limited memory and programming capabilities. Some of these programmable calculators can accept plug-in semiconductor memory cards or programming modules for special applications, such as financial calculations, unit, currency, or number-system conversions, or engineering calculations. Others are also available that include nonmathematical functions such as data storage and schedule organizing. The personal digital assistant, a hand-held device optimized as an organizer with communications capability and accepting handwritten input, is a bridge from calculators to full computer function.

Early electronic calculators had numeric displays made from light-emitting diodes (LEDs). They have been supplanted by liquid-crystal displays (LCDs), whose lower power consumption helps to reduce battery drain. Some calculators use an LCD readout to provide a graphic, as well as numeric, display. CMOS, or complementary metal-oxide-semiconductor (see integrated circuitintegrated circuit
(IC), electronic circuit built on a semiconductor substrate, usually one of single-crystal silicon. The circuit, often called a chip, is packaged in a hermetically sealed case or a nonhermetic plastic capsule, with leads extending from it for input, output,
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), technology is also preferred for battery-operated models because of its low-power requirements. Some calculators are powered by solar cellssolar cell,
semiconductor devised to convert light to electric current. It is a specially constructed diode, usually made of forms of crystalline silicon or of thin films (as of copper indium gallium selenide or amorphous silicon).
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 in ordinary room light.


See B. Randell, The Origins of Digital Computers: Selected Papers (1982); J. P. Haney, Calculators (3d ed. 1985).


(computer science)
A device that performs logic and arithmetic digital operations based on numerical data which are entered by pressing numerical and control keys. Also known as calculating machine.


1. a device for performing mathematical calculations, esp an electronic device that can be held in the hand
2. a set of tables used as an aid to calculations



A machine that provides arithmetic capabilities. The most basic calculators, which can cost pennies to purchase, add, subtract, multiply and divide. More advanced devices handle sines, cosines and other trigonometric functions. Whether mechanical or electronic, all calculators accept numeric input from dials, levers or a keypad. The results are displayed as mechanical digits, on punched paper tape or on a screen, such as an LCD. Unlike computers, calculators perform a finite set of functions, and they cannot handle text.

The First Handheld
In 1967, Texas Instruments introduced the first handheld calculator. The opened unit in the picture shows the paper tape used as output. (Image courtesy of Texas Instruments, Inc.)

The Curta Pepper Grinder
Completed in a World War II concentration camp in the 1940s, Curt Herzstark was given permission to perfect the calculator he patented earlier. These mechanical marvels were used up to the 1980s for their accuracy and ruggedness in hostile conditions such as car rallies. The sliders on the side hold the number multiplied by the number of times the "grinder" on top is turned. The mechanical results appear on top as well. (Image courtesy of Clive "Max" Maxfield,
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