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STARS:Electronic Calculators: Desktop to Pocket

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{{STARSArticle|citation=
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{{STARSArticle
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|myname=Earl Swartzlander
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|citation=Starting in 1960, desktop calculators based on vacuum tubes were introduced to replace the mechanical and electromechanical calculators that had been widely used in business, engineering and science.  Electronic calculators were more durable, faster, and silent.  In the mid-1960s vacuum tubes were replaced by discrete transistors to provide more functionality and greater durability.  By the mid-1970s, small battery-powered pocket calculators, implemented with integrated circuits, had replaced desktop calculators and were rapidly replacing the previously indispensable engineering slide rules.
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|timeline={{STARSEvent
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|year=1960
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|event=ANITA desktop calculator is the first electronic desktop calculator
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}}{{STARSEvent
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|year=1963
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|event=Friden EC-130 desktop calculator is the first transistorized desktop calculator
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}}{{STARSEvent
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|year=1965
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|event=Wang LOCI desktop calculator is introduced
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}}{{STARSEvent
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|year=1968
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|event=HP 9100A Desktop Engineering Calculator is introduced
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}}{{STARSEvent
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|year=1972
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|event=HP-35, the first pocket engineering calculator, is introduced
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}}{{STARSEvent
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|year=1976
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|event=TI-30 scientific pocket calculator is introduced
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}}
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|essay=Starting in 1960 electronic desktop calculators were developed and began replacing the widely used mechanical and electromechanical calculators.  By the end of the 1970s, small battery-powered pocket calculators, implemented with integrated circuits, had largely replaced electronic desktop calculators.
  
|timeline={{STARSTimeline|year1=1886|event1=Mechanical integrators created to help with things such as analysis of ocean tides |year2=1931|event2=Bush torque amplifier and first differential analyzer built|year3=1934|event3=Differential analyzers began to be built in the US, Britain, Norway, Sweden, and elsewhere|year4=1942|event4=Rockefeller Differential Analyzer (RDA2) built|year5=1943|event5=ENIAC, an early digital device, used vacuum tube electronics to calculate ballistics tables|year6=1949|event6=Analog differential analyzers eventually replaced by digital differential analyzers|year7=1959|event7=Differential analyzers finally replaced by general purpose digital computers }}|essay=Many problems encountered in practical science and engineering involve changing values of speed, voltage, heights, acceleration, and similar measurements.  These problems are fundamental to the design of almost everything we take for granted today: electrical power systems, radio and television, prediction of tides and ocean currents, design of airplanes, and ballistic problems such as accurate aiming of artillery.  The solutions to most of these problems involve representing the situation as a mathematical model, and this model usually involves an area of mathematics known as differential equations.  To obtain useful numerical results from these models required integrating these differential equations.  The numerical solution of differential equations by hand usually involves some form of numerical integration, a process that is labor intensive, error prone, and difficult, occasionally even impossible, without modern digital computing machines.
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=== Mechanical Calculators ===
  
The process of integration is essentially finding the area under the graph of the function.  While this sounds simple, it can be difficult in practice because the equation of the graph is sometimes not known—for example the amount of light received from a variable star can be measured and graphed, but the equation that results in this graph is not knownSimple expedients can be used to gain some idea of the numerical solution to these problemsOne involves nothing more than graph paper and an accurate chemical balance. If you plot the function to be integrated on the graph paper and cut out the resulting area between the x axis and the function value (the y axis), then the weight of this cut-out piece of paper is proportional to the area.  If you then cut out a unit square from the same paper, you can weigh the graph, divide it by the weight of the unit square, and you will have a reasonable approximation to the areaThe method is, of course, full of potential sources of error.
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Prior to 1960 there were three general types of calculating devices: mechanical adding machines, calculators (both mechanical and electromechanical), and slide rulesAdding machines were used by accountants, bankers and merchants to add and subtract (often with a paper tape record of the calculation)Successful brands of adding machines were Burroughs, Comptometer and Victor. Calculators were larger units (often about the size of a typewriter) that could add, subtract, multiply, and divide.  Calculators were used by engineers and scientists as well as in the business world.  Important calculator manufacturers were Friden, Marchant and MonroeSlide rules were simple mechanical devices used by engineers to multiply, divide, and perform other calculations that are based on logarithms and trigonometric relations.  Keuffel & Esser and Pickett were the most common brands.
  
=== Some Early Efforts ===
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One of the most significant advances of the 20th century was the replacement of mechanical and electromechanical devices with electronic devices.  This technological transition occurred with calculators as well as in many other fields such as television, music players, etc.  The earliest machines were mechanical devices.  Later machines included an electric motor (hence the term electromechanical) that reduced the effort required to operate the machines.  Especially during World War II, large groups of electromechanical calculators (operated by teams of people referred to as “computers”) were used for many purposes, including computing trajectory tables for ballistics and as part of the Manhattan project. 
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In mechanical machines, the inertia of wheels, levers, and shafts severely limit the speed of computation.  In contrast, the circuits in the electronic calculators operate at speeds that are limited only by the speed of light.  Also mechanical machines are quite noisy, whereas electronic machines are silent.
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Another important issue is that mechanical devices are susceptible to wear that could cause intermittent errors.  Such intermittent errors can be far more devastating than complete failures because the user might get wrong answers without being aware that an error has occurred.
  
While modern digital computers represent all their data by “digital” zeros and ones, it is easily forgotten that data can also be represented and manipulated by “analog” devices.  For example it is possible to represent numerical quantities by voltages (the larger the number, the larger the voltage used), by lengths (rods of various lengths can represent various numbers), or by more convenient quantities such as the rotation of a mechanical shaft (the number of rotations representing the number being considered).  Analog representations have advantages and disadvantages with respect to digital.  For example, it is often easier to construct an electrical or mechanical “analog” to a situation than it is to program a digital computer to simulate it (the example given above of finding areas by weighing bits of paper being a good example).  On the other hand, it is easy to represent small numbers by values such as lengths or voltages, but very difficult, if not impossible, to deal with quantities in the hundreds of thousands by lengths or voltages in that range.
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=== Electronic Desktop Calculators ===
  
Various simple mechanical analog devices have been invented for performing this integrating step.  By the late 19th century analog instruments had been devised for determining areas of randomly shaped portions of survey maps or to integrate functions plotted as graphs (see reference by Abdank-Abakanowicz). Various mathematicians and physicists then began attempting to adapt these to solve differential equations.  For example, in the 1860s and 1870s the Scotsman James Thomson (a professor of engineering at Edinburgh University) and his brother William Thomson (a professor of physics at Glasgow, better known today as Lord Kelvin) were engaged in trying to predict the heights of tides.  Their attempts to determine an equation that represented tide heights required them to analyze tide records from different ports, and this became so difficult that they proposed using a mechanical disk-sphere-cylinder integrating mechanism as shown in Figure 1.  Rotation of the disk corresponds to moving along the x axis of the graph, and the distance of the sphere from the center of the disk corresponds to the height of the graph (the y value).  As the disk rotates, an operator must move the sphere in and out corresponding to the y values.  If the sphere is close to the center of the disk it will rotate very slowly (a small y value), and if near the edge of the disk (a large y value) it will rotate rapidly. This rotation of the sphere will be transferred (simply by friction) to the cylinder, and the total number of rotations of the cylinder will correspond to the integral of the equation being studied.
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[[Image:electronic calculators - image003.jpg|thumb|right|Figure 1, ANITA Mark VII Desktop Calculator (photo Frank Eggebrecht, used with permission of Nigel Tout of Vintage Calculators Web Museum)]]
  
[[Image:Differential analyzer 1.jpg|thumb|right|Figure 1.  Source: M. Bowles, IEEE Annals of the History of Computing, vol. 18, no. 4, 1996, p. 6, with permission.]]
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[[Image:electronic calculators - image001.jpg|thumb|right|Figure 2, Nixie tube (copyright Georg-Johann Lay, used with permission)]]
  
The problem with many of these mechanisms is that they were limited to elementary situations.  More complex problems often require the solution of several different differential equations at the same time, and the delicate nature of the friction couplings of the moving components prevented them being joined together into more complex machinesAny attempt to use the output of the cylinder to move another piece of mechanical equipment (say the sphere in a second integrator or some mechanism to add the results of two integrators together) would simply cause the sphere to slip on either the rotating table or the cylinder and thus render useless any potential results.  The problem of friction was further exacerbated when, in order to gain more accuracy in the system, the cylinder was replaced by an integrating disk (usually of polished steel or plate glass) and the sphere by an integrating wheel with a knife edge allowing very accurate positioning along the y axis (Figure 2).
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The first electronic desktop calculator was the ANITA (the name is an acronym for “A New Inspiration To Accounting”) (Figure 1), designed and produced by Sumlock Comptometer, LtdThis British company had a line of mechanical calculators, but the ANITA Mk VII that was introduced in 1960 was a radical departure from their previous products.  The ANITA used gas-filled thyratron tubes and selenium rectifiers for the logic circuits to perform the computations.  The 12-digit display used a Nixie tube (with metal numbers in a neon filled vacuum tube) for each digit (Figure 2).  Since the ANITA calculators had no moving parts, they were fast, silent, and needed minimal maintenance.  The ANITAs were four-function calculators that could add, subtract, multiply, and divide.
  
[[Image:Differential analyzer 2.jpg|thumb|left|Figure 2Source: M. Bowles, IEEE Annals of the History of Computing, vol. 18, no. 4, 1996, p. 6, with permission.]]
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[[Image:electronic calculators - image005.jpg|thumb|right|Figure 3Friden EC-130 Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).]]
  
An elementary differential analyzer, capable of integrating only one equation, can theoretically be made by having an input table (labeled I in Figure 3), and integrating device (D) and an output table (O)A motor will drive a curve follower down the x axis of a graph on the input table, while at the same time rotating the integrating disk and driving a pen along the x axis of the output table.  The human operator would turn the crank on the curve follower to keep the pointer over the current y value of the graph (thus moving the integrating wheel, W, across the rotating disk), while the output from the integrating shaft, C, moves the output pen up and down recording the results on graph paper.  
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One of the first transistorized calculators was the Friden EC-130 (Figure 3) introduced in June 1963.  It used discrete transistors and diodes for the logicIt used a small cathode-ray tube to display the 13-digit values of four registers.  The registers showed the previous entries and result of the calculation.  Since there were 4 registers of 13 digits, a sizable memory was required.  The EC-130 used a steel-wire ultrasonic delay line for its memory.  At one end, the wire was given a small twist for each bit to be stored.  The twist propagated along the wire at the relatively slow speed of sound and was detected at the far end.  Upon detection, the bit could be used or it could be reentered into the delay line.  Like the ANITA, the Friden EC-130 was a four-function calculator.  A few years later, Friden introduced the EC-132 that added a square root operation to the four basic functions of the EC-130.
  
[[Image:Differential analyzer 3.jpg|thumb|right|Figure 3An elementary differential analyzer.  Source: W. W. Soroka, Analog Methods in Computation and Simulation, McGraw-Hill, 1954.]]
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[[Image:electronic calculators - image007.jpg|thumb|right|Figure 4Wang LOCI Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).]]
  
The major difficulty with this simple device is that it is not suitable for use in complex real-world situations where the mathematical models have several sequential integration steps, i.e., the output of one integration has to be used as the input to the next, and so on.  The output from the integrating wheel (W) cannot be mechanically connected to other units because the friction between the knife-edge steel wheel (W) and the steel or glass rotating disk (D) is so small that it does not have the force to drive a second stage of integrating devices.
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Another transistorized desktop calculator was the Wang LOCI (LOgarithmic Calculating Instrument) (Figure 4), introduced in 1965. By using the factor-combining method of calculating logarithms and anti-logarithms, this calculator provided functions useful for engineering, such as calculating roots and powers.  The display unit was separate from the keyboard, and multiple keyboards could be ganged to a single LOCI display unit.  Although it pioneered the concept of a programmable calculator, the LOCI was an engineering calculator that was too difficult to use for business and commercial applications.  For example, the LOCI produced an answer of 3.999999999 for the multiplication of 2 x 2.  While this was not a problem for engineers who were accustomed to slide rules with three digit accuracy, it was not acceptable for most non-technical users.  In late 1966, Wang started selling the Model 300 calculator that was better suited for general use.  Wang’s experience with the Model 300 led to a line of stand-alone word processors that were very successful in business applications.
  
Lord Kelvin realized that his attempt at creating a mechanical analog device to solve problems involving differential equations would need some type of device to amplify the power (torque) generated by the turning cylinder before it could be coupled to any other systemUnfortunately the technical knowledge of the time did not allow the delicate and highly precise mechanisms to be created.  
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[[Image:electronic calculators - image009.jpg|thumb|right|Figure 5Hewlett Packard 9100A Desktop Calculator.]]
  
=== Achieving Practical Devices ===
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The Hewlett Packard 9100A (Figure 5), introduced in 1968, was the ultimate desktop engineering calculator.  This calculator was based on a prototype designed by Tom Osborne, who had worked for the Marchant Company, which was one of the pioneers in mechanical and electro-mechanical calculators.  The production model (as implemented by Hewlett Packard) used discrete transistors to perform the computations.  Like the Friden electronic calculators, it used a small cathode-ray tube to display the contents of three registers.  The registers showed the operands and result of each calculation.  In addition to the basic four functions, the 9100A provided a full suite of engineering functions, including transcendental, logarithmic and trigonometric functions.  To provide the engineering functions, a read-only memory of 32,000 bits was required for the constants needed for the CORDIC algorithms.  The read-only memory was constructed with inductive coupling between lines on the two sides of a printed circuit board.  Both the Wang LOCI and the HP-9100A used random-access memories (RAM for short) implemented with magnetic cores to hold data and the results of calculations.  The RAM could also hold sequences of instructions allowing the machines to be programmed to perform repetitive computations.  In fact they could be viewed as small computers with capability similar to the personal computers that were introduced a decade later.  The HP- 9100 could store the programs on a magnetic card the size of a credit-card.
  
The problem was finally solved in 1930 by Vannevar Bush, a professor at MIT.  (He was later to become President of MIT and a very influential advisor to the President of the USA during the Second World War.)  Bush began to consider the problem of how to construct a mechanical integrating mechanism when he had to solve some differential equations concerned with an electrical power network.  After spending several months attempting to solve just one equation, he decided it was better to spend his time designing an analog computing mechanism that could solve many such equations.
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=== Pocket Calculators ===
  
Bush finally resolved the problem of connecting several disk-wheel integrators together for the solution of real word problems when he invented a device that would amplify the torque in the rotating shaft (C), giving enough power to drive other devices while still permitting the delicate movements of the integrating wheel on the disk.  This torque amplifier, based on the same principles as a capstan used to raise an anchor on a ship, was an extremely delicate device to construct and maintain.  One of the very best differential analyzers had been constructed at the Institute of Physics in Oslo Norway in 1938, just prior to World War Two.  Svend Rosseland, an astrophysicist in charge of the machine, realized that the German military would be interested in using this device.  After Norway was invaded by Germany, Svend removed the delicate torque amplifiers and, after carefully wrapping them to prevent corrosion, buried them in the garden.  This simple expedient rendered this fine machine useless until they were dug up and reinstalled after the war was over.
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[[Image:electronic calculators - image011.jpg|thumb|right|Figure 6. Texas Instruments 2500 Datamath Pocket Calculator (used with permission of Nigel Tout of Vintage Calculators Web Museum).]]
  
[[Image:Differential analyzer 4.jpg|thumb|left|Figure 4: Bush’s torque amplifier mechanismSource: V. Bush, "The differential analyzer" (see reference of historical significance).]]
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Starting in the mid-1960s, Texas Instruments began the development of the “Cal-Tech”, a prototype for a handheld four-function electronic calculator with a paper tape to display the results. The Canon Pocketronic battery-powered pocket calculator introduced in 1970 was based on the “Cal-Tech. In 1972 Texas Instruments began making and selling battery-powered pocket calculators under its own name. The first unit sold under the Texas Instruments name was the TI-2500 Datamath calculator (Figure 6) that was introduced in June 1972.  It used light emitting diode (LED) displays with distinctive red numbers that were attractive and easy to read, but consumed a lot of power.  Ultimately they were displaced by liquid-crystal displays (LCD) that consume very little power.  In the five years after introduction of the Datamath, TI introduced at least 70 different models with a wide range of capabilities.  As pocket electronic calculator sales volume increased at an exponential rate, the prices fell: by 1976 the TI-30 scientific pocket calculator was selling for less than $24.95.  At this time, desktop four-function calculators had become almost obsolete except for applications that required a record of the calculation.
  
The torque amplifier consisted of two “friction drums” that were rotated by belts attached to electrical motors.  An input shaft was connected to the knife-edge wheel of an integrator, and that, in turn, would gently nudge an input arm. The slight movement of the input arm would cause the string to momentarily tighten on the right hand friction drum, giving a pull on the output arm which would then cause the output shaft to rotate with considerable force, the power coming from the left hand friction drum.
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[[Image:electronic calculators - image013.jpg|thumb|right|Figure 7.  Hewlett Packard HP-35 Pocket Calculator.]]
  
[[Image:Differential analyzer 5.jpg|thumb|right|Figure 5: An integrating mechanism from a differential analyzer constructed at Manchester University, EnglandThe steel integrating disk and knife-edge wheel are on the right and torque amplifier on the leftSource: photo by the author.]]
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In 1972 Hewlett Packard introduced the HP-35 (Figure 7), a pocket calculator that performed most of the functions of the Hewlett Packard 9100A at about 1/10th of the priceThis really caught the attention of engineers and scientists.  Originally simply called “the Calculator,” when put in production it was named the HP-35 because it has 35 keys.  It displayed only a single 10-digit number on its red LED display (either the most recent entry or the result of the calculation)The calculator maintained a stack of four internal data registers that minimized the need to enter operands.  Unlike the desktop calculators that used magnetic cores for the data memory, the HP-35 used a small serial shift register implemented on a separate integrated circuit. The data register contents could be accessed by stack manipulation instructions.  Since it was battery powered and small enough to fit into a pocket, the HP-35 was particularly useful for working engineers.  A few years later Hewlett Packard introduced the HP-65, a programmable pocket calculator that used small magnetic strips to store the programs.
  
It was now possible to have several integrating units with their power amplified outputs being mechanically connected together via gears and the final result connected to a plotting table. The usual format was to have several input tables (one for each function being integrated) on one side of the machine.  As human operators followed the graphs with pointers (usually with the aid of magnifying glasses), the output from these tables would be used to position the knife-edge wheel along the radius of the integrating diskThe rotations of the knife-edge disk would be enhanced by the torque amplifiers and fed into an interconnection table of gears and other mechanisms.  These mechanisms could add, subtract, and even multiply together two quantities, and then these would, in turn, be combined with others until the final result was obtained.  The result was usually sent to a plotting table to produce a graphical representation on paper.
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Although initially quite expensive (the HP-35 cost $395.00 when it was introduced in 1972) the prices of engineering pocket calculators dropped rapidly due to competitionAs a result, pocket calculators initiated a dramatic change in the engineering community, as engineers discarded their beloved slide rules for the greater precision of electronic computation.
  
The gearing for the arithmetic operations was well understood.  For example, the gears required to add together two sets of values (rotations) is nothing other than the differential gear mechanism used in rear axle of rear-wheel-drive automobilesSimilar gearing systems were well understood for other types of arithmetic operations.  The only real problem was that gears have backlash.  That is, when a gear is rotated it tends to rotate slightly in the opposite direction when stoppedThis lead to inaccuracies in the final result that became more significant as the number of interconnecting gears increased for complex problems.  This problem was solved by using gears with specially shaped teeth.
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The first electronic calculator (the ANITA) only had memory for the result of the calculation.  The Friden EC-130 with its ultrasonic delay-line memory had enough memory to store previous operands and the resultBoth the Wang LOCI and the Hewlett Packard 9100 had large memories that could hold the operands as well as a sizeable sequence of operations.  In a sense they were like primitive personal computersThe early pocket calculators had very limited memory: the Datamath (and most early pocket calculators) were similar to the ANITA, while the HP-35 had 4 registers (each of which held one operand or result) like the Friden EC-130 although the memory technology was quite different.
  
[[Image:Differential analyzer 6.jpg|thumb|left|Figure 6.  Vannevar Bush examining the interconnection gearing of a differential analyzer at the Aberdeen Proving Ground in Maryland.  The integrating mechanisms are on the far side and one of the input or output tables is immediately behind him.  Source: photo courtesy of MIT.]]
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Similar transitions took place with display technology: first there were mechanical displays, these were displaced by Nixie tubes and cathode ray tube displays. Then these were displaced by light emitting diode displays, which in turn were displaced by liquid-crystal displays.  
  
=== Differential Analyzers in Use ===
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Between 1960 and the early 1970s, large electronic calculators (based on vacuum tubes) displaced electro-mechanical calculators and then were themselves displaced by calculators based on transistors which were eventually displaced by small battery-powered pocket electronic calculators that were based on integrated circuits.  The technology transformation of calculators from mechanical to electromechanical to vacuum tubes to discrete transistors and finally to integrated circuits is typical of the transitions of many products during the 20th century.  The price of the early electronic desktop calculators was two to five times that of the electromechanical calculators, but it was not long before the pocket calculators cost orders of magnitude less.  This, together with their small size and portability, meant that calculators came to be used in many new ways and new contexts.
  
Differential analyzers were one of the main calculating tools in use for solving differential equation problems from the 1930s into the 1950s.  Many different machines were produced, usually with increasing numbers of integrator mechanisms and sophisticated interconnection schemes, in universities and research establishments in Europe and America.  They were heavily used by the military in doing ballistic calculations to produce the tables that were necessary for artillery aiming.  Also, the military used them, or versions of the integrating devices, in such applications as anti-aircraft gun directors and bombsights.  In addition they were valuable in solving problems in meteorology, radio antenna propagation, crystallography, electrical networks, and many other fields.
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=== Acknowledgements ===
  
Perhaps the most sophisticated differential analyzer, known as the RDA2 (Rockefeller Differential Analyzer Number 2), was produced by a group led by Vannevar Bush and funded by the Rockefeller Foundation during the Second World War.  One of the problems with the entirely mechanical versions was that programming the problem to be solved required the dismantling and recreating of all the gearing mechanisms in the middle of the machine.  This process could often take many hours and had to be accomplished with wrenches and other tools.  While not a difficult process, it had to be done with care because any slight slack in the system or even slightly misaligned, loose, or slightly worn gears would introduce unacceptable errors in the results.
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The author thanks members of the STARS Editorial Board and others for careful review and constructive criticism, with special thanks to Frederik Nebeker, Emerson Pugh, and James Cortada for helpful comments and suggestions.
 
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|significance references={{STARSSignificanceRef
The RDA2 overcame these problems by replacing the torque amplifiers with sensors that would detect the rotations of the integrating shaft from the knife-edge wheel and pass these values to other parts of the machine via electrical connections.  The RDA2 used a special device which could read a paper tape describing the connections to be made, then automatically route the correct signals to the required equipment.  This machine was to be used in war-related calculation, and thus Bush was much more concerned with functionality than with cost. Indeed, the cost was so large than no others were ever built. The RDA2 contained 18 integrators and could function at an accuracy of about one part in 1,000 in its calculations—an increase of about a factor of 10 over most differential analyzers at the time.
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|author=Ernst Martin
 
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|year=1992
The existence of this machine, first operational in December 1941, was kept secret during the war. While the machine had been funded and designed prior to America entering World War II, no publicity was given to its completion, and false stories were issued claiming that it had been a failure. It was, in fact, a great success, and it was used in solving countless military problems including such things as tracing back the trajectory of V2 rockets—a calculation that eventually led to the discovery and bombing of their launch site at Peenemünde.
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|title=The Calculating Machines (Die Rechenmaschinen): Their History and Development
 
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|publisher=Translated and edited by P. A. Kidwell and M. R. Williams. Cambridge, MA: MIT Press, 1992
=== Replacement by Electronic Devices ===
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}}{{STARSSignificanceRef
 
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|author=Jack Volder
Prior to the Second World War, the American military had commissioned the construction of differential analyzers similar to Bush’s original machine.  These were used in such places as the Army Ballistics Research Laboratory in Maryland and in institutes that were doing work for various military groups.  One of the most prominent of these non-military institutes was the Moore School of Electrical Engineering in Philadelphia.  They had close connections to the Ballistics Research Laboratory and were also doing work on antenna design and other problems of interest to military groups.  When, during the Second World War, it became necessary to recompute a vast number of artillery tables, the differential analyzer at the Moore School was conscripted by the military to help in this work.  Despite the fact that all such available resources were being used, the tables project was not making fast enough progress, and the Army sought help from any source it could.  This led to a team at the Moore School making a proposal to use vacuum tube electronics to construct a large digital machine capable of integrating the required functions numerically.  This machine, named the Electronic Numerical Integrator and Calculator, or ENIAC for short, was to be used on the tables project. While not completed in time to help with its intended purpose, it showed that the analog methods used by devices such as the differential analyzers could, in principle, be replaced by high speed digital machines.
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|year=1959
 
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|title="The CORDIC Trigonometric Computing Technique"
The use of a digital computer to accurately numerically integrate differential equations usually requires it to execute hundreds of thousands of arithmetic instructions. Initially, computers were hugely expensive undertakings and were, for the most part, constructed only in universities and research establishments on an experimental basis. The limited availability and problematic reliability of these machines meant that they were not an effective alternative for solving many of the engineering problems that were arising immediately after World War II. Even when commercially produced electronic computers were obtainable, they seldom had the speed and cost effectiveness that allowed them to compete in solving differential equation problems with the mechanical analog differential analyzers.  Several differential analyzers were constructed in the 1950s, usually at major universities, and were kept busy solving military, commercial and research problems.  However the development of ever more powerful digital computers meant that, by the early 1960s, most of these problems were being solved on digital computers.
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|publisher=IRE Transactions on Electronic Computers, vol. EC-8, 1959, pp. 330-334
 
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}}{{STARSSignificanceRef
A few attempts were made to create affordable electronic alternatives to the mechanical differential analyzer. The most famous was a machine developed by Northrup Aircraft Inc. in the United States.  Known as a MADDIDA (Magnetic Drum Digital Differential Analyzer), it was entirely electronic, and the information for 44 electronic integrators was contained on tracks on a small magnetic drum.  First developed in 1949 and demonstrated in 1950, it was designed for smaller research and engineering establishments that could not afford either the expense or the space requirements of a traditional mechanical analog machine.  While MADDIDA was an impressive accomplishment, one that received high praise from scientists such as John von Neumann, the Northrup management were more concerned with their other government/military contracts and did little to encourage the MADDIDA creators.  Another firm, spun off from Northrup, did produce several different models of the MADDIDA, including ones for airborne military use, but it never achieved any substantial presence in the research marketplace.  The developing general purpose digital computer soon was in a position to compete with the MADDIDA, and all work on subsequent improvements stopped.
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|author=Jack S. Kilby, Jerry D. Merryman, and James H. Van Tassel
|bibliography={{STARSBibliography|Pauthor1=Vannevar E. Bush and Harold Locke Hazen|Pyear1=November 1927|Ptitle1=Integraph solution of differential equations.|Ppublisher1=Journal of the Franklin Institute, vol. 204, no. 5. The Bush integraph was the precursor to his much more famous differential analyzer, announced in the pages of this same journal in 1931. The integraph described in this paper contained two stages of integration, allowing the solution of second-order differential equations.|Pauthor2=Vannevar E. Bush|Pyear2=October 1931|Ptitle2=The differential analyzer|Ppublisher2=Journal of the Franklin Institute, Philadelphia, PA, vol. 212, no. 4.  While still a professor at MIT, Bush was responsible for the development of the torque amplifier, the mechanism that made it possible to construct an accurate differential analyzer.  His machine was ready for use in 1931, and this paper not only gives construction details but also shows how it might be set up to solve differential equations.|Pauthor3=|Pyear3=|Ptitle3=|Ppublisher3=|Pauthor4=|Pyear4=|Ptitle4=|Ppublisher4=|Pauthor5=|Pyear5=|Ptitle5=|Ppublisher5=|Sauthor1=Bruno Abdank-Abakanowicz|Syear1=1886|Stitle1=Les intégraphes. La courbe intégrale et ses applications. Étude sur un nouveau système d’intégrateurs mécaniques|Spublisher1=Gauthier-Villars, Paris. The integraph (an instrument able to solve elementary differential equations graphically) is an elaboration and extension of the planimeter, an earlier, simpler instrument used to measure area. The book also includes a short discussion of planimeters.  The second half of the book describes advanced applications such as finding moments of inertia and solving problems arising in the design of ships.|Sauthor2=John Crank|Syear2=1947|Stitle2=The Differential Analyzer|Spublisher2=Longmans, Green & Co., London.  In this book, Crank describes both the theory and practical details of the differential analyzer with illustrations from the British versions constructed at Manchester and Cambridge Universities. Of particular interest is a photograph showing part of the first experimental differential analyzer model built at Manchester University by Douglas Hartree and Arthur Porter using a Meccano (known in the United States as Erector) construction set. |Sauthor5=Owens, Larry W.|Syear5=January 1986|Stitle5=Vannevar Bush and the differential analyzer: The text and context of an early computer|Spublisher5=Technology and Culture.|Sauthor4=Mark Bowles|Syear4=1996|Stitle4=U.S. technological enthusiasm and British technological skepticism in the age of the analogue brain|Spublisher4=IEEE Annals of the History of Computing, vol. 18, no. 4.|Sauthor3=H.E. Rose|Syear3=1948|Stitle3=The mechanical differential analyser. Its principles, development and applications.|Spublisher3=In Proceedings of the Institution of Mechanical Engineers, vol. 159, War Emergency Issue no. 38. This is a paper, well illustrated with diagrams and photographs, on the theory and application of differential analyzers.  It covers not only the original Bush machine and the subsequent developments at Manchester (including both the Meccano and full-scale machines) but also the second Bush machine (Rockefeller DA II, which the author refers to as the Bush and Caldwell machine) and such developments as an electrical integrator using a cathode ray tube.|Sauthor6=|Syear6=|Stitle6=|Spublisher6=}}|resume=Michael R. Williams earned a BSc in chemistry from the University of Alberta and a PhD in computer science from the University of Glasgow, Scotland. In 1969 he joined the University of Calgary, first in the Department of Mathematics, and then as a Professor of Computer Science.  The history of computing became his main research and teaching interest.  He has participated in the publishing of 11 books, 88 articles, and 58 technical reviews. He has worked at several different universities, at the National Museum of American History, and, as Head Curator, at the Computer History Museum in Silicon Valley.|complete=1263926}}[[Category:]]
+
|year=1974
 +
|title="Miniature Electronic Calculator"
 +
|publisher=U. S. Patent 3,819,921, 25 June 1974
 +
}}
 +
|reading references={{STARSReadingRef
 +
|author=Earl Swartzlander
 +
|year=2002
 +
|title="Calculating Machines"
 +
|publisher=in Atsushi Akera and Frederik Nebeker, eds., From 0 to 1: An Authoritative History of Modern Computing. New York: Oxford University Press, 2002, pp. 51-62
 +
}}{{STARSReadingRef
 +
|author=Bruce Flamm
 +
|year=1998
 +
|title=“An Early Electronic Calculator, the Friden EC-130”
 +
|publisher=IEEE Annals of the History of Computing, vol. 20, no. 3, 1998, pp. 72-73
 +
}}{{STARSReadingRef
 +
|author=An Wang
 +
|year=1986
 +
|title=Lessons, An Autobiography
 +
|publisher=Reading, MA: Addison-Wesley Publishing Company, Inc., 1986, pp. 125-130
 +
}}{{STARSReadingRef
 +
|author=Chuck House
 +
|year=1988
 +
|title="Hewlett-Packard and Personal Computing Systems"
 +
|publisher=in Adele Goldberg, ed., A History of Personal Workstations. New York: ACM Press, 1988, pp. 403-406
 +
}}{{STARSReadingRef
 +
|author=Guy Ball and Bruce Flamm
 +
|year=1997
 +
|title=The Complete Collector’s Guide to Pocket Calculators
 +
|publisher=Tustin, CA: Wilson/Barnett Publishing, 1997, pp. 10-15
 +
}}
 +
|resume=Earl E. Swartzlander, Jr. holds a B.S.E.E. degree from Purdue University, an M.S.E.E. degree from the University of Colorado, and a Ph.D. in Electrical Engineering from the University of Southern California. In his current position as a Professor of Electrical and Computer Engineering at the University of Texas at Austin, he and his students conduct research in computer engineering with emphasis on application specific processor design, including high-speed computer arithmetic, processor architecture and emerging technologies. He was the Editor-in-Chief of the IEEE Transactions on Computers from 1990-1994 and was the founding Editor-in-Chief of the Journal of VLSI Signal Processing.
 +
|complete=1285615061
 +
}}
 +
[[Category:Computers and information processing]]

Revision as of 14:08, 28 October 2013

Earl Swartzlander

Citation

Starting in 1960, desktop calculators based on vacuum tubes were introduced to replace the mechanical and electromechanical calculators that had been widely used in business, engineering and science. Electronic calculators were more durable, faster, and silent. In the mid-1960s vacuum tubes were replaced by discrete transistors to provide more functionality and greater durability. By the mid-1970s, small battery-powered pocket calculators, implemented with integrated circuits, had replaced desktop calculators and were rapidly replacing the previously indispensable engineering slide rules.

Timeline

1960 ANITA desktop calculator is the first electronic desktop calculator
1963 Friden EC-130 desktop calculator is the first transistorized desktop calculator
1965 Wang LOCI desktop calculator is introduced
1968 HP 9100A Desktop Engineering Calculator is introduced
1972 HP-35, the first pocket engineering calculator, is introduced
1976 TI-30 scientific pocket calculator is introduced

Essay

Starting in 1960 electronic desktop calculators were developed and began replacing the widely used mechanical and electromechanical calculators. By the end of the 1970s, small battery-powered pocket calculators, implemented with integrated circuits, had largely replaced electronic desktop calculators.

Mechanical Calculators

Prior to 1960 there were three general types of calculating devices: mechanical adding machines, calculators (both mechanical and electromechanical), and slide rules. Adding machines were used by accountants, bankers and merchants to add and subtract (often with a paper tape record of the calculation). Successful brands of adding machines were Burroughs, Comptometer and Victor. Calculators were larger units (often about the size of a typewriter) that could add, subtract, multiply, and divide. Calculators were used by engineers and scientists as well as in the business world. Important calculator manufacturers were Friden, Marchant and Monroe. Slide rules were simple mechanical devices used by engineers to multiply, divide, and perform other calculations that are based on logarithms and trigonometric relations. Keuffel & Esser and Pickett were the most common brands.

One of the most significant advances of the 20th century was the replacement of mechanical and electromechanical devices with electronic devices. This technological transition occurred with calculators as well as in many other fields such as television, music players, etc. The earliest machines were mechanical devices. Later machines included an electric motor (hence the term electromechanical) that reduced the effort required to operate the machines. Especially during World War II, large groups of electromechanical calculators (operated by teams of people referred to as “computers”) were used for many purposes, including computing trajectory tables for ballistics and as part of the Manhattan project. In mechanical machines, the inertia of wheels, levers, and shafts severely limit the speed of computation. In contrast, the circuits in the electronic calculators operate at speeds that are limited only by the speed of light. Also mechanical machines are quite noisy, whereas electronic machines are silent. Another important issue is that mechanical devices are susceptible to wear that could cause intermittent errors. Such intermittent errors can be far more devastating than complete failures because the user might get wrong answers without being aware that an error has occurred.

Electronic Desktop Calculators

Figure 1, ANITA Mark VII Desktop Calculator (photo Frank Eggebrecht, used with permission of Nigel Tout of Vintage Calculators Web Museum)
Figure 1, ANITA Mark VII Desktop Calculator (photo Frank Eggebrecht, used with permission of Nigel Tout of Vintage Calculators Web Museum)
Figure 2, Nixie tube (copyright Georg-Johann Lay, used with permission)
Figure 2, Nixie tube (copyright Georg-Johann Lay, used with permission)

The first electronic desktop calculator was the ANITA (the name is an acronym for “A New Inspiration To Accounting”) (Figure 1), designed and produced by Sumlock Comptometer, Ltd. This British company had a line of mechanical calculators, but the ANITA Mk VII that was introduced in 1960 was a radical departure from their previous products. The ANITA used gas-filled thyratron tubes and selenium rectifiers for the logic circuits to perform the computations. The 12-digit display used a Nixie tube (with metal numbers in a neon filled vacuum tube) for each digit (Figure 2). Since the ANITA calculators had no moving parts, they were fast, silent, and needed minimal maintenance. The ANITAs were four-function calculators that could add, subtract, multiply, and divide.

Figure 3.  Friden EC-130 Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).
Figure 3. Friden EC-130 Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).

One of the first transistorized calculators was the Friden EC-130 (Figure 3) introduced in June 1963. It used discrete transistors and diodes for the logic. It used a small cathode-ray tube to display the 13-digit values of four registers. The registers showed the previous entries and result of the calculation. Since there were 4 registers of 13 digits, a sizable memory was required. The EC-130 used a steel-wire ultrasonic delay line for its memory. At one end, the wire was given a small twist for each bit to be stored. The twist propagated along the wire at the relatively slow speed of sound and was detected at the far end. Upon detection, the bit could be used or it could be reentered into the delay line. Like the ANITA, the Friden EC-130 was a four-function calculator. A few years later, Friden introduced the EC-132 that added a square root operation to the four basic functions of the EC-130.

Figure 4.  Wang LOCI Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).
Figure 4. Wang LOCI Desktop Calculator (used with permission of the Old Calculator Museum, http://oldcalculatormuseum.com).

Another transistorized desktop calculator was the Wang LOCI (LOgarithmic Calculating Instrument) (Figure 4), introduced in 1965. By using the factor-combining method of calculating logarithms and anti-logarithms, this calculator provided functions useful for engineering, such as calculating roots and powers. The display unit was separate from the keyboard, and multiple keyboards could be ganged to a single LOCI display unit. Although it pioneered the concept of a programmable calculator, the LOCI was an engineering calculator that was too difficult to use for business and commercial applications. For example, the LOCI produced an answer of 3.999999999 for the multiplication of 2 x 2. While this was not a problem for engineers who were accustomed to slide rules with three digit accuracy, it was not acceptable for most non-technical users. In late 1966, Wang started selling the Model 300 calculator that was better suited for general use. Wang’s experience with the Model 300 led to a line of stand-alone word processors that were very successful in business applications.

Figure 5.  Hewlett Packard 9100A Desktop Calculator.
Figure 5. Hewlett Packard 9100A Desktop Calculator.

The Hewlett Packard 9100A (Figure 5), introduced in 1968, was the ultimate desktop engineering calculator. This calculator was based on a prototype designed by Tom Osborne, who had worked for the Marchant Company, which was one of the pioneers in mechanical and electro-mechanical calculators. The production model (as implemented by Hewlett Packard) used discrete transistors to perform the computations. Like the Friden electronic calculators, it used a small cathode-ray tube to display the contents of three registers. The registers showed the operands and result of each calculation. In addition to the basic four functions, the 9100A provided a full suite of engineering functions, including transcendental, logarithmic and trigonometric functions. To provide the engineering functions, a read-only memory of 32,000 bits was required for the constants needed for the CORDIC algorithms. The read-only memory was constructed with inductive coupling between lines on the two sides of a printed circuit board. Both the Wang LOCI and the HP-9100A used random-access memories (RAM for short) implemented with magnetic cores to hold data and the results of calculations. The RAM could also hold sequences of instructions allowing the machines to be programmed to perform repetitive computations. In fact they could be viewed as small computers with capability similar to the personal computers that were introduced a decade later. The HP- 9100 could store the programs on a magnetic card the size of a credit-card.

Pocket Calculators

Figure 6. Texas Instruments 2500 Datamath Pocket Calculator (used with permission of Nigel Tout of Vintage Calculators Web Museum).
Figure 6. Texas Instruments 2500 Datamath Pocket Calculator (used with permission of Nigel Tout of Vintage Calculators Web Museum).

Starting in the mid-1960s, Texas Instruments began the development of the “Cal-Tech”, a prototype for a handheld four-function electronic calculator with a paper tape to display the results. The Canon Pocketronic battery-powered pocket calculator introduced in 1970 was based on the “Cal-Tech.” In 1972 Texas Instruments began making and selling battery-powered pocket calculators under its own name. The first unit sold under the Texas Instruments name was the TI-2500 Datamath calculator (Figure 6) that was introduced in June 1972. It used light emitting diode (LED) displays with distinctive red numbers that were attractive and easy to read, but consumed a lot of power. Ultimately they were displaced by liquid-crystal displays (LCD) that consume very little power. In the five years after introduction of the Datamath, TI introduced at least 70 different models with a wide range of capabilities. As pocket electronic calculator sales volume increased at an exponential rate, the prices fell: by 1976 the TI-30 scientific pocket calculator was selling for less than $24.95. At this time, desktop four-function calculators had become almost obsolete except for applications that required a record of the calculation.

Figure 7.  Hewlett Packard HP-35 Pocket Calculator.
Figure 7. Hewlett Packard HP-35 Pocket Calculator.

In 1972 Hewlett Packard introduced the HP-35 (Figure 7), a pocket calculator that performed most of the functions of the Hewlett Packard 9100A at about 1/10th of the price. This really caught the attention of engineers and scientists. Originally simply called “the Calculator,” when put in production it was named the HP-35 because it has 35 keys. It displayed only a single 10-digit number on its red LED display (either the most recent entry or the result of the calculation). The calculator maintained a stack of four internal data registers that minimized the need to enter operands. Unlike the desktop calculators that used magnetic cores for the data memory, the HP-35 used a small serial shift register implemented on a separate integrated circuit. The data register contents could be accessed by stack manipulation instructions. Since it was battery powered and small enough to fit into a pocket, the HP-35 was particularly useful for working engineers. A few years later Hewlett Packard introduced the HP-65, a programmable pocket calculator that used small magnetic strips to store the programs.

Although initially quite expensive (the HP-35 cost $395.00 when it was introduced in 1972) the prices of engineering pocket calculators dropped rapidly due to competition. As a result, pocket calculators initiated a dramatic change in the engineering community, as engineers discarded their beloved slide rules for the greater precision of electronic computation.

The first electronic calculator (the ANITA) only had memory for the result of the calculation. The Friden EC-130 with its ultrasonic delay-line memory had enough memory to store previous operands and the result. Both the Wang LOCI and the Hewlett Packard 9100 had large memories that could hold the operands as well as a sizeable sequence of operations. In a sense they were like primitive personal computers. The early pocket calculators had very limited memory: the Datamath (and most early pocket calculators) were similar to the ANITA, while the HP-35 had 4 registers (each of which held one operand or result) like the Friden EC-130 although the memory technology was quite different.

Similar transitions took place with display technology: first there were mechanical displays, these were displaced by Nixie tubes and cathode ray tube displays. Then these were displaced by light emitting diode displays, which in turn were displaced by liquid-crystal displays.

Between 1960 and the early 1970s, large electronic calculators (based on vacuum tubes) displaced electro-mechanical calculators and then were themselves displaced by calculators based on transistors which were eventually displaced by small battery-powered pocket electronic calculators that were based on integrated circuits. The technology transformation of calculators from mechanical to electromechanical to vacuum tubes to discrete transistors and finally to integrated circuits is typical of the transitions of many products during the 20th century. The price of the early electronic desktop calculators was two to five times that of the electromechanical calculators, but it was not long before the pocket calculators cost orders of magnitude less. This, together with their small size and portability, meant that calculators came to be used in many new ways and new contexts.

Acknowledgements

The author thanks members of the STARS Editorial Board and others for careful review and constructive criticism, with special thanks to Frederik Nebeker, Emerson Pugh, and James Cortada for helpful comments and suggestions.

Bibliography

References of Historical Significance

Ernst Martin. 1992. The Calculating Machines (Die Rechenmaschinen): Their History and Development. Translated and edited by P. A. Kidwell and M. R. Williams. Cambridge, MA: MIT Press, 1992

Jack Volder. 1959. "The CORDIC Trigonometric Computing Technique". IRE Transactions on Electronic Computers, vol. EC-8, 1959, pp. 330-334

Jack S. Kilby, Jerry D. Merryman, and James H. Van Tassel. 1974. "Miniature Electronic Calculator". U. S. Patent 3,819,921, 25 June 1974

References for Further Reading

Earl Swartzlander. 2002. "Calculating Machines". in Atsushi Akera and Frederik Nebeker, eds., From 0 to 1: An Authoritative History of Modern Computing. New York: Oxford University Press, 2002, pp. 51-62

Bruce Flamm. 1998. “An Early Electronic Calculator, the Friden EC-130”. IEEE Annals of the History of Computing, vol. 20, no. 3, 1998, pp. 72-73

An Wang. 1986. Lessons, An Autobiography. Reading, MA: Addison-Wesley Publishing Company, Inc., 1986, pp. 125-130

Chuck House. 1988. "Hewlett-Packard and Personal Computing Systems". in Adele Goldberg, ed., A History of Personal Workstations. New York: ACM Press, 1988, pp. 403-406

Guy Ball and Bruce Flamm. 1997. The Complete Collector’s Guide to Pocket Calculators. Tustin, CA: Wilson/Barnett Publishing, 1997, pp. 10-15

About the Author(s)

Earl E. Swartzlander, Jr. holds a B.S.E.E. degree from Purdue University, an M.S.E.E. degree from the University of Colorado, and a Ph.D. in Electrical Engineering from the University of Southern California. In his current position as a Professor of Electrical and Computer Engineering at the University of Texas at Austin, he and his students conduct research in computer engineering with emphasis on application specific processor design, including high-speed computer arithmetic, processor architecture and emerging technologies. He was the Editor-in-Chief of the IEEE Transactions on Computers from 1990-1994 and was the founding Editor-in-Chief of the Journal of VLSI Signal Processing.