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ulations that involved multiplication and division d a modern slide rule since real numbers can be represented as distances or intervals on a line the slide rule was invented in the 1620s shortly after napier s work to allow multiplication and division operations to be carried out significantly faster than was previously possible 15 edmund gunter built a calculating device with a single logarithmic scale at the university of oxford his device greatly simplified arithmetic calculations including multiplication and division william oughtred greatly improved this in 1630 with his circular slide rule he followed this up with the modern slide rule in 1632 essentially a combination of two gunter rules held together with the hands slide rules were used by generations of engineers and other mathematically involved professional workers until the invention of the pocket calculator 16 mechanical calculators edit in 1609 guidobaldo del monte made a mechanical multiplier to calculate fractions of a degree based on a system of four gears the rotation of an index on one quadrant corresponds to 60 rotations of another index on an opposite quadrant 17 thanks to this machine errors in the calculation of first second third and quarter degrees can be avoided guidobaldo is the first to document the use of gears for mechanical calculation wilhelm schickard a german polymath designed a calculating machine in 1623 which combined a mechanized form of napier s rods with the world s first mechanical adding machine built into the base because it made use of a single tooth gear there were circumstances in which its carry mechanism would jam 18 a fire destroyed at least one of the machines in 1624 and it is believed schickard was too disheartened to build another view through the back of pascal s calculator pascal invented his machine in 1642 in 1642 while still a teenager blaise pascal started some pioneering work on calculating machines and after three years of effort and 50 prototypes 19 he invented a mechanical calculator 20 21 he built twenty of these machines called pascal s calculator or pascaline in the following ten years 22 nine pascalines have survived most of which are on display in european museums e a continuing debate exists over whether schickard or pascal should be regarded as the inventor of the mechanical calculator and the range of issues to be considered is discussed elsewhere 23 a set of john napier s calculating tables from around 1680 gottfried wilhelm von leibniz invented the stepped reckoner and his famous stepped drum mechanism around 1672 he attempted to create a machine that could be used not only for addition and subtraction but would use a moveable carriage to enable multiplication and division leibniz once said it is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used 24 however leibniz did not incorporate a fully successful carry mechanism leibniz also described the binary numeral system 25 a central ingredient of all modern computers however up to the 1940s many subsequent designs including charles babbage s machines of 1822 and even eniac of 1945 were based on the decimal system f detail of an arithmometer built before 1851 the one digit multiplier cursor ivory top is the leftmost cursor around 1820 charles xavier thomas de colmar created what would over the rest of the century become the first successful mass produced mechanical calculator the thomas arithmometer it could be used to add and subtract and with a moveable carriage the operator could also multiply and divide by a process of long multiplication and long division 26 it utilised a stepped drum similar in conception to that invented by leibniz mechanical calculators remained in use until the 1970s punched card data processing edit in 1804 french weaver joseph marie jacquard developed a loom in which the pattern being woven was controlled by a paper tape constructed from punched cards the paper tape could be changed without altering the mechanical design of the loom this was a landmark achievement in programmability his machine was an improvement over similar weaving looms punched cards were preceded by punch bands as in the machine proposed by basile bouchon these bands would inspire information recording for automatic pianos and more recently numerical control machine tools ibm punched card accounting machines 1936 in the late 1880s the american herman hollerith invented data storage on punched cards that could then be read by a machine 27 to process these punched cards he invented the tabulator and the keypunch machine his machines used electromechanical relays and counters 28 hollerith s method was used in the 1890 united states census that census was processed two years faster than the prior census had been 29 hollerith s company eventually became the core of ibm by 1920 electromechanical tabulating machines could add subtract and print accumulated totals 30 machine functions were directed by inserting dozens of wire jumpers into removable control panels when the united states instituted social security in 1935 ibm punched card systems were used to process records of 26 million workers 31 punched cards became ubiquitous in industry and government for accounting and administration leslie comrie s articles on punched card methods 32 and w j eckert s publication of punched card methods in scientific computation in 1940 described punched card techniques sufficiently advanced to solve some differential equations or perform multiplication and division using floating point representations all on punched cards and unit record machines 33 such machines were used during world war ii for cryptographic statistical processing 34 as well as a vast number of administrative uses the astronomical computing bureau of columbia university performed astronomical calculations representing the state of the art in computing 35 36 calculators edit main article calculator the curta calculator could also do multiplication and division by the 20th century earlier mechanical calculators cash registers accounting machines and so on were redesigned to use electric motors with gear position as the representation for the state of a variable the word computer was a job title assigned to primarily women who used these calculators to perform mathematical calculations 37 by the 1920s british scientist lewis fry richardson s interest in weather prediction led him to propose human computers and numerical analysis to model the weather to this day the most powerful computers on earth are needed to adequately model its weather using the navier stokes equations 38 companies like friden marchant calculator and monroe made desktop mechanical calculators from the 1930s that could add subtract multiply and divide 39 in 1948 the curta was introduced by austrian inventor curt herzstark it was a small hand cranked mechanical calculator and as such a descendant of gottfried leibniz s stepped reckoner and thomas arithmometer the world s first all electronic desktop calculator was the british bell punch anita released in 1961 40 41 it used vacuum tubes cold cathode tubes and dekatrons in its circuits with 12 cold cathode nixie tubes for its display the anita sold well since it was the only electronic desktop calculator available and was silent and quick the tube technology was superseded in june 1963 by the u s manufactured friden ec 130 which had an all transistor design a stack of four 13 digit numbers displayed on a 5 inch 13 cm crt and introduced reverse polish notation rpn first proposed general purpose computing device edit main article analytical engine a portion of babbage s difference engine trial model of a part of the analytical engine built by babbage as displayed at the science museum london the industrial revolution late 18th to early 19th century had a significant impact on the evolution of computing hardware as the era s rapid advancements in machinery and manufacturing laid the groundwork for mechanized and automated computing industrial needs for precise large scale calculations especially in fields such as navigation engineering and finance prompted innovations in both design and function setting the stage for devices like charles babbage s difference engine 1822 42 43 this mechanical device was intended to automate the calculation of polynomial functions and represented one of the earliest applications of computational logic 44 babbage often regarded as the father of the computer envisioned a fully mechanical system of gears and wheels powered by steam capable of handling complex calculations that previously required intensive manual labor 45 his difference engine designed to aid navigational calculations ultimately led him to conceive the analytical engine in 1833 46 this concept far more advanced than his difference engine included an arithmetic logic unit control flow through conditional branching and loops and integrated memory 47 babbage s plans made his analytical engine the first general purpose design that could be described as turing complete in modern terms 48 49 the analytical engine was programmed using punched cards a method adapted from the jacquard loom invented by joseph marie jacquard in 1804 which controlled textile patterns with a sequence of punched cards 50 these cards became foundational in later computing systems as well 51 babbage s machine would have featured multiple output devices including a printer a curve plotter and even a bell demonstrating his ambition for versatile computational applications beyond simple arithmetic 52 ada lovelace expanded on babbage s vision by conceptualizing algorithms that could be executed by his machine 53 her notes on the analytical engine written in the 1840s are now recognized as the earliest examples of computer programming 54 lovelace saw potential in computers to go beyond numerical calculations predicting that they might one day generate complex musical compositions or perform tasks like language processing 55 although babbage s designs were never fully realized due to technical and financial challenges they influenced a range of subsequent developments in computing hardware notably in the 1890s herman hollerith adapted the idea of punched cards for automated data processing which was utilized in the u s census and sped up data tabulation significantly bridging industrial machinery with data processing 56 the industrial revolution s advancements in mechanical systems demonstrated the potential for machines to conduct complex calculations influencing engineers like leonardo torres quevedo and vannevar bush in the early 20th century torres quevedo designed an electromechanical machine with floating point arithmetic 57 while bush s later work explored electronic digital computing 58 by the mid 20th century these innovations paved the way for the first fully electronic computers 59 analog computers edit main article analog computer further information mechanical computer sir william thomson s third tide predicting machine design 1879 81 in the first half of the 20th century analog computers were considered by many to be the future of computing these devices used the continuously changeable aspects of physical phenomena such as electrical mechanical or hydraulic quantities to model the problem being solved in contrast to digital computers that represented varying quantities symbolically as their numerical values change as an analog computer does not use discrete values but rather continuous values processes cannot be reliably repeated with exact equivalence as they can with turing machines 60 the first modern analog computer was a tide predicting machine invented by sir william thomson later lord kelvin in 1872 it used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location and was of great utility to navigation in shallow waters his device was the foundation for further developments in analog computing 61 the differential analyser a mechanical analog computer designed to solve differential equations by integration using wheel and disc mechanisms was conceptualized in 1876 by james thomson the brother of the more famous lord kelvin he explored the possible construction of such calculators but was stymied by the limited output torque of the ball and disk integrators 62 in a differential analyzer the output of one integrator drove the input of the next integrator or a graphing output a notable series of analog calculating machines were developed by leonardo torres quevedo since 1895 including one that was able to compute the roots of arbitrary polynomials of order eight including the complex ones with a precision down to thousandths 63 64 65 a mk i drift sight the lever just in front of the bomb aimer s fingertips sets the altitude the wheels near his knuckles set the wind and airspeed an important advance in analog computing was the development of the first fire control systems for long range ship gunlaying when gunnery ranges increased dramatically in the late 19th century it was no longer a simple matter of calculating the proper aim point given the flight times of the shells various spotters on board the ship would relay distance measures and observations to a central plotting station there the fire direction teams fed in the location speed and direction of the ship and its target as well as various adjustments for coriolis effect weather effects on the air and other adjustments the computer would then output a firing solution which would be fed to the turrets for laying in 1912 british engineer arthur pollen developed the first electrically powered mechanical analogue computer called at the time the argo clock citation needed it was used by the imperial russian navy in world war i citation needed the alternative dreyer table fire control system was fitted to british capital ships by mid 1916 mechanical devices were also used to aid the accuracy of aerial bombing drift sight was the first such aid developed by harry wimperis in 1916 for the royal naval air service it measured the wind speed from the air and used that measurement to calculate the wind s effects on the trajectory of the bombs the system was later improved with the course setting bomb sight and reached a climax with world war ii bomb sights mark xiv bomb sight raf bomber command and the norden 66 united states army air forces the art of mechanical analog computing reached its zenith with the differential analyzer 67 built by h l hazen and vannevar bush at mit starting in 1927 which built on the mechanical integrators of james thomson and the torque amplifiers invented by h w nieman a dozen of these devices were built before their obsolescence became obvious the most powerful was constructed at the university of pennsylvania s moore school of electrical engineering where the eniac was built ...
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