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onardo 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 a fully electronic analog computer was built by helmut hölzer in 1942 at peenemünde army research center 68 69 70 by the 1950s the success of digital electronic computers had spelled the end for most analog computing machines but hybrid analog computers controlled by digital electronics remained in substantial use into the 1950s and 1960s and later in some specialized applications advent of the digital computer edit parts from four early computers 1962 from left to right eniac board edvac board ordvac board and brlesc i board showing the trend toward miniaturization the principle of the modern computer was first described by computer scientist alan turing who set out the idea in his seminal 1936 paper 71 on computable numbers turing reformulated kurt gödel s 1931 results on the limits of proof and computation replacing gödel s universal arithmetic based formal language with the formal and simple hypothetical devices that became known as turing machines he proved that some such machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm he went on to prove that there was no solution to the entscheidungsproblem by first showing that the halting problem for turing machines is undecidable in general it is not possible to decide algorithmically whether a given turing machine will ever halt he also introduced the notion of a universal machine now known as a universal turing machine with the idea that such a machine could perform the tasks of any other machine or in other words it is provably capable of computing anything that is computable by executing a program stored on tape allowing the machine to be programmable john von neumann acknowledged that the central concept of the modern computer was due to this paper 72 turing machines are to this day a central object of study in theory of computation except for the limitations imposed by their finite memory stores modern computers are said to be turing complete which is to say they have algorithm execution capability equivalent to a universal turing machine electromechanical computers edit further information mechanical computer electro mechanical computers the era of modern computing began with a flurry of development before and during world war ii most digital computers built in this period were electromechanical electric switches drove mechanical relays to perform the calculation these mechanical components had a low operating speed due to their mechanical nature and were eventually superseded by much faster all electric components originally using vacuum tubes and later transistors the z2 was one of the earliest examples of an electric operated digital computer built with electromechanical relays and was created by civil engineer konrad zuse in 1940 in germany it was an improvement on his earlier mechanical z1 although it used the same mechanical memory it replaced the arithmetic and control logic with electrical relay circuits 73 in the same year electro mechanical devices called bombes were built by british cryptologists to help decipher german enigma machine encrypted secret messages during world war ii the bombe s initial design was created in 1939 at the uk government code and cypher school at bletchley park by alan turing 74 with an important refinement devised in 1940 by gordon welchman 75 the engineering design and construction was the work of harold keen of the british tabulating machine company it was a substantial development from a device that had been designed in 1938 by polish cipher bureau cryptologist marian rejewski and known as the cryptologic bomb polish bomba kryptologiczna replica of zuse s z3 the first fully automatic digital electromechanical computer in 1941 zuse followed his earlier machine up with the z3 73 the world s first working electromechanical programmable fully automatic digital computer 76 the z3 was built with 2000 relays implementing a 22 bit word length that operated at a clock frequency of about 5 10 hz 77 program code and data were stored on punched film it was similar to modern machines in several respects pioneering numerous advances such as floating point numbers replacement of the hard to implement decimal system used in charles babbage s earlier design by the simpler binary system meant that zuse s machines were easier to build and potentially more reliable given the technologies available at that time 78 despite lacking explicit conditional execution the z3 was proven to have been a theoretically turing complete machine in 1998 by raúl rojas 79 in two 1936 patent applications zuse also anticipated that machine instructions could be stored in the same storage used for data the key insight of what became known as the von neumann architecture first implemented in 1948 in america in the electromechanical ibm ssec and in britain in the fully electronic manchester baby 80 zuse suffered setbacks during world war ii when some of his machines were destroyed in the course of allied bombing campaigns apparently his work remained largely unknown to engineers in the uk and us until much later although at least ibm was aware of it as it financed his post war startup company in 1946 in return for an option on zuse s patents in 1944 the harvard mark i was constructed at ibm s endicott laboratories 81 it was a similar general purpose electro mechanical computer to the z3 but was not quite turing complete digital computation edit the term digital was first suggested by george robert stibitz and refers to where a signal such as a voltage is not used to directly represent a value as it would be in an analog computer but to encode it in november 1937 stibitz then working at bell labs 1930 1941 82 completed a relay based calculator he later dubbed the model k for k itchen table on which he had assembled it which became the first binary adder 83 typically signals have two states low usually representing 0 and high usually representing 1 but sometimes three valued logic is used especially in high density memory modern computers generally use binary logic but many early machines were decimal computers in these machines the basic unit of data was the decimal digit encoded in one of several schemes including binary coded decimal or bcd bi quinary excess 3 and two out of five code the mathematical basis of digital computing is boolean algebra developed by the british mathematician george boole in his work the laws of thought published in 1854 his boolean algebra was further refined in the 1860s by william jevons and charles sanders peirce and was first presented systematically by ernst schröder and a n whitehead 84 in 1879 gottlob frege developed the formal approach to logic and proposes the first logic language for logical equations 85 in the 1930s and working independently american electronic engineer claude shannon and soviet logician victor shestakov both showed a one to one correspondence between the concepts of boolean logic and certain electrical circuits now called logic gates which are now ubiquitous in digital computers 86 they showed that electronic relays and switches can realize the expressions of boolean algebra 87 this thesis essentially founded practical digital circuit design in addition shannon s paper gives a correct circuit diagram for a 4 bit digital binary adder 88 electronic data processing edit atanasoff berry computer replica at first floor of durham center iowa state university purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents at the same time that digital calculation replaced analog machines such as the z3 the atanasoff berry computer the colossus computers and the eniac were built by hand using circuits containing relays or valves vacuum tubes and often used punched cards or punched paper tape for input and as the main non volatile storage medium 89 engineer tommy flowers joined the telecommunications branch of the general post office in 1926 while working at the research station in dollis hill in the 1930s he began to explore the possible use of electronics for the telephone exchange experimental equipment that he built in 1934 went into operation 5 years later converting a portion of the telephone exchange network into an electronic data processing system using thousands of vacuum tubes 61 in the us in 1940 arthur dickinson ibm invented the first digital electronic computer 90 this calculating device was fully electronic control calculations and output the first electronic display 91 john vincent atanasoff and clifford e berry of iowa state university developed the atanasoff berry computer abc in 1942 92 the first binary electronic digital calculating device 93 this design was semi electronic electro mechanical control and electronic calculations and used about 300 vacuum tubes with capacitors fixed in a mechanically rotating drum for memory however its paper card writer reader was unreliable and the regenerative drum contact system was mechanical the machine s special purpose nature and lack of changeable stored program distinguish it from modern computers 94 computers whose logic was primarily built using vacuum tubes are now known as first generation computers the electronic programmable computer edit main articles colossus computer and eniac colossus was the first electronic digital programmable computing device and was used to break german ciphers during world war ii it remained unknown as a military secret well into the 1970s during world war ii british codebreakers at bletchley park 40 miles 64 km north of london achieved a number of successes at breaking encrypted enemy military communications the german encryption machine enigma was first attacked with the help of the electro mechanical bombes 95 they ruled out possible enigma settings by performing chains of logical deductions implemented electrically most possibilities led to a contradiction and the few remaining could be tested by hand the germans also developed a series of teleprinter encryption systems quite different from enigma the lorenz sz 40 42 machine was used for high level army communications code named tunny by the british the first intercepts of lorenz messages began in 1941 as part of an attack on tunny max newman and his colleagues developed the heath robinson a fixed function machine to aid in code breaking 96 tommy flowers a senior engineer at the post office research station 97 was recommended to max newman by alan turing 98 and spent eleven months from early february 1943 designing and building the more flexible colossus computer which superseded the heath robinson 99 100 after a functional test in december 1943 colossus was shipped to bletchley park where it was delivered on 18 january 1944 101 and attacked its first message on 5 february 102 by the time germany surrendered in may 1945 there were ten colossi working at bletchley park 103 wartime photo of colossus no 10 colossus was the world s first electronic digital programmable computer 61 it used a large number of valves vacuum tubes it had paper tape input and was capable of being configured to perform a variety of boolean logical operations on its data 104 but it was not turing complete data input to colossus was by photoelectric reading of a paper tape transcription of the enciphered intercepted message this was arranged in a continuous loop so that it could be read and re read multiple times there being no internal store for the data the reading mechanism ran at 5 000 characters per second with the paper tape moving at 40 ft s 12 2 m s 27 3 mph colossus mark 1 contained 1500 thermionic valves tubes but mark 2 with 2400 valves and five processors in parallel was both 5 times faster and simpler to operate than mark 1 greatly speeding the decoding process mark 2 was designed while mark 1 was being constructed allen coombs took over leadership of the colossus mark 2 project when tommy flowers moved on to other projects 105 the first mark 2 colossus became operational on 1 june 1944 just in time for the allied invasion of normandy on d day most of the use of colossus was in determining the start positions of the tunny rotors for a message which was called wheel setting colossus included the first ever use of shift registers and systolic arrays enabling five simultaneous tests each involving up to 100 boolean calculations this enabled five different possible start positions to be examined for one transit of the paper tape 106 as well as wheel setting some later colossi included mechanisms intended to help determine pin patterns known as wheel breaking both models were p...
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