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Early computing machines had fixed programs. Changing its function required the re-wiring and re-structuring of the machine. With the proposal of the stored-program computer this changed. A stored-program computer includes by design an instruction set and can store in memory a set of instructions (a program) that details the computation. The theoretical basis for the stored-program computer was laid by Alan Turing in his 1936 paper. In 1945 Turing joined the National Physical Laboratory and began work on developing an electronic stored-program digital computer. His 1945 report "Proposed Electronic Calculator" was the first specification for such a device. John von Neumann at the University of Pennsylvania also circulated his First Draft of a Report on the EDVAC in 1945.

The Manchester Small-Scale Experimental Machine, nicknamed Baby, was the world's first stored-program computer. It was built at the Victoria University of Manchester by Frederic C. Williams, Tom Kilburn and Geoff Tootill, and ran its first program on 21 June 1948. It was designed as a testbed for the Williams tube, the first random-access digital storage device. Although the computer was considered "small and primitive" by the standards of its time, it was the first working machine to contain all of the elements essential to a modern electronic computer. As soon as the SSEM had demonstrated the feasibility of its design, a project was initiated at the university to develop it into a more usable computer, the Manchester Mark 1.

The bipolar transistor was invented in 1947. From 1955 onwards transistors replaced vacuum tubes in computer designs, giving rise to the "second generation" of computers. Compared to vacuum tubes, transistors have many advantages: they are smaller, and require less power than vacuum tubes, so give off less heat. Silicon junction transistors were much more reliable than vacuum tubes and had longer, indefinite, service life. Transistorized computers could contain tens of thousands of binary logic circuits in a relatively compact space.

At the University of Manchester, a team under the leadership of Tom Kilburn designed and built a machine using the newly developed transistors instead of valves.Lavington, Simon (1998), A History of Manchester Computers (2 ed.), Swindon: The British Computer Society, pp. 34-35 Their first transistorised computer and the first in the world, was operational by 1953, and a second version was completed there in April 1955. However, the machine did make use of valves to generate its 125 kHz clock waveforms and in the circuitry to read and write on its magnetic drum memory, so it was not the first completely transistorized computer. That distinction goes to the Harwell CADET of 1955, Cooke-Yarborough, E. H. (June 1998), "Some early transistor applications in the UK", Engineering and Science Education Journal, London, UK: IEE, 7 (3): 100-106 built by the electronics division of the Atomic Energy Research Establishment at Harwell. Cooke-Yarborough, E. H. (June 1998), "Some early transistor applications in the UK", Engineering and Science Education Journal, London, UK: IEE, 7 (3): 100-106 Cooke-Yarborough, E.H. (1957). Introduction to Transistor Circuits. Edinburgh: Oliver and Boyd. p. 139.

The next great advance in computing power came with the advent of the integrated circuit. The idea of the integrated circuit was first conceived by a radar scientist working for the Royal Radar Establishment of the Ministry of Defence, Geoffrey W.A. Dummer. Dummer presented the first public description of an integrated circuit at the Symposium on Progress in Quality Electronic Components in Washington, D.C. on 7 May 1952

The first practical ICs were invented by Jack Kilby at Texas Instruments and Robert Noyce at Fairchild Semiconductor. Kilby recorded his initial ideas concerning the integrated circuit in July 1958, successfully demonstrating the first working integrated example on 12 September 1958. In his patent application of 6 February 1959, Kilby described his new device as "a body of semiconductor material ... wherein all the components of the electronic circuit are completely integrated". Noyce also came up with his own idea of an integrated circuit half a year later than Kilby. His chip solved many practical problems that Kilby's had not. Produced at Fairchild Semiconductor, it was made of silicon, whereas Kilby's chip was made of germanium.

This new development heralded an explosion in the commercial and personal use of computers and led to the invention of the microprocessor. While the subject of exactly which device was the first microprocessor is contentious, partly due to lack of agreement on the exact definition of the term "microprocessor", it is largely undisputed that the first single-chip microprocessor was the Intel 4004, designed and realized by Ted Hoff, Federico Faggin, and Stanley Mazor at Intel.

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