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History 398 Lecture 20 FROM ENIAC TO EDVAC

History 398 Lecture 20 FROM ENIAC TO EDVAC. ENIAC - 1946. digital calculation. telephone switches. binary arithmetic. mechanical calculation. relay calculator. decimal ring counter. ENIAC. vacuum tubes. electronic diff’l analyzer. card reader and punch. organization of computation.

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History 398 Lecture 20 FROM ENIAC TO EDVAC

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  1. History 398 Lecture 20FROM ENIAC TO EDVAC History 398 Fall 2004

  2. ENIAC - 1946 History 398 Fall 2004

  3. digital calculation telephone switches binary arithmetic mechanical calculation relay calculator decimal ring counter ENIAC vacuum tubes electronic diff’l analyzer card reader and punch organization of computation differential analyzer IBM electrical accounting machinery analog calculation tabulation History 398 Fall 2004

  4. 1945 History 398 Fall 2004

  5. History 398 Fall 2004

  6. The Stored-Program Computer • John von Neumann (1903-1957) • joined ENIAC toward end • What he saw in the device (his "reading"): "First Draft of a Report on the EDVAC" (1945) History 398 Fall 2004

  7. The Stored-Program Computer • John von Neumann (1903-1957) • Warren McCulloch and Walter Pitts, "A logical calculus of the ideas immanent in nervous activity" (1943) • nerve nets modeled as binary units are in turn model of propositional and quantificational logic, therefore • equivalent to Turing Machine History 398 Fall 2004

  8. Nerve Nets and Turing Machines One more thing is to be remarked in conclusion. It is easily shown: first, that every net, if furnished with a tape, scanners connected to afferents, and suitable efferents to perform the necessary motor-operations, can compute only such numbers as can a Turing machine; second, that each of the latter numbers can be computed by such a net; and that nets with circles can be computed by such a net; and that nets with circles can compute, without scanners and a tape, some of the numbers the machine can, but no others, and not all of them. This is of interest as affording a psychological justification of the Turing definition of computability and its equivalents, Church's l-definability, and Kleene's primitive recursiveness: If any number can be computed by an organism, it is computable by these definitions, and conversely. (McCulloch and Pitts, p.129 ) History 398 Fall 2004

  9. Alan Turing (1912-1954) and Turing Machines • "On computable numbers, with an application to the Entscheidungsproblem" (1936) • Three central questions concerning the foundations of mathematics: • consistent? • complete? • decidable (Entscheidungsproblem)? History 398 Fall 2004

  10. To Boole and Back • George Boole (1815-64) • An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (1854) • Boolean algebra as (symbolic) algebra of logic • Logic of mathematics • Gottlob Frege, Begriffschrift (1879) • Bertrand Russell and Alfred North Whitehead, Principia mathematica (1910) • Kurt Gödel, “On formally undecidable propositions of Principia mathematica and related systems" (1931) History 398 Fall 2004

  11. Kurt Gödel (1906-78) Gottlob Frege (1848-1925) Bertrand Russell (1872-1970) History 398 Fall 2004

  12. R/W Head 0 0 1 1 0 1 0 1 0 1 1 1 0 current state shift L/R next state input output State Table Turing Machine Alan M. Turing *38 (1912-54) History 398 Fall 2004

  13. Copy 1 R 1 1 1 1 R 2 2 L 3 2 1 1 R 2 3 S 3 1 R 4 4 R 5 4 1 1 R 4 5 1 L 6 5 1 1 R 5 6 L 7 6 1 1 L 6 7 1 L 3 7 1 1 L 1 History 398 Fall 2004

  14. John von Neumann et al., EDVAC Architecture CControl    I CArithmetic (A) O J   Memory Recording + A I + J - A  I - J * A  A + I*J / A  I/J i A  I j A  J s A  (A >= 0 ? I : J) Circuit diagram from the John W. Mauchly Papers University of Pennsylvania History 398 Fall 2004 msm 98

  15. Modifying stored commands Remark: Orders w (or wh) ®mr (or f) transfer a standard number x', from CA into a minor cycle. If this minor cycle is of the type Nx (i.e. i0 = 0), then it should clear its 31 digits representing x and accept the 31 digits of x [x']. If it is a minor cycle ending in mr (i.e. i0 = 1, order w ® mr or wh ® mr or A ¬ mr or C ¬ mr), then it should clear only its 13 digits representing mr, and accept the last 13 digits of x'. (Papers, 82) History 398 Fall 2004

  16. EDSAC, Cambridge University, 1949 History 398 Fall 2004

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