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

2. History 398 Fall 2004 ENIAC - 1946

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

4. History 398 Fall 2004 1945

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)

7. History 398 Fall 2004 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

8. History 398 Fall 2004 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 -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 )

9. History 398 Fall 2004 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)?

10. History 398 Fall 2004 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)

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

12. History 398 Fall 2004 Turing Machine 10 0 11 11 1 1 0 00 0 State Table R/W Head current state input output next state shift L/R Alan M. Turing *38 (1912-54)

13. History 398 Fall 2004 Copy 1R1 1 1 1R2 2L3 2 1 1R2 3S 31R4 4R5 411R4 51L6 511R5 6L7 611L6 71L3 711L1

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

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

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