History 398 Fall 2004

History 398 Lecture 20

FROM ENIAC TO EDVAC

History 398 Fall 2004

ENIAC - 1946

History 398 Fall 2004

telephone switches

relay calculator

vacuum tubes

binary arithmeticmechanical calculation

ENIAC

analog calculation

differential analyzer

digital calculation

electronic diff’l analyzer

decimal ring counter

IBM electrical accounting machinery

card reader and punch

organizationof computation

tabulation

History 398 Fall 2004

1945

History 398 Fall 2004

History 398 Fall 2004

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

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

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 )

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)?

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)

History 398 Fall 2004

Gottlob Frege (1848-1925)

Bertrand Russell (1872-1970)

Kurt Gödel (1906-78)

History 398 Fall 2004

Turing Machine

1

0 01

1

1

1

1

1

0000

StateTable

R/W

H

ead

currentstate

input

output nextstate

shiftL/R

Alan M. Turing *38 (1912-54)

History 398 Fall 2004

Copy

1 R 11 1 1 R 22 L 32 1 1 R 23 S 3 1 R 44 R 54 1 1 R 45 1 L 65 1 1 R 56 L 76 1 1 L 67 1 L 37 1 1 L 1

History 398 Fall 2004

CControl

CArithmeticI

J

Memory

Recording

John von Neumann et al., EDVAC Architecture

+ A I + J- A I - J* A A + I*J/ A I/Ji A Ij A Js A (A >= 0 ? I : J)

(A) O

msm 98

Circuit diagram from the John W. Mauchly PapersUniversity of Pennsylvania

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. i0 = 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. i0 = 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)

History 398 Fall 2004

EDSAC, Cambridge University, 1949