chapter 1 introducing the universal...

©

Christian Jacob

Chapter Overview

Chapter 1

Introducing the Universal Machine

1.1 The Very Idea of the Universal Machine

1.1.1 Universal versus Special-Purpose Machines

1.1.2 What is a “Computer”?

1.1.3 Areas of Computer Science

1.1.4 Early Devices to Facilitate Numerical Operations

1.1.5 Babbage’s Engines

1.1.6 Babbage’s Idea and Modern Computers

1.2 Turing’s Symbol Manipulator

1.3 References

Chapter 1: Introducing the Universal Machine

© Christian Jacob

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Machine

l-manipulating ent as a

program

.

eps.

ersal machine.

chines

he following

r, piano

First Back TOC The Very Idea of the Universal Machine

1.1 The Very Idea of the Universal

A universal machine is a general-purpose symbomachine, capable of any task that one can repres

A

program

is an organized sequence of logical st

Any actual computer approximates an ideal univ

1.1.1 Universal versus Special-Purpose Ma

What are the differences and commonalities of t“machines”?

• car, microwave oven, TV set, CD player, elevato

• pocket calculator, game boy, computer

Chapter 1: Introducing the Universal Machine © Christian Jacob

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reckon´)

alculate ???

cifically a person ry, in surveying,

ions ... (Grolier

essing data (usually to it in a variable

Edition).


1.1.2 What is a “Computer”?

to compute: (Latin computare; as COM-, putare ´

Computer Science = Science of how to

C

Computer:

• One who computes, a calculator, reckoner, speemployed to make calculations in an observatoetc.” (

Oxford English Dictionary, 1926).

• An apparatus built to perform routine calculat

Multimedia Encyclopedia, 1993).

• A usually electronic device for

storing

and

proc

in binary form), according to

instructions

given

program

” (

The Concise Oxford Dictionary, 9th


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formation:

mputers


Computers are machines for the processing of in

- storage - generation- retrieval - transformation- analyzation - …

Computer Science

=

Science of Processing Information by Co

=

Informatics


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erating Systems

Database Systems

puter Graphics

System Simulation


1.1.3 Areas of Computer Science

Theoretical CS

Programming Languages

Computer Structures

Op

Pattern Recognition

Communication Systems

Artificial IntelligenceCom

Computers & their Environment

Computational “X”

New Frontiers …


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Operations

.

can be performed s a series of vertical

wed to slide freely.

sections, known as


1.1.4 Early Devices to Facilitate Numerical

Abacus (about 200 B.C.)

The abacus is a mechanical aid used for counting

Addition, subtraction, division and multiplicationon a standard abacus. The frame of the abacus harods on which a number of wooden beads

are allo

A horizontal beam separates the frame into twothe

upper deck

and the

lower deck

.


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ion

aun & Vayringe in

ents for quick and aps, photographs, a with the tracer

direction is sensed.


Mathematical Instruments for Analog Computat

Left: The image shows a calculator created by Br1735.

Right: Planimeters (1906) are very precise instrumaccurate determination of areas on blueprints, mdrawings, etc. By following the outline of the arethe revolution of the measuring wheel in either


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bage (1791-ned this engine pt to mechanize

tation of mathe-les.

e principle of the differences, i.e., ements (= ) to intermediate

urpose calculator


1.1.5 Babbage’s Engines

Charles Babbage´s Difference Engine (1833)

Charles Bab1871) desigin an attemthe compumatical tab

He used thmethod ofadding incrdifferencesresults.

⇒ special p


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ursue a better idea:

lving mathematical


Charles Babbage´s Analytical Engine (1871)

Babbage abandoned the Difference Engine, to pa general purpose computer for automatically soequations.


©

Christian Jacob

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oxes of punched

(a sequence of table that the

ning machine-ble software).

ivide


The Analytical Engine would be able to

• carry out any mathematical operation

• by use of stored programs.

One could modify its behaviour by altering two bcards:

• one box of variables, or data, and

• one box of

instruction codes

.

Thus a box of punched cards might be a programinstructions), or it might be data (for example, a engine had already computed and punched).

Babbage also noticed the importance of maintaireadable libraries of programs and data ( ⇒ reusa

Add Subtract Multiply D


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ers

ill”.

ponents of a

any sequence of

mory.

ternal files) stored hatever virtual


1.1.6 Babbage’s Idea and Modern Comput

Babbage’s engine separates a “store” from a “m

These correspond to the two most important commodern computer:

• the main memory and

• the central processing unit (CPU).

A modern

stored-program machine

can execute instructions stored in its memory.

Both instructions and data are read into main me

⇒

By reading externally originated programs (exwithin its memory, the

actual machine

becomes w

machine

the programmer wishes.


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Personal Computer

r 3

nch

. . .

. . .

Floppy disks, ZIP drives

RAM

Processor

CDs, DVDs

(CPU)


Structure of a stored-program machine

Babbage’s Machine von Neumann Machine

Register 1 Register 2 RegisteInstructionPointer

ControlUnit + Load- Store Bra

primitive operations

Main memory

External filesPunched cards

Store

Mill


© Christian Jacob

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perform a small

xt instruction in

n.

truction pointer, so m.


How does a stored-program machine work?

Like Babbage’s machine, a modern machine can number of primitive operations.

The instruction pointer tells where to find the nemain memory.

The control unit

• fetches an instruction from memory,

• decodes it and

• executes the corresponding primitive operatio

A

branch

instruction changes the value of the insthat it would jump to another part of the progra


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. . .

0 0 0 0

T A G C

o the next blank

Write Move Next state

B Right 2

X Right 2

B STOP

First Back TOC Turing’s Symbol Manipulator

1.2 Turing’s Symbol Manipulator

X

Controlprogram

X X X X X X X X. . .

1 1 0 1 0 1 1 1 0 1 1 0 0 1

C A A G T T A AA T T G A C

Read/writeheadLeft Right

Moving right t

State Read

1 B

2 X

2 B


©

Christian Jacob

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ny other Turing

s M’s rules as a

e computed by

, etc. program.

pe.

First Back TOC Turing’s Symbol Manipulator

Alan Turing’s universal machine, U, can imitate amachine, M.

Just encode

M

’s rules onto

U

’s tape. Then

U

read

program

.

Church-Turing Thesis

: anything computable can bsome Turing machine,some register machine, some Pascal, C, C++, Java

X

Controlprogram

X X X X X X X X

Read/writehead

machine U:

Control program for machine M on the tape

Read all information on the ta


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, Boston, MA: WCB/

logy

, Los Alamitos, 4.

First Back TOC References

1.3 References

• G. Blank and R. Barnes, The Universal MachineMcGraw-Hill, 1998. Chapters 1.1 and 1.2.

• M. R. Williams, A History of Computing TechnoCA: IEEE Compute Society Press, 1997. Chapter

chapter 1 introducing the universal...

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