Computer Arithmetic: Pergamon Programmed Texts

218 Pages·1966·3.01 MB·English

by  F. H. George

CERTIFICATE OF VALIDATION
The results in validating this text
will be found on page vi
PERGAMON PROGRAMMED TEXTS
Computer Arithmetic
by
F. H. GEORGE
Educational and Scientific Development
PERGAMON PRESS
OXFORD · LONDON · EDINBURGH · NEW YORK
TORONTO ' PARIS · BRAUNSCHWEIG
Pergamon Press Ltd., Headington Hill Hall, Oxford
4 & 5 Fitzroy Square, London W.l
Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1
Pergamon Press Inc., 44-01 21st Street, Long Island City, New York 11101
Pergamon of Canada, Ltd., 6 Adelaide Street East, Toronto, Ontario
e
Pergamon Press S.A.R.L., 24 rue des Ecoles, Paris 5
Friedr. Vieweg & Sohn Verlag, Postfach 185, 33 Braunschweig, West
Germany
Copyright © 1966 Pergamon Press Ltd.
First edition 1966
Library of Congress Catalog Card No. 65-28100
Printed in Great Britain by Page Bros. (Norwich) Ltd. Norwich
This book is sold subject to the condition
that it shall not, by way of trade, be lent,
resold, hired out, or otherwise disposed
of without the publisher's consent,
in any form of binding or cover
other than that in which
it is published.
(2466/66)
VALIDATION CERTIFICATE
THIS programme was validated by 20 students from sixth forms and
University. Their ages ranged from 17 years to 26 years.
A Pre-requisite test was given to ensure that the students possessed
sufficient mathematical background to enable them to commence the
programme. This consisted of ten questions on Basic Arithmetic. The
students were then given a Pre-test to discover whether they had any
knowledge of the subject matter contained in the programme.
The students then worked through the programme, recording their
responses on the forms provided. On completion of the programme the
students answered the Post-test which was the same as the Pre-test. In
order that a direct measure of learning could be calculated the Pre-test
scores were subtracted from the Post-test scores.
The average time taken to complete the programme was 6J hours.
Results
Pre-requisite test: Maximum Score 100%
Minimum Score 70%
Average Score 83-6%
Pre-test: Maximum Score 18%
Minimum Score 10%
Average Score 14-4%
Post-test: Maximum Score 93%
Minimum Score 74%
Average Score 85-4%
% Gain: Maximum Score 80%
Minimum Score 61%
Average Score 71%
vi
Editor's Preface
THIS new series of programmed books represents a major step
towards the universal availability of programmed material. It
is hoped ultimately to supply books for every subject that
human beings may wish to learn.
The text of these programmed books is not arranged in the
sequence to which we are accustomed in ordinary books. The
reader follows the routing directions on each page, so that in the
branching type of programme he will simply select, from among
the alternatives offered to him at the foot of the frame, the
number of the frame which he believes contains the right
answer. This method has been evolved because it has great
advantages, from the instructional point of view, over the
usual page-to-page sequence, and it will very soon be found to
be equally easy to follow.
In the linear programme, the reader will generally proceed in
the usual way to the frame on the immediately following page,
unless he is specifically told to turn to some other frame.
The programmes are written in a manner which gives the
reader the maximum clarity of exposition. He is taken through
the subject step by step, and each step is reinforced with a
question which must be answered correctly before he can
proceed to the next step.
In addition to its value as an instructional work, each pro-
grammed text is followed by an index; this not only enables the
reader to refer to definitions of vital terms, but also serves the
purpose of a reference book.
It is intended that this new library of programmed books
will gradually accumulate texts in every subject, including
science, the arts, engineering, mathematics, specialized topics
such as digital computers, as well as subjects with the broad
sweep of architecture and planning.
vii
viii EDITOR'S PREFACE
With the development of a large number of such programmed
books, it is planned to supply programmed texts that will them-
selves offer integrating material, and such titles as Philosophy
of Science, and Dynamic Planning, will appear in due course.
These texts will be closely associated with guide books that can
route the student through the sets of various texts, in pursuit of
some particular goal. This can be done in much the same way
as a student is routed through a single text.
A student wishing to achieve, say, "A"-Level in three sub-
jects, will be able to find, in the near future, the set of pro-
grammed books that he needs to carry him to the required
standard; though a person who wants to understand some new
branch of engineering, for example, may have to select his
books carefully, to compile precisely the information he re-
quires.
It is because this library hopes to satisfy people with vastly
differing needs, that each volume will be autonomous. Each
subject may be repeated in more than one text to give instruc-
tion appropriate to different sorts of requirements, such as
different age groups, and research is being carried out on the
possibility of catering for other individual differences.
It may be that the linear form of programming is more suit-
able for some subjects, and branching programmes more
suitable for others. We shall, however, provide texts in both
forms whenever there is a good case for so doing.
The first batch of programmed books—due to arrive on the
market in 1966—contains texts on mathematics, science, and
computers, as well as topics of general interest. These will be
followed by many more programmed books written at every
level of complexity, for our scope is no less than the educational
needs of the community as a whole. We are confident that
they will have a wide appeal, and consequently they will be
presented in a flexiback binding that is economical to produce,
as well as being highly durable.
An important feature of these books is that they are all
carefully checked and validated. This means that each text will
EDITOR'S PREFACE ix
have been read through by a number of experienced pro-
grammers and tried out on a sample of the people for whom the
book is intended. A statement to this effect, as well as a note
as to what has been assumed about the reader's background,
will be found in the Author's Preface.
It is considered that this series represents a major advance
in publishing, in that it will gradually accumulate information,
properly prepared in a specialized way, that may well revolu-
tionize teaching facilities, both in this country and overseas.
In conclusion, we offer a word of warning. For the same
reasons that it is impossible to achieve agreement among
teachers as to the best approach to any particular subject, we
do not expect that all our texts, however good, will meet with
universal approval. Readers are individuals, with varying back-
grounds and often with special needs, and this is why we must
have many different treatments of the same subject in the field
of programmed instruction.
F. H. GEORGE
Author's Preface
THIS programme was first written four years ago and since
then has been extensively tested and rewritten on a number of
different occasions. The present manuscript is thus the result
of a very lengthy preparation period.
Validation was carried out on middle management from
industry and commerce, sixth form students at schools and
university students. These students were both scientific and
non-scientific and normally did not have any special know-
ledge of computers.
The average for the pre-test was 14% and for the post-test
85%, showing an average gain of 71 % over all the validation
tests. The average study time taken during these tests was
five hours per student.
The course is intended for a wide audience of people between
the ages of 17 and 50 and the only qualification needed to
attempt this programmed book is an understanding of "O"-
Level Mathematics and preferably a general understanding of
the nature of digital computers. In fact, very little knowledge
is needed of computers since the book starts with a summary
of the general principles involved.
After having gone through this programmed book the student
should be able to devise arithmetic codes for the internal
representation of numbers in computers; should understand
fixed and floating point arithmetic, and the principles of
scaling.
Finally, although the author has been satisfied by the exten-
sive validation and testing, he readily recognizes that this pro-
gramme will still be unsuitable for certain people who want
to know about computer arithmetic; it is only hoped that this
forms a small minority of the total public.
F. H. GEORGE
xi
To the Reader
IN THIS book the material does not generally follow serially
in the usual way; furthermore each page may contain more
than one block of information, or frames as we call them.
Each frame contains several numbers. In the top outside
corner is the frame number itself : in the top left hand corner
is a number showing the frame which the reader has just left.
At the bottom of each frame are instructions for reaching the
next frame. These may be simply:
Turn to 256
Alternatively the reader may be given a number of different
frames to choose from, where the actual choice depends upon
his answer to the question on that frame.
The reader should also have paper or a notebook for making
notes or doing calculations. To obtain maximum benefit
from the programme, calculations should be done before the
answer is looked up, and the instructions given should be
obeyed.
xiii
1
Introduction: Digital Computers
A DIGITAL COMPUTER is a system, with Input, Storage, Arith-
metic Unit, Control Unit and Output, at the very least.
You put the information into storage via the input, and the
computer automatically carries out the instructions (a part of the
information you put in), which operate on the numbers (the
other part of the information you put in). The result, at the
output, provided you specify that the computer must print out
its results, is the answer to your mathematical problem.
The control unit uses the arithmetic unit to produce, under
orders, the answers you have asked for. So if you wish to add
2 and 2, order the computer to do so and it will tell you that the
answer is 4. But, of course, you do not need a computer for that.
Go to 2