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It is
as if there were a big wall between the hardware (the computer and how it actu-
ally works) and the software (the programs that direct the computer to do their
bidding), and that one should be content to remain on one side of that wall or
the other.
The power of abstraction allows us to usually operate at a level where we
do not have to think about the underlying layers all the time. This is a good thing. | [
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] |
The power of abstraction allows us to usually operate at a level where we
do not have to think about the underlying layers all the time. This is a good thing.
It enables us to be more productive. But if we are clueless about the underlying
layers, then we are not able to take advantage of the nuances of those underlying
layers when it is very important to be able to.
That is not to say that you must work at the lower level of abstraction and not
take advantage of the productivity enhancements that the abstractions provide. | [
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] |
But if we are clueless about the underlying
layers, then we are not able to take advantage of the nuances of those underlying
layers when it is very important to be able to.
That is not to say that you must work at the lower level of abstraction and not
take advantage of the productivity enhancements that the abstractions provide.
On the contrary, you are encouraged to work at the highest level of abstraction
available to you. | [
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] |
That is not to say that you must work at the lower level of abstraction and not
take advantage of the productivity enhancements that the abstractions provide.
On the contrary, you are encouraged to work at the highest level of abstraction
available to you. But in doing so, if you are able to, at the same time, keep in
mind the underlying levels, you will nd yourself able to do a much better job. | [
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] |
On the contrary, you are encouraged to work at the highest level of abstraction
available to you. But in doing so, if you are able to, at the same time, keep in
mind the underlying levels, you will nd yourself able to do a much better job.
As you approach your study and practice of computing, we urge you to take
the approach that hardware and software are names for components of two parts
of a computing system that work best when they are designed by people who take
into account the capabilities and limitations of both. | [
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] |
But in doing so, if you are able to, at the same time, keep in
mind the underlying levels, you will nd yourself able to do a much better job.
As you approach your study and practice of computing, we urge you to take
the approach that hardware and software are names for components of two parts
of a computing system that work best when they are designed by people who take
into account the capabilities and limitations of both.
Microprocessor designers who understand the needs of the programs that
will execute on the microprocessor they are designing can design much more
eective microprocessors than those who dont. | [
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] |
As you approach your study and practice of computing, we urge you to take
the approach that hardware and software are names for components of two parts
of a computing system that work best when they are designed by people who take
into account the capabilities and limitations of both.
Microprocessor designers who understand the needs of the programs that
will execute on the microprocessor they are designing can design much more
eective microprocessors than those who dont. For example, Intel, AMD, ARM,
and other major producers of microprocessors recognized a few years ago that a
large fraction of future programs would contain video clips as part of e-mail,
video games, and full-length movies. | [
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] |
Microprocessor designers who understand the needs of the programs that
will execute on the microprocessor they are designing can design much more
eective microprocessors than those who dont. For example, Intel, AMD, ARM,
and other major producers of microprocessors recognized a few years ago that a
large fraction of future programs would contain video clips as part of e-mail,
video games, and full-length movies. They recognized that it would be impor-
tant for such programs to execute eciently. | [
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] |
For example, Intel, AMD, ARM,
and other major producers of microprocessors recognized a few years ago that a
large fraction of future programs would contain video clips as part of e-mail,
video games, and full-length movies. They recognized that it would be impor-
tant for such programs to execute eciently. The result: most microprocessors
today contain special hardware capability to process those video clips. | [
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They recognized that it would be impor-
tant for such programs to execute eciently. The result: most microprocessors
today contain special hardware capability to process those video clips. Intel
dened additional instructions, initially called their MMX instruction set, and
developed special hardware for it. Motorola, IBM, and Apple did essentially
the same thing, resulting in the AltiVec instruction set and special hardware to
support it. | [
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] |
Intel
dened additional instructions, initially called their MMX instruction set, and
developed special hardware for it. Motorola, IBM, and Apple did essentially
the same thing, resulting in the AltiVec instruction set and special hardware to
support it.
A similar story can be told about software designers. The designer of a large
computer program who understands the capabilities and limitations of the hard-
ware that will carry out the tasks of that program can design the program so it
executes more eciently than the designer who does not understand the nature of
the hardware. | [
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A similar story can be told about software designers. The designer of a large
computer program who understands the capabilities and limitations of the hard-
ware that will carry out the tasks of that program can design the program so it
executes more eciently than the designer who does not understand the nature of
the hardware. One important task that almost all large software systems need to
carry out is called sorting, where a number of items have to be arranged in some
order. | [
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] |
The designer of a large
computer program who understands the capabilities and limitations of the hard-
ware that will carry out the tasks of that program can design the program so it
executes more eciently than the designer who does not understand the nature of
the hardware. One important task that almost all large software systems need to
carry out is called sorting, where a number of items have to be arranged in some
order | [
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] |
A similar story can be told about software designers. The designer of a large
computer program who understands the capabilities and limitations of the hard-
ware that will carry out the tasks of that program can design the program so it
executes more eciently than the designer who does not understand the nature of
the hardware. One important task that almost all large software systems need to
carry out is called sorting, where a number of items have to be arranged in some
order. | [
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] |
The designer of a large
computer program who understands the capabilities and limitations of the hard-
ware that will carry out the tasks of that program can design the program so it
executes more eciently than the designer who does not understand the nature of
the hardware. One important task that almost all large software systems need to
carry out is called sorting, where a number of items have to be arranged in some
order. The words in a dictionary are arranged in alphabetical order. | [
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One important task that almost all large software systems need to
carry out is called sorting, where a number of items have to be arranged in some
order. The words in a dictionary are arranged in alphabetical order. Students in
a class are often graded based on a numerical order, according to their scores
on the nal exam. There is a large number of fundamentally dierent programs
one can write to arrange a collection of items in order. | [
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Students in
a class are often graded based on a numerical order, according to their scores
on the nal exam. There is a large number of fundamentally dierent programs
one can write to arrange a collection of items in order. Donald Knuth, one of the | [
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] |
top computer scientists in the world, devoted 391 pages to the task in The Art
of Computer Programming, vol. 3. Which sorting program works best is often
very dependent on how much the software designer is aware of the underlying
characteristics of the hardware.
The Bottom Line
We believe that whether your inclinations are in the direction
of a computer hardware career or a computer software career, you will be much
more capable if you master both. | [
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] |
Which sorting program works best is often
very dependent on how much the software designer is aware of the underlying
characteristics of the hardware.
The Bottom Line
We believe that whether your inclinations are in the direction
of a computer hardware career or a computer software career, you will be much
more capable if you master both. This book is about getting you started on the
path to mastering both hardware and software. | [
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] |
The Bottom Line
We believe that whether your inclinations are in the direction
of a computer hardware career or a computer software career, you will be much
more capable if you master both. This book is about getting you started on the
path to mastering both hardware and software. Although we sometimes ignore
making the point explicitly when we are in the trenches of working through a
concept, it really is the case that each sheds light on the other. | [
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] |
This book is about getting you started on the
path to mastering both hardware and software. Although we sometimes ignore
making the point explicitly when we are in the trenches of working through a
concept, it really is the case that each sheds light on the other.
When you study data types, a software concept, in C (Chapter 12), you will
understand how the nite word length of the computer, a hardware concept,
aects our notion of data types. | [
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] |
Although we sometimes ignore
making the point explicitly when we are in the trenches of working through a
concept, it really is the case that each sheds light on the other.
When you study data types, a software concept, in C (Chapter 12), you will
understand how the nite word length of the computer, a hardware concept,
aects our notion of data types.
When you study functions in C (Chapter 14), you will be able to tie the rules
of calling a function with the hardware implementation that makes those rules
necessary. | [
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] |
When you study data types, a software concept, in C (Chapter 12), you will
understand how the nite word length of the computer, a hardware concept,
aects our notion of data types.
When you study functions in C (Chapter 14), you will be able to tie the rules
of calling a function with the hardware implementation that makes those rules
necessary.
When you study recursion, a powerful algorithmic device (initially in
Chapter 8 and more extensively in Chapter 17), you will be able to tie it to the
hardware. | [
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] |
When you study functions in C (Chapter 14), you will be able to tie the rules
of calling a function with the hardware implementation that makes those rules
necessary.
When you study recursion, a powerful algorithmic device (initially in
Chapter 8 and more extensively in Chapter 17), you will be able to tie it to the
hardware. If you take the time to do that, you will better understand when the
additional time to execute a procedure recursively is worth it. | [
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] |
When you study recursion, a powerful algorithmic device (initially in
Chapter 8 and more extensively in Chapter 17), you will be able to tie it to the
hardware. If you take the time to do that, you will better understand when the
additional time to execute a procedure recursively is worth it.
When you study pointer variables in C (in Chapter 16), your knowledge of
computer memory will provide a deeper understanding of what pointers pro-
vide, and very importantly, when they should be used and when they should be
avoided. | [
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] |
If you take the time to do that, you will better understand when the
additional time to execute a procedure recursively is worth it.
When you study pointer variables in C (in Chapter 16), your knowledge of
computer memory will provide a deeper understanding of what pointers pro-
vide, and very importantly, when they should be used and when they should be
avoided.
When you study data structures in C (in Chapter 19), your knowledge of com-
puter memory will help you better understand what must be done to manipulate
the actual structures in memory eciently. | [
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] |
When you study pointer variables in C (in Chapter 16), your knowledge of
computer memory will provide a deeper understanding of what pointers pro-
vide, and very importantly, when they should be used and when they should be
avoided.
When you study data structures in C (in Chapter 19), your knowledge of com-
puter memory will help you better understand what must be done to manipulate
the actual structures in memory eciently.
We realize that most of the terms in the preceding ve short paragraphs may
not be familiar to you yet. | [
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] |
When you study data structures in C (in Chapter 19), your knowledge of com-
puter memory will help you better understand what must be done to manipulate
the actual structures in memory eciently.
We realize that most of the terms in the preceding ve short paragraphs may
not be familiar to you yet. That is OK; you can reread this page at the end of the
semester. What is important to know right now is that there are important topics
in the software that are very deeply interwoven with topics in the hardware. | [
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] |
That is OK; you can reread this page at the end of the
semester. What is important to know right now is that there are important topics
in the software that are very deeply interwoven with topics in the hardware. Our
contention is that mastering either is easier if you pay attention to both.
Most importantly, most computing problems yield better solutions when the
problem solver has the capability of both at his or her disposal. | [
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Our
contention is that mastering either is easier if you pay attention to both.
Most importantly, most computing problems yield better solutions when the
problem solver has the capability of both at his or her disposal.
1.4 A Computer System
We have used the word computer more than two dozen times in the preceding
pages, and although we did not say so explicitly, we used it to mean a system
consisting of the software (i. | [
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] |
1.4 A Computer System
We have used the word computer more than two dozen times in the preceding
pages, and although we did not say so explicitly, we used it to mean a system
consisting of the software (i.e., computer programs) that directs and species the
processing of information and the hardware that performs the actual processing
of information in response to what the software asks the hardware to do. | [
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e., computer programs) that directs and species the
processing of information and the hardware that performs the actual processing
of information in response to what the software asks the hardware to do. When
we say performing the actual processing, we mean doing the actual additions,
multiplications, and so forth in the hardware that are necessary to get the job | [
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] |
done. A more precise term for this hardware is a central processing unit (CPU),
or simply a processor or microprocessor. This textbook is primarily about the
processor and the programs that are executed by the processor.
1.4.1 A (Very) Little History for a (Lot) Better Perspective
Before we get into the detail of how the processor and the software associated
with it work, we should take a moment and note the enormous and unparalleled
leaps of performance that the computing industry has made in the relatively short
time computers have been around. | [
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] |
4.1 A (Very) Little History for a (Lot) Better Perspective
Before we get into the detail of how the processor and the software associated
with it work, we should take a moment and note the enormous and unparalleled
leaps of performance that the computing industry has made in the relatively short
time computers have been around. After all, it wasnt until the 1940s that the
first computers showed their faces. | [
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] |
1 A (Very) Little History for a (Lot) Better Perspective
Before we get into the detail of how the processor and the software associated
with it work, we should take a moment and note the enormous and unparalleled
leaps of performance that the computing industry has made in the relatively short
time computers have been around. After all, it wasnt until the 1940s that the
first computers showed their faces. One of the first computers was the ENIAC
(the Electronic Numerical Integrator and Calculator), a general purpose electronic
computer that could be reprogrammed for different tasks. | [
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] |
After all, it wasnt until the 1940s that the
first computers showed their faces. One of the first computers was the ENIAC
(the Electronic Numerical Integrator and Calculator), a general purpose electronic
computer that could be reprogrammed for different tasks. It was designed and built
in 19431945 attheUniversityofPennsylvaniabyPresperEckertandhiscolleagues.
It contained more than 17,000 vacuum tubes. | [
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] |
It was designed and built
in 19431945 attheUniversityofPennsylvaniabyPresperEckertandhiscolleagues.
It contained more than 17,000 vacuum tubes. It was approximately 8 feet high, more
than 100 feet wide, and about 3 feet deep (about 300 square feet of floor space). It
weighed 30 tons and required 140 kW to operate. Figure 1.1 shows three operators
programming the ENIAC by plugging and unplugging cables and switches. | [
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] |
Figure 1.1 shows three operators
programming the ENIAC by plugging and unplugging cables and switches.
About 40 years and many computer companies and computers later, in the
early 1980s, the Burroughs A series was born. One of the dozen or so 18-inch
oards that comprise that machine is shown in Figure 1.2. Each board contained
Figure 1.1
The ENIAC, designed and built at University of Pennsylvania, 194345. | [
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Each board contained
Figure 1.1
The ENIAC, designed and built at University of Pennsylvania, 194345.
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] |
Figure 1.2
A processor board, vintage 1980s. Courtesy of Emilio Salguerio
Fast forward another 30 or so years and we nd many of todays computers on
desktops (Figure 1.3), in laptops (Figure 1.4), and most recently in smartphones
(Figure 1.5). Their relative weights and energy requirements have decreased
enormousl
and the s eed at which the
rocess information has also increased
eno
how
com
Figu
A de
cJo
Futu
Shutterstock. | [
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5). Their relative weights and energy requirements have decreased
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10
c
Figure 1.6
A microprocessor. cPeter Gudella/Shutterstock
The integrated circuit packages that comprise modern digital computers have
also seen phenomenal improvement. An example of one of todays microproces-
sors is shown in Figure 1.6. The rst microprocessor, the Intel 4004 in 1971,
contained 2300 transistors and operated at 106 KHz. By 1992, those numbers
had jumped to 3.1 million transistors at a frequency of 66 MHz on the Intel
Pentium microprocessor, an increase in both parameters of a factor of about 1000. | [
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] |
By 1992, those numbers
had jumped to 3.1 million transistors at a frequency of 66 MHz on the Intel
Pentium microprocessor, an increase in both parameters of a factor of about 1000.
Todays microprocessors contain upwards of ve billion transistors and can oper-
ate at upwards of 4 GHz, another increase in both parameters of about a factor
of 1000.
This factor of one million since 1971 in both the number of transistors and
the frequency that the microprocessor operates at has had very important impli-
cations. | [
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] |
Todays microprocessors contain upwards of ve billion transistors and can oper-
ate at upwards of 4 GHz, another increase in both parameters of about a factor
of 1000.
This factor of one million since 1971 in both the number of transistors and
the frequency that the microprocessor operates at has had very important impli-
cations. The fact that each operation can be performed in one millionth of the
time it took in 1971 means the microprocessor can do one million things today
in the time it took to do one thing in 1971. | [
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] |
This factor of one million since 1971 in both the number of transistors and
the frequency that the microprocessor operates at has had very important impli-
cations. The fact that each operation can be performed in one millionth of the
time it took in 1971 means the microprocessor can do one million things today
in the time it took to do one thing in 1971. The fact that there are more than a
million times as many transistors on a chip means we can do a lot more things at
the same time today than we could in 1971. | [
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] |
The fact that each operation can be performed in one millionth of the
time it took in 1971 means the microprocessor can do one million things today
in the time it took to do one thing in 1971. The fact that there are more than a
million times as many transistors on a chip means we can do a lot more things at
the same time today than we could in 1971.
The result of all this is we have today computers that seem able to understand
the languages people speak English, Spanish, Chinese, for example. | [
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The fact that there are more than a
million times as many transistors on a chip means we can do a lot more things at
the same time today than we could in 1971.
The result of all this is we have today computers that seem able to understand
the languages people speak English, Spanish, Chinese, for example. We have
computers that seem able to recognize faces. Many see this as the magic of arti-
cial intelligence. | [
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We have
computers that seem able to recognize faces. Many see this as the magic of arti-
cial intelligence. We will see as we get into the details of how a computer works
that much of what appears to be magic is really due to how blazingly fast very
simple mindless operations (many at the same time) can be carried out.
1.4.2 The Parts of a Computer System
When most people use the word computer, they usually mean more than just
the processor (i. | [
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] |
4.2 The Parts of a Computer System
When most people use the word computer, they usually mean more than just
the processor (i.e., CPU) that is in charge of doing what the software directs. | [
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] |
They usually mean the collection of parts that in combination form their computer
system. Today that computer system is often a laptop (see Figure 1.4), augmented
with many additional devices.
A computer system generally includes, in addition to the processor, a key-
board for typing commands, a mouse or keypad or joystick for positioning on
menu entries, a monitor for displaying information that the computer system has
produced, memory for temporarily storing information, disks and USB memory
sticks of one sort or another for storing information for a very long time, even after
the computer has been turned o, connections to other devices such as a printer
for obtaining paper copies of that information, and the collection of programs
(the software) that the user wishes to execute. | [
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] |
4), augmented
with many additional devices.
A computer system generally includes, in addition to the processor, a key-
board for typing commands, a mouse or keypad or joystick for positioning on
menu entries, a monitor for displaying information that the computer system has
produced, memory for temporarily storing information, disks and USB memory
sticks of one sort or another for storing information for a very long time, even after
the computer has been turned o, connections to other devices such as a printer
for obtaining paper copies of that information, and the collection of programs
(the software) that the user wishes to execute.
All these items help computer users to do their jobs. | [
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A computer system generally includes, in addition to the processor, a key-
board for typing commands, a mouse or keypad or joystick for positioning on
menu entries, a monitor for displaying information that the computer system has
produced, memory for temporarily storing information, disks and USB memory
sticks of one sort or another for storing information for a very long time, even after
the computer has been turned o, connections to other devices such as a printer
for obtaining paper copies of that information, and the collection of programs
(the software) that the user wishes to execute.
All these items help computer users to do their jobs. Without a printer, for
example, the user would have to copy by hand what is displayed on the monitor. | [
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] |
All these items help computer users to do their jobs. Without a printer, for
example, the user would have to copy by hand what is displayed on the monitor.
Without a mouse, keypad, or joystick, the user would have to type each command,
rather than simply position the mouse, keypad, or joystick.
So, as we begin our journey, which focuses on the CPU that occupies a small
fraction of 1 square inch of silicon and the software that makes the CPU do our
bidding, we note that the computer systems we use contain a lot of additional
components. | [
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Without a mouse, keypad, or joystick, the user would have to type each command,
rather than simply position the mouse, keypad, or joystick.
So, as we begin our journey, which focuses on the CPU that occupies a small
fraction of 1 square inch of silicon and the software that makes the CPU do our
bidding, we note that the computer systems we use contain a lot of additional
components.
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] |
So, as we begin our journey, which focuses on the CPU that occupies a small
fraction of 1 square inch of silicon and the software that makes the CPU do our
bidding, we note that the computer systems we use contain a lot of additional
components.
1.5 Two Very Important Ideas
Before we leave this rst chapter, there are two very important ideas that we
would like you to understand, ideas that are at the core of what computing is all
about. | [
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] |
1.5 Two Very Important Ideas
Before we leave this rst chapter, there are two very important ideas that we
would like you to understand, ideas that are at the core of what computing is all
about.
Idea 1:
All computers (the biggest and the smallest, the fastest and the
slowest, the most expensive and the cheapest) are capable of comput-
ing exactly the same things if they are given enough time and enough
memory. | [
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] |
5 Two Very Important Ideas
Before we leave this rst chapter, there are two very important ideas that we
would like you to understand, ideas that are at the core of what computing is all
about.
Idea 1:
All computers (the biggest and the smallest, the fastest and the
slowest, the most expensive and the cheapest) are capable of comput-
ing exactly the same things if they are given enough time and enough
memory. That is, anything a fast computer can do, a slow computer can
do also. | [
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] |
Idea 1:
All computers (the biggest and the smallest, the fastest and the
slowest, the most expensive and the cheapest) are capable of comput-
ing exactly the same things if they are given enough time and enough
memory. That is, anything a fast computer can do, a slow computer can
do also. The slow computer just does it more slowly. A more expensive
computer cannot gure out something that a cheaper computer is unable
to gure out as long as the cheaper computer can access enough mem-
ory. | [
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] |
The slow computer just does it more slowly. A more expensive
computer cannot gure out something that a cheaper computer is unable
to gure out as long as the cheaper computer can access enough mem-
ory. (You may have to go to the store to buy more memory whenever it
runs out of memory in order to keep increasing memory.) All computers
can do exactly the same things. Some computers can do things faster,
but none can do more than any other. | [
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] |
) All computers
can do exactly the same things. Some computers can do things faster,
but none can do more than any other.
Idea 2:
We describe our problems in English or some other language
spoken by people. Yet the problems are solved by electrons running
around inside the computer. It is necessary to transform our problem
from the language of humans to the voltages that inuence the ow of
electrons. | [
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] |
Yet the problems are solved by electrons running
around inside the computer. It is necessary to transform our problem
from the language of humans to the voltages that inuence the ow of
electrons. This transformation is really a sequence of systematic trans-
formations, developed and improved over the last 70 years, which
combine to give the computer the ability to carry out what appear to. | [
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] |
It is necessary to transform our problem
from the language of humans to the voltages that inuence the ow of
electrons. This transformation is really a sequence of systematic trans-
formations, developed and improved over the last 70 years, which
combine to give the computer the ability to carry out what appear to | [
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be some very complicated tasks. In reality, these tasks are simple and
straightforward.
The rest of this chapter is devoted to discussing these two ideas.
1.6 Computers as Universal
Computational Devices
It may seem strange that an introductory textbook begins by describing how
computers work. After all, mechanical engineering students begin by studying
physics, not how car engines work. | [
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] |
6 Computers as Universal
Computational Devices
It may seem strange that an introductory textbook begins by describing how
computers work. After all, mechanical engineering students begin by studying
physics, not how car engines work. Chemical engineering students begin by
studying chemistry, not oil reneries. Why should computing students begin by
studying computers?
The answer is that computers are dierent. | [
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] |
Chemical engineering students begin by
studying chemistry, not oil reneries. Why should computing students begin by
studying computers?
The answer is that computers are dierent. To learn the fundamental prin-
ciples of computing, you must study computers or machines that can do what
computers can do. The reason for this has to do with the notion that computers
are universal computational devices. | [
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] |
To learn the fundamental prin-
ciples of computing, you must study computers or machines that can do what
computers can do. The reason for this has to do with the notion that computers
are universal computational devices. Lets see what that means.
Before modern computers, there were many kinds of calculating machines.
Some were analog machinesmachines that produced an answer by measuring
some physical quantity such as distance or voltage. | [
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Before modern computers, there were many kinds of calculating machines.
Some were analog machinesmachines that produced an answer by measuring
some physical quantity such as distance or voltage. For example, a slide rule is
an analog machine that multiplies numbers by sliding one logarithmically graded
ruler next to another. The user can read a logarithmic distance on the sec-
ond ruler. | [
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For example, a slide rule is
an analog machine that multiplies numbers by sliding one logarithmically graded
ruler next to another. The user can read a logarithmic distance on the sec-
ond ruler. Some early analog adding machines worked by dropping weights on a
scale. The diculty with analog machines is that it is very hard to increase their
accuracy.
This is why digital machinesmachines that perform computations by
manipulating a xed nite set of digits or letterscame to dominate comput-
ing. | [
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The diculty with analog machines is that it is very hard to increase their
accuracy.
This is why digital machinesmachines that perform computations by
manipulating a xed nite set of digits or letterscame to dominate comput-
ing. You are familiar with the distinction between analog and digital watches. An
analog watch has hour and minute hands, and perhaps a second hand. It gives
the time by the positions of its hands, which are really angular measures. | [
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] |
An
analog watch has hour and minute hands, and perhaps a second hand. It gives
the time by the positions of its hands, which are really angular measures. Digital
watches give the time in digits. You can increase accuracy just by adding more
digits. For example, if it is important for you to measure time in hundredths of
a second, you can buy a watch that gives a reading like 10:35.16 rather than just
10:35. | [
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] |
For example, if it is important for you to measure time in hundredths of
a second, you can buy a watch that gives a reading like 10:35.16 rather than just
10:35. How would you get an analog watch that would give you an accurate read-
ing to one one-hundredth of a second? You could do it, but it would take a mighty
long second hand! When we talk about computers in this book, we will always
mean digital machines. | [
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] |
16 rather than just
10:35. How would you get an analog watch that would give you an accurate read-
ing to one one-hundredth of a second? You could do it, but it would take a mighty
long second hand! When we talk about computers in this book, we will always
mean digital machines.
Before modern digital computers, the most common digital machines in the
West were adding machines. In other parts of the world another digital machine,
the abacus, was common. | [
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] |
Before modern digital computers, the most common digital machines in the
West were adding machines. In other parts of the world another digital machine,
the abacus, was common. Digital adding machines were mechanical or elec-
tromechanical devices that could perform a specic kind of computation: adding
integers. There were also digital machines that could multiply integers. There
were digital machines that could put a stack of cards with punched names in
alphabetical order. | [
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] |
There were also digital machines that could multiply integers. There
were digital machines that could put a stack of cards with punched names in
alphabetical order. The main limitation of all these machines is that they could
do only one specic kind of computation. If you owned only an adding machine | [
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] |
and wanted to multiply two integers, you had some pencil-and-paper work
to do.
This is why computers are dierent. You can tell a computer how to add num-
bers. You can tell it how to multiply. You can tell it how to alphabetize a list or
perform any computation you like. When you think of a new kind of computation,
you do not have to buy or design a new computer. You just give the old computer
a new set of instructions (a program) to carry out the new computation. | [
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] |
When you think of a new kind of computation,
you do not have to buy or design a new computer. You just give the old computer
a new set of instructions (a program) to carry out the new computation. This is
why we say the computer is a universal computational device. Computer scien-
tists believe that anything that can be computed, can be computed by a computer
provided it has enough time and enough memory. | [
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] |
This is
why we say the computer is a universal computational device. Computer scien-
tists believe that anything that can be computed, can be computed by a computer
provided it has enough time and enough memory. When we study computers, we
study the fundamentals of all computing. We learn what computation is and what
can be computed.
The idea of a universal computational device is due to Alan Turing. | [
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] |
We learn what computation is and what
can be computed.
The idea of a universal computational device is due to Alan Turing. Turing
proposed in 1937 that all computations could be carried out by a particular kind of
machine, which is now called a Turing machine. He gave a mathematical descrip-
tion of this kind of machine, but did not actually build one. Digital computers
were not operating until several years later. | [
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] |
He gave a mathematical descrip-
tion of this kind of machine, but did not actually build one. Digital computers
were not operating until several years later. Turing was more interested in solv-
ing a philosophical problem: dening computation. He began by looking at the
kinds of actions that people perform when they compute; these include making
marks on paper, writing symbols according to certain rules when other symbols
are present, and so on. | [
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Turing was more interested in solv-
ing a philosophical problem: dening computation. He began by looking at the
kinds of actions that people perform when they compute; these include making
marks on paper, writing symbols according to certain rules when other symbols
are present, and so on. He abstracted these actions and specied a mechanism that
could carry them out. He gave some examples of the kinds of things that these
machines could do. | [
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He abstracted these actions and specied a mechanism that
could carry them out. He gave some examples of the kinds of things that these
machines could do. One Turing machine could add two integers; another could
multiply two integers.
Figure 1.7 shows what we call black box models of Turing machines that
add and multiply. In each case, the operation to be performed is described in
the box. | [
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] |
7 shows what we call black box models of Turing machines that
add and multiply. In each case, the operation to be performed is described in
the box. The data elements on which to operate are shown as inputs to the box.
The r
provi
there
a, b
(Turing machine
that adds)
(Turing machine
that multiplies)
Figure 1.7
Black box models of Turing machines.
Turing proposed that every computation can be performed by some Turing
machine. | [
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] |
7
Black box models of Turing machines.
Turing proposed that every computation can be performed by some Turing
machine. We call this Turings thesis. Although Turings thesis has never been
proved, there does exist a lot of evidence to suggest it is true. We know, for exam-
ple, that various enhancements one can make to Turing machines do not result in
machines that can compute more.
Perhaps the best argument to support Turings thesis was provided by Turing
himself in his original paper. | [
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] |
We know, for exam-
ple, that various enhancements one can make to Turing machines do not result in
machines that can compute more.
Perhaps the best argument to support Turings thesis was provided by Turing
himself in his original paper. He said that one way to try to construct a machine
more powerful than any particular Turing machine was to make a machine U
that could simulate all Turing machines. | [
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Perhaps the best argument to support Turings thesis was provided by Turing
himself in his original paper. He said that one way to try to construct a machine
more powerful than any particular Turing machine was to make a machine U
that could simulate all Turing machines. You would simply describe to U the | [
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] |
particular Turing machine you wanted it to simulate, say a machine to add two
integers, give U the input data, and U would compute the appropriate output,
in this case the sum of the inputs. Turing then showed that there was, in fact,
a Turing machine that could do this, so even this attempt to nd something that
could not be computed by Turing machines failed.
e, f, g
v
Turing machine)
Figure 1. | [
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] |
Turing then showed that there was, in fact,
a Turing machine that could do this, so even this attempt to nd something that
could not be computed by Turing machines failed.
e, f, g
v
Turing machine)
Figure 1.8
Black box model of a universal Turing machine.
In specifying U, Turing had provided us with a deep insight: He had given us
the rst description of what computers do. In fact, both a computer (with as much
memory as it wants) and a universal Turing machine can compute exactly the
same things. | [
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] |
In specifying U, Turing had provided us with a deep insight: He had given us
the rst description of what computers do. In fact, both a computer (with as much
memory as it wants) and a universal Turing machine can compute exactly the
same things. In both cases, you give the machine a description of a computation
and the data it needs, and the machine computes the appropriate answer. Comput-
ers and universal Turing machines can compute anything that can be computed
because they are programmable. | [
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] |
In both cases, you give the machine a description of a computation
and the data it needs, and the machine computes the appropriate answer. Comput-
ers and universal Turing machines can compute anything that can be computed
because they are programmable.
This is the reason that a big or expensive computer cannot do more than a
small, cheap computer. More money may buy you a faster computer, a monitor
with higher resolution, or a nice sound system. | [
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] |
This is the reason that a big or expensive computer cannot do more than a
small, cheap computer. More money may buy you a faster computer, a monitor
with higher resolution, or a nice sound system. But if you have a small, cheap
computer, you already have a universal computational device.
1.7 How Do We Get the Electrons to
Do the Work?
Figure 1.9 shows the process we must go through to get the electrons (which
actually do the work) to do our bidding. | [
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] |
7 How Do We Get the Electrons to
Do the Work?
Figure 1.9 shows the process we must go through to get the electrons (which
actually do the work) to do our bidding. We call the steps of this process the
Levels of Transformation. As we will see, at each level we have choices. If we
ignore any of the levels, our ability to make the best use of our computing system
can be very adversely aected. | [
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] |
As we will see, at each level we have choices. If we
ignore any of the levels, our ability to make the best use of our computing system
can be very adversely aected.
1.7.1 The Statement of the Problem
We describe the problems we wish to solve in a natural language. Natural lan-
guages are languages that people speak, like English, French, Japanese, Italian,
and so on. They have evolved over centuries in accordance with their usage. | [
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guages are languages that people speak, like English, French, Japanese, Italian,
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] |
15
Devices
Figure 1.9
Levels of transformation.
computer. Most important of these unacceptable attributes is ambiguity. Natural
language is lled with ambiguity. To infer the meaning of a sentence, a listener is
often helped by the tone of voice of the speaker, or at the very least, the context
of the sentence.
An example of ambiguity in English is the sentence, Time ies like an
arrow. | [
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] |
To infer the meaning of a sentence, a listener is
often helped by the tone of voice of the speaker, or at the very least, the context
of the sentence.
An example of ambiguity in English is the sentence, Time ies like an
arrow. At least three interpretations are possible, depending on whether (1) one is
noticing how fast time passes, (2) one is at a track meet for insects, or (3) one is
writing a letter to the Dear Abby of Insectville. | [
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] |
An example of ambiguity in English is the sentence, Time ies like an
arrow. At least three interpretations are possible, depending on whether (1) one is
noticing how fast time passes, (2) one is at a track meet for insects, or (3) one is
writing a letter to the Dear Abby of Insectville. In the rst case, a simile; one
is comparing the speed of time passing to the speed of an arrow that has been
released. | [
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] |
At least three interpretations are possible, depending on whether (1) one is
noticing how fast time passes, (2) one is at a track meet for insects, or (3) one is
writing a letter to the Dear Abby of Insectville. In the rst case, a simile; one
is comparing the speed of time passing to the speed of an arrow that has been
released. In the second case, one is telling the timekeeper to do his/her job much
like an arrow would. | [
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] |
In the rst case, a simile; one
is comparing the speed of time passing to the speed of an arrow that has been
released. In the second case, one is telling the timekeeper to do his/her job much
like an arrow would. In the third case, one is relating that a particular group of
ies (time ies, as opposed to fruit ies) are all in love with the same arrow.
Such ambiguity would be unacceptable in instructions provided to a com-
puter. | [
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] |
In the third case, one is relating that a particular group of
ies (time ies, as opposed to fruit ies) are all in love with the same arrow.
Such ambiguity would be unacceptable in instructions provided to a com-
puter. The computer, electronic idiot that it is, can only do as it is told. To tell it to
do something where there are multiple interpretations would cause the computer
to not know which interpretation to follow. | [
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The computer, electronic idiot that it is, can only do as it is told. To tell it to
do something where there are multiple interpretations would cause the computer
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