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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. cHistorical/Getty Images
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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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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. 1.
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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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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. They are fraught with a lot of things unacceptable for providing instructions to a
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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 to not know which interpretation to follow.
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