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1.7.2 The Algorithm
The rst step in the sequence of transformations is to transform the natural lan-
guage description of the problem to an algorithm, and in so doing, get rid of the
objectionable characteristics of the natural language. An algorithm is a step-by-
step procedure that is guaranteed to terminate, such that each step is precisely
stated and can be carried out by the computer. | [
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] |
2 The Algorithm
The rst step in the sequence of transformations is to transform the natural lan-
guage description of the problem to an algorithm, and in so doing, get rid of the
objectionable characteristics of the natural language. An algorithm is a step-by-
step procedure that is guaranteed to terminate, such that each step is precisely
stated and can be carried out by the computer. There are terms to describe each
of these properties. | [
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] |
An algorithm is a step-by-
step procedure that is guaranteed to terminate, such that each step is precisely
stated and can be carried out by the computer. There are terms to describe each
of these properties.
We use the term deniteness to describe the notion that each step is precisely
stated. A recipe for excellent pancakes that instructs the preparer to stir until
lumpy lacks deniteness, since the notion of lumpiness is not precise. | [
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] |
We use the term deniteness to describe the notion that each step is precisely
stated. A recipe for excellent pancakes that instructs the preparer to stir until
lumpy lacks deniteness, since the notion of lumpiness is not precise.
We use the term eective computability to describe the notion that each step
can be carried out by a computer. A procedure that instructs the computer to take
the largest prime number lacks eective computability, since there is no largest
prime number. | [
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] |
We use the term eective computability to describe the notion that each step
can be carried out by a computer. A procedure that instructs the computer to take
the largest prime number lacks eective computability, since there is no largest
prime number.
We use the term niteness to describe the notion that the procedure termi-
nates.
For every problem there are usually many dierent algorithms for solving
that problem. | [
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] |
We use the term niteness to describe the notion that the procedure termi-
nates.
For every problem there are usually many dierent algorithms for solving
that problem. One algorithm may require the fewest steps. Another algorithm
may allow some steps to be performed concurrently. A computer that allows
more than one thing to be done at a time can often solve the problem in less
time, even though it is likely that the total number of steps to be performed has
increased. | [
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] |
Another algorithm
may allow some steps to be performed concurrently. A computer that allows
more than one thing to be done at a time can often solve the problem in less
time, even though it is likely that the total number of steps to be performed has
increased.
1.7.3 The Program
The next step is to transform the algorithm into a computer program in one of the
programming languages that are available. | [
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] |
7.3 The Program
The next step is to transform the algorithm into a computer program in one of the
programming languages that are available. Programming languages are mechan-
ical languages. That is, unlike natural languages, mechanical languages did not
evolve through human discourse. Rather, they were invented for use in specify-
ing a sequence of instructions to a computer. Therefore, mechanical languages do
not suer from failings such as ambiguity that would make them unacceptable for
specifying a computer program. | [
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] |
Rather, they were invented for use in specify-
ing a sequence of instructions to a computer. Therefore, mechanical languages do
not suer from failings such as ambiguity that would make them unacceptable for
specifying a computer program.
There are more than 1000 programming languages. Some have been designed
for use with particular applications, such as Fortran for solving scientic calcula-
tions and COBOL for solving business data-processing problems. | [
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] |
There are more than 1000 programming languages. Some have been designed
for use with particular applications, such as Fortran for solving scientic calcula-
tions and COBOL for solving business data-processing problems. In the second
half of this book, we will use C and C++, languages that were designed for
manipulating low-level hardware structures.
Other languages are useful for still other purposes. | [
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] |
In the second
half of this book, we will use C and C++, languages that were designed for
manipulating low-level hardware structures.
Other languages are useful for still other purposes. Prolog is the language of
choice for many applications that require the design of an expert system. LISP
was for years the language of choice of a substantial number of people working
on problems dealing with articial intelligence. | [
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] |
Prolog is the language of
choice for many applications that require the design of an expert system. LISP
was for years the language of choice of a substantial number of people working
on problems dealing with articial intelligence. Pascal is a language invented as
a vehicle for teaching beginning students how to program.
There are two kinds of programming languages, high-level languages and
low-level languages. | [
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] |
Pascal is a language invented as
a vehicle for teaching beginning students how to program.
There are two kinds of programming languages, high-level languages and
low-level languages. High-level languages are at a distance (a high level) from
the underlying computer. At their best, they are independent of the computer on
which the programs will execute. We say the language is machine independent. | [
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At their best, they are independent of the computer on
which the programs will execute. We say the language is machine independent. | [
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] |
All the languages mentioned thus far are high-level languages. Low-level lan-
guages are tied to the computer on which the programs will execute. There is
generally one such low-level language for each computer. That language is called
the assembly language for that computer.
1.7.4 The ISA
The next step is to translate the program into the instruction set of the particular
computer that will be used to carry out the work of the program. | [
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] |
7.4 The ISA
The next step is to translate the program into the instruction set of the particular
computer that will be used to carry out the work of the program. The instruction
set architecture (ISA) is the complete specication of the interface between pro-
grams that have been written and the underlying computer hardware that must
carry out the work of those programs.
An analogy that may be helpful in understanding the concept of an ISA is
provided by the automobile. | [
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The instruction
set architecture (ISA) is the complete specication of the interface between pro-
grams that have been written and the underlying computer hardware that must
carry out the work of those programs.
An analogy that may be helpful in understanding the concept of an ISA is
provided by the automobile. Corresponding to a computer program, represented
as a sequence of 0s and 1s in the case of the computer, is the human sitting in the
drivers seat of a car. | [
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] |
An analogy that may be helpful in understanding the concept of an ISA is
provided by the automobile. Corresponding to a computer program, represented
as a sequence of 0s and 1s in the case of the computer, is the human sitting in the
drivers seat of a car. Corresponding to the microprocessor hardware is the car
itself. The ISA of the automobile is the specication of everything the human
needs to know to tell the automobile what to do, and everything the automobile
needs to know to carry out the tasks specied by the human driver. | [
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Corresponding to the microprocessor hardware is the car
itself. The ISA of the automobile is the specication of everything the human
needs to know to tell the automobile what to do, and everything the automobile
needs to know to carry out the tasks specied by the human driver. For example,
one element of the automobiles ISA is the pedal on the oor known as the
brake, and its function. | [
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] |
The ISA of the automobile is the specication of everything the human
needs to know to tell the automobile what to do, and everything the automobile
needs to know to carry out the tasks specied by the human driver. For example,
one element of the automobiles ISA is the pedal on the oor known as the
brake, and its function. The human knows that if he/she steps on the brake, the
car will stop. | [
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For example,
one element of the automobiles ISA is the pedal on the oor known as the
brake, and its function. The human knows that if he/she steps on the brake, the
car will stop. The automobile knows that if it feels pressure from the human on
that pedal, the hardware of the automobile must engage those elements necessary
to stop the car. The full ISA of the car includes the specication of the other
pedals, the steering wheel, the ignition key, the gears, windshield wipers, etc. | [
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] |
The automobile knows that if it feels pressure from the human on
that pedal, the hardware of the automobile must engage those elements necessary
to stop the car. The full ISA of the car includes the specication of the other
pedals, the steering wheel, the ignition key, the gears, windshield wipers, etc. For
each, the ISA species (a) what the human has to do to tell the automobile what
he/she wants done, and (b) correspondingly, what the automobile will interpret
those actions to mean so it (the automobile) can carry out the specied task. | [
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The full ISA of the car includes the specication of the other
pedals, the steering wheel, the ignition key, the gears, windshield wipers, etc. For
each, the ISA species (a) what the human has to do to tell the automobile what
he/she wants done, and (b) correspondingly, what the automobile will interpret
those actions to mean so it (the automobile) can carry out the specied task.
The ISA of a computer serves the same purpose as the ISA of an auto-
mobile, except instead of the driver and the car, the ISA of a computer species
the interface between the computer program directing the computer hardware
and the hardware carrying out those directions. | [
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For
each, the ISA species (a) what the human has to do to tell the automobile what
he/she wants done, and (b) correspondingly, what the automobile will interpret
those actions to mean so it (the automobile) can carry out the specied task.
The ISA of a computer serves the same purpose as the ISA of an auto-
mobile, except instead of the driver and the car, the ISA of a computer species
the interface between the computer program directing the computer hardware
and the hardware carrying out those directions. For example, consider the set of
instructions that the computer can carry outthat is, what operations the com-
puter can perform and where to get the data needed to perform those operations. | [
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] |
The ISA of a computer serves the same purpose as the ISA of an auto-
mobile, except instead of the driver and the car, the ISA of a computer species
the interface between the computer program directing the computer hardware
and the hardware carrying out those directions. For example, consider the set of
instructions that the computer can carry outthat is, what operations the com-
puter can perform and where to get the data needed to perform those operations.
The term opcode is used to describe the operation. | [
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] |
For example, consider the set of
instructions that the computer can carry outthat is, what operations the com-
puter can perform and where to get the data needed to perform those operations.
The term opcode is used to describe the operation. The term operand is used to
describe individual data values. The ISA species the acceptable representations
for operands. They are called data types. | [
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] |
The ISA species the acceptable representations
for operands. They are called data types. A data type is a representation of an
operand such that the computer can perform operations on that representation.
The ISA species the mechanisms that the computer can use to gure out where
the operands are located. These mechanisms are called addressing modes.
The number of opcodes, data types, and addressing modes specied by an
ISA vary among dierent ISAs. | [
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0.0489475317299366,
-0.026056714355945587,
-0.013861126266419888,
0.0205095112323761,
0.02228516712784767,
-0.00793539173901081,
-0.015912078320980072,
-0.012188706547021866,
-0.0028493080753833055,
0.008251981809735298,
-0.0010099902283400297,
0.014934778213500977,
-0.03683453053236008,
0.018830209970474243,
-0.046524930745363235,
0.013496359810233116,
-0.0142603050917387,
-0.005385467316955328,
-0.00949081126600504,
0.0014194921823218465,
0.015843253582715988,
-0.018775150179862976,
0.008843866176903248,
0.004772935062646866,
-0.047571055591106415,
0.0016216622898355126,
-0.03402651846408844,
0.014053832739591599,
-0.009284338913857937,
-0.03149380162358284,
0.0048486413434147835,
-0.010378639213740826,
0.029952146112918854,
0.003905754303559661,
-0.013117828406393528,
0.006638061720877886,
0.014618189074099064,
-0.015691841021180153,
-0.01588454842567444,
-0.00850662961602211,
-0.028630727902054787,
-0.0024587325751781464,
-0.013131593354046345,
0.0030213675927370787,
-0.0026187479961663485,
-0.02302846498787403,
-0.005619468633085489,
0.02896108292043209,
-0.02155563421547413,
0.01236764807254076,
0.012223117984831333,
0.02067468874156475,
0.03397145867347717,
0.04476303979754448,
0.006077147088944912,
-0.02011033333837986,
0.004852082580327988,
-0.008024862967431545,
0.00985557772219181,
-0.018307147547602654,
-0.013124710880219936,
0.013400006107985973,
0.0034601197112351656,
-0.004642169456928968,
0.0284380204975605,
0.020743513479828835,
0.01322106458246708,
-0.020385628566145897,
-0.0034497962333261967,
-0.022615522146224976,
0.028245314955711365,
0.0026996161323040724,
-0.005908528808504343,
-0.00610811822116375,
0.050268951803445816,
-0.016462668776512146,
-0.006115000229328871,
-0.014549365267157555,
0.0018599649192765355,
-0.008754395879805088,
-0.027102837339043617,
0.017398672178387642,
0.008609865792095661,
-0.024446235969662666,
-0.02089492604136467,
0.025451065972447395,
0.011693174950778484,
-0.023221172392368317,
0.047047995030879974,
0.0031572948209941387,
0.002785645890980959,
0.00400210777297616,
0.013640889897942543,
0.0036855179350823164,
0.016338786110281944,
0.008059274405241013,
-0.01308341696858406,
0.015375250950455666,
0.037577830255031586,
-0.011273348703980446,
-0.005168672185391188,
0.008561688475310802,
-0.03650417923927307,
-0.014921014197170734,
-0.019821273162961006,
0.02334505505859852,
-0.028988610953092575,
0.013592713512480259,
0.011954705230891705,
-0.009745459072291851,
-0.004827993921935558,
0.005117054563015699,
0.02111516147851944,
0.009587164036929607,
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-0.0013506683753803372,
-0.004394403658807278,
-0.012691120617091656,
-0.014976073056459427,
0.02103257365524769,
-0.03410910815000534,
-0.008843866176903248,
-0.031383682042360306,
0.0412667877972126,
-0.01876138523221016,
0.011142583563923836,
0.021142691373825073,
0.00559537997469306,
-0.01626996137201786,
0.019133035093545914,
-0.011589938774704933,
-0.010302932932972908,
-0.0057123806327581406,
0.016820551827549934,
0.0027804840356111526,
0.006507296580821276,
0.0011433364124968648,
-0.004160402808338404,
0.0037440182641148567,
0.03119097463786602,
0.03262251242995262,
-0.03201686218380928,
-0.004975965246558189,
0.02085363119840622,
0.009566517546772957,
-0.006531384773552418,
-0.0007020034245215356,
-0.026758719235658646,
-0.012154294177889824,
-0.008988396264612675,
0.0018995386781170964,
0.007233388256281614,
0.017467496916651726,
0.07515566051006317,
0.03625641018152237,
0.019256917759776115,
0.0017524276627227664,
0.00007947005360620096,
0.01117011345922947,
0.009786753915250301,
0.00863739475607872,
0.006875504273921251,
-0.046745169907808304,
0.02045445330440998,
-0.032567452639341354,
-0.009346281178295612,
-0.007907861843705177,
0.011927175335586071,
0.017990557476878166,
-0.04925035685300827,
0.016861846670508385,
-0.019903860986232758,
-0.018857738003134727,
0.01610478386282921,
-0.0015519781736657023,
0.011176995933055878,
0.0040743728168308735,
-0.016380079090595245,
-0.0014375584432855248,
0.00397113710641861,
-0.003774988930672407,
-0.017784086987376213,
-0.05516920983791351,
0.0014470217283815145,
-0.0069030337035655975,
-0.023592820391058922,
-0.029153788462281227,
-0.009690400213003159,
-0.013757890090346336,
0.00472131697461009,
-0.024005763232707977,
0.03870654106140137,
0.007694507949054241,
-0.009174221195280552,
-0.021101396530866623,
-0.01604972593486309,
-0.04947059229016304,
0.013028357177972794,
0.03768794983625412,
-0.006142530124634504,
-0.00022238711244426668,
-0.03892677649855614
] |
These mechanisms are called addressing modes.
The number of opcodes, data types, and addressing modes specied by an
ISA vary among dierent ISAs. Some ISAs have as few as a half dozen opcodes,
whereas others have as many as several hundred. Some ISAs have only one data
type, while others have more than a dozen | [
-0.022077154368162155,
0.0065914299339056015,
0.017705850303173065,
-0.03499801084399223,
-0.025952031835913658,
0.044981684535741806,
-0.02635193057358265,
-0.015540882013738155,
-0.013107017613947392,
-0.025896873325109482,
0.029482170939445496,
0.02712414786219597,
-0.013286282308399677,
0.005729579832404852,
0.0013013937277719378,
0.027827417477965355,
0.015885621309280396,
0.006777589675039053,
0.013555179350078106,
0.02076714113354683,
-0.017057739198207855,
0.007225751876831055,
0.013672390952706337,
0.000595107558183372,
-0.007929021492600441,
0.02233915589749813,
0.006849985104054213,
-0.02800668217241764,
-0.03279167413711548,
-0.012479590252041817,
0.006191531661897898,
-0.014851401560008526,
0.0012272746535018086,
-0.01192111149430275,
-0.00047961960081011057,
0.006001924630254507,
0.007308489177376032,
-0.025510765612125397,
-0.014492872171103954,
0.002626919187605381,
0.025166025385260582,
-0.006129478104412556,
-0.0008183267200365663,
0.006098451558500528,
-0.003685271367430687,
0.02882026880979538,
-0.00391624728217721,
-0.0012031428050249815,
-0.03508074954152107,
-0.005936423782259226,
-0.003657692112028599,
0.030364705249667168,
-0.01776100881397724,
-0.015113404020667076,
0.02501433901488781,
-0.008570238016545773,
0.008149655535817146,
0.0018650437705218792,
-0.004588490352034569,
-0.017112895846366882,
0.002459720242768526,
0.00097389065194875,
-0.015471934340894222,
0.022146102041006088,
-0.010424939915537834,
0.004953914787620306,
0.031716085970401764,
0.04299598187208176,
0.005188337992876768,
-0.0036370076704770327,
0.02206336334347725,
0.018960703164339066,
0.009066663682460785,
0.012555433437228203,
0.020284505560994148,
-0.03607359901070595,
-0.0019960450008511543,
-0.003481874708086252,
0.009618247859179974,
0.003414650447666645,
0.0010988590074703097,
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0.006491455249488354,
0.010955839417874813,
0.022808002308011055,
-0.009239033795893192,
0.012114166282117367,
0.019084809347987175,
-0.0029009876307100058,
-0.00845992099493742,
0.013465547002851963,
0.00005989858618704602,
0.032929569482803345,
0.017664480954408646,
0.00928729772567749,
0.012348589487373829,
0.021070512011647224,
0.03447400778532028,
-0.035108327865600586,
0.026738040149211884,
0.005022862926125526,
0.01671299897134304,
-0.022201260551810265,
-0.006239795126020908,
-0.015885621309280396,
0.004681569989770651,
-0.004881519358605146,
0.010211200453341007,
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0.046443380415439606,
-0.008977031335234642,
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0.020877458155155182,
0.009687195532023907,
-0.007122329901903868,
-0.003816272597759962,
-0.04004500433802605,
0.0021615203004330397,
0.015375406481325626,
0.031716085970401764,
0.026572564616799355,
0.007029249798506498,
0.0050125205889344215,
-0.010252569802105427,
-0.0422513410449028,
-0.029895858839154243,
0.005719237495213747,
-0.00963203702121973,
0.014161922037601471,
0.012093481607735157,
-0.002249429002404213,
0.0031750560738146305,
-0.01809195801615715,
-0.018478067591786385,
-0.0243662279099226,
0.024876443669199944,
0.0015444355085492134,
-0.01414813194423914,
0.024986760690808296,
0.013279386796057224,
-0.018312592059373856,
0.011210947297513485,
-0.007846283726394176,
-0.014244659803807735,
0.03039228357374668,
0.02591066248714924,
0.010955839417874813,
-0.025965820997953415,
0.0071981726214289665,
-0.0009764762362465262,
-0.002740683499723673,
-0.021870309486985207,
0.016285520046949387,
0.036239076405763626,
0.036845818161964417,
0.01805059053003788,
-0.01074899546802044,
-0.025386657565832138,
0.009859565645456314,
0.03601844236254692,
-0.00575715908780694,
-0.0017142199212685227,
0.003468085080385208,
0.007563597057014704,
0.007735967170447111,
0.008453026413917542,
-0.0025993401650339365,
0.012196903117001057,
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0.004485068377107382,
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0.000019297363905934617,
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0.016781946644186974,
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0.0019339917926117778,
-0.00735675310716033,
0.0122865354642272,
0.023138953372836113,
0.023856012150645256,
0.01261059194803238,
0.025552133098244667,
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0.013203544542193413,
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0.022973477840423584,
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0.011500528082251549,
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0.01635446771979332,
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] |
The ISA species the mechanisms that the computer can use to gure out where
the operands are located. These mechanisms are called addressing modes.
The number of opcodes, data types, and addressing modes specied by an
ISA vary among dierent ISAs. Some ISAs have as few as a half dozen opcodes,
whereas others have as many as several hundred. Some ISAs have only one data
type, while others have more than a dozen. | [
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-0.005884087644517422,
-0.01544139813631773,
0.026627402752637863,
0.022898733615875244,
0.007727629505097866,
-0.02551850490272045,
-0.013480035588145256,
-0.01844928227365017,
0.024118520319461823,
-0.008600886911153793,
-0.001567184110172093,
-0.02115222066640854,
0.04737764596939087,
-0.006251409649848938,
0.00869098398834467,
-0.02837391570210457,
0.009931563399732113,
-0.018698785454034805,
-0.023605655878782272,
0.01817205734550953,
0.010291955433785915,
-0.027680855244398117,
-0.018934424966573715,
0.014900810085237026,
0.007658323738723993,
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0.03883913531899452,
-0.0037771821953356266,
0.00022784378961659968,
0.024562079459428787,
0.00896820891648531,
0.004903406370431185,
0.017867110669612885,
0.0068023931235075,
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0.00369054963812232,
0.040031202137470245,
-0.0051425122655928135,
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0.012246387079358101,
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0.013334493152797222,
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0.00799099262803793,
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0.003863814752548933,
-0.020154211670160294,
0.003000953933224082,
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0.0015888422494754195,
0.002261111279949546,
0.007263278588652611,
0.028526388108730316,
0.03678767383098602,
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0.012454305775463581,
0.02786105126142502,
0.0016113667516037822,
0.0067261564545333385,
-0.02780560590326786,
-0.014401806518435478,
-0.01584337279200554,
0.013729537837207317,
0.0013869882095605135,
0.012052330188453197,
0.07152388989925385,
0.03315603733062744,
0.018698785454034805,
-0.0038950026500970125,
0.0031672886107116938,
0.000787923694588244,
0.015025561675429344,
0.005849434528499842,
0.01584337279200554,
-0.04410639777779579,
0.017645331099629402,
-0.019724514335393906,
-0.0055340914987027645,
-0.021124497056007385,
0.012475097551941872,
0.016896825283765793,
-0.03576194494962692,
0.01304340735077858,
-0.01201767660677433,
-0.019211649894714355,
0.022566065192222595,
-0.012662223540246487,
0.01059690210968256,
-0.006601405795663595,
-0.005832107737660408,
0.008975139819085598,
0.006490516010671854,
0.0004500564537011087,
-0.023411599919199944,
-0.06647840887308121,
-0.0008373042801395059,
-0.016092875972390175,
-0.0260313693434,
-0.028637278825044632,
-0.011331547051668167,
-0.01983540505170822,
0.0058113159611821175,
-0.023910602554678917,
0.041805434972047806,
0.0013471372658386827,
-0.02458980306982994,
-0.003486096626147628,
-0.020140351727604866,
-0.04746081307530403,
0.012052330188453197,
0.024714553728699684,
-0.0145542798563838,
0.009287016466259956,
-0.03883913531899452
] |
Some ISAs have as few as a half dozen opcodes,
whereas others have as many as several hundred. Some ISAs have only one data
type, while others have more than a dozen. Some ISAs have one or two addressing
modes, whereas others have more than 20. The x86, the ISA used in the PC, has
more than 200 opcodes, more than a dozen data types, and more than two dozen
addressing modes. | [
-0.011647547595202923,
-0.006830186117440462,
0.017873886972665787,
-0.03674076497554779,
-0.015069350600242615,
0.029548272490501404,
-0.03676760569214821,
0.007373649161309004,
-0.020933380350470543,
-0.023187745362520218,
0.01688089221715927,
0.029440920799970627,
-0.010567331686615944,
-0.008299548178911209,
0.013754304498434067,
0.039800260215997696,
0.010459980927407742,
0.003777401754632592,
0.011473102495074272,
0.024489371106028557,
-0.005719777662307024,
0.002549578435719013,
-0.00006667483103228733,
0.016330720856785774,
-0.006984503008425236,
0.031185369938611984,
-0.0011406008852645755,
-0.01259357575327158,
-0.007051596883684397,
-0.035318370908498764,
0.019510984420776367,
-0.02352321520447731,
-0.018276451155543327,
-0.004310800228267908,
-0.015834223479032516,
0.009144934825599194,
-0.002831373829394579,
-0.011714641936123371,
0.0038746881764382124,
-0.0002170077059417963,
0.04047120362520218,
0.005216571502387524,
-0.013304773718118668,
0.032339390367269516,
-0.005907641723752022,
0.031158531084656715,
-0.015337727032601833,
0.0072193327359855175,
-0.04031017795205116,
0.008970490656793118,
-0.013767722994089127,
0.020799191668629646,
-0.015807386487722397,
-0.012955883517861366,
0.02106756903231144,
-0.006229693535715342,
0.008749079890549183,
-0.007541384547948837,
-0.02732074446976185,
-0.009607885032892227,
0.011372461915016174,
0.0080110440030694,
-0.009648141451179981,
0.024140480905771255,
-0.026743736118078232,
0.0010827321093529463,
0.01984645426273346,
0.03298349305987358,
0.008339805528521538,
0.008950361981987953,
0.027441514655947685,
0.031587935984134674,
0.0010030578123405576,
0.038673076778650284,
0.01857166551053524,
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0.0009082873002626002,
0.0034419307485222816,
0.0051125758327543736,
0.005572170484811068,
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0.015015674754977226,
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0.022033724933862686,
0.006692643277347088,
0.013673791661858559,
0.013009559363126755,
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-0.007299845572561026,
0.028716303408145905,
0.006370591465383768,
0.03539888188242912,
0.007366939913481474,
0.0058841584250330925,
0.008749079890549183,
0.014599691145122051,
0.016773542389273643,
-0.03910247981548309,
0.011694513261318207,
0.00504883611574769,
-0.00391494482755661,
-0.02353663370013237,
-0.013626825995743275,
-0.008957071229815483,
0.013915330171585083,
0.0001512763847131282,
0.02180560491979122,
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-0.0026233820244669914,
0.0504816509783268,
0.01008425373584032,
-0.0214298777282238,
0.022194750607013702,
0.0012873694067820907,
0.012861952185630798,
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-0.026113050058484077,
-0.003549281507730484,
0.023268258199095726,
0.028206387534737587,
0.030380239710211754,
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0.005518495570868254,
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-0.03682127967476845,
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0.021335946395993233,
0.018665596842765808,
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0.024583302438259125,
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0.01425080094486475,
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0.03805581107735634,
0.0066054207272827625,
0.0018048331839963794,
-0.011238273233175278,
0.009352927096188068,
0.005733196623623371,
0.01008425373584032,
-0.012768019922077656,
0.005847256630659103,
0.01096318755298853,
0.010191604495048523,
0.01940363273024559,
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-0.004985096864402294,
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0.003747209208086133,
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0.010392886586487293,
0.03166844695806503,
0.03126588091254234,
0.014022680930793285,
0.010768613778054714,
0.024663817137479782,
0.007152238395065069,
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0.027414677664637566,
0.023845266550779343,
0.0016622580587863922,
0.004263834562152624,
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0.007420614827424288,
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0.0061693089082837105,
0.021698253229260445,
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-0.022369196638464928,
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0.000359582802047953,
0.01685405522584915,
0.017055338248610497,
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0.004039068706333637,
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0.014747298322618008,
0.009869552217423916,
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0.0019289572956040502,
0.014022680930793285,
0.0005916866939514875,
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0.01342554297298193,
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0.028796816244721413,
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0.008950361981987953,
0.027830660343170166,
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0.022905949503183365,
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0.012264814227819443,
0.005518495570868254,
0.008427027612924576,
0.02346953935921192,
-0.030836479738354683,
-0.0019625043496489525,
0.012123916298151016,
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0.02938724495470524,
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0.016773542389273643,
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-0.012580156326293945,
0.00027948914794251323,
-0.008306258358061314,
-0.006534972228109837,
-0.024623559787869453,
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0.018276451155543327,
0.0019172158790752292,
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-0.02432834543287754,
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-0.0226778294891119,
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] |
The ISA also species the number of unique locations that comprise the com-
puters memory and the number of individual 0s and 1s that are contained in each
location.
Many ISAs are in use today. The most widely known example is the x86,
introduced by Intel Corporation in 1979 and currently also manufactured by
AMD and other companies. Other ISAs and the companies responsible for them
include ARM and THUMB (ARM), POWER and z/Architecture (IBM), and
SPARC (Oracle). | [
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The most widely known example is the x86,
introduced by Intel Corporation in 1979 and currently also manufactured by
AMD and other companies. Other ISAs and the companies responsible for them
include ARM and THUMB (ARM), POWER and z/Architecture (IBM), and
SPARC (Oracle).
The translation from a high-level language (such as C) to the ISA of the
computer on which the program will execute (such as x86) is usually done by
a translating program called a compiler. | [
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] |
Other ISAs and the companies responsible for them
include ARM and THUMB (ARM), POWER and z/Architecture (IBM), and
SPARC (Oracle).
The translation from a high-level language (such as C) to the ISA of the
computer on which the program will execute (such as x86) is usually done by
a translating program called a compiler. To translate from a program written in
C to the x86 ISA, one would need a C to x86 compiler. | [
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The translation from a high-level language (such as C) to the ISA of the
computer on which the program will execute (such as x86) is usually done by
a translating program called a compiler. To translate from a program written in
C to the x86 ISA, one would need a C to x86 compiler. For each high-level lan-
guage and each desired target ISA, one must provide a corresponding compiler. | [
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] |
To translate from a program written in
C to the x86 ISA, one would need a C to x86 compiler. For each high-level lan-
guage and each desired target ISA, one must provide a corresponding compiler.
The translation from the unique assembly language of a computer to its ISA
is done by an assembler.
1.7.5 The Microarchitecture
The next step is the implementation of the ISA, referred to as its microarchitec-
ture. | [
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] |
7.5 The Microarchitecture
The next step is the implementation of the ISA, referred to as its microarchitec-
ture. The automobile analogy that we used in our discussion of the ISA is also
useful in showing the relationship between an ISA and a microarchitecture that
implements that ISA. The automobiles ISA describes what the driver needs to
know as he/she sits inside the automobile to make the automobile carry out the
drivers wishes. | [
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] |
The automobile analogy that we used in our discussion of the ISA is also
useful in showing the relationship between an ISA and a microarchitecture that
implements that ISA. The automobiles ISA describes what the driver needs to
know as he/she sits inside the automobile to make the automobile carry out the
drivers wishes. All automobiles have the same ISA. If there are three pedals on
the oor, it does not matter what manufacturer produced the car, the middle one
is always the brake. | [
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] |
All automobiles have the same ISA. If there are three pedals on
the oor, it does not matter what manufacturer produced the car, the middle one
is always the brake. The one on the right is always the accelerator, and the more
it is depressed, the faster the car will move. Because there is only one ISA for
automobiles, one does not need one drivers license for Buicks and a dierent
drivers license for Hondas. | [
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] |
The one on the right is always the accelerator, and the more
it is depressed, the faster the car will move. Because there is only one ISA for
automobiles, one does not need one drivers license for Buicks and a dierent
drivers license for Hondas.
The microarchitecture (or implementation) of the automobiles ISA, on
the other hand, is about what goes on underneath the hood. Here all automo-
bile makes and models can be dierent, depending on what cost/performance
tradeos the automobile designer made before the car was manufactured. | [
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] |
The microarchitecture (or implementation) of the automobiles ISA, on
the other hand, is about what goes on underneath the hood. Here all automo-
bile makes and models can be dierent, depending on what cost/performance
tradeos the automobile designer made before the car was manufactured. Some
automobiles come with disc brakes, others (in the past, at least) with drums.
Some automobiles have eight cylinders, others run on six cylinders, and still oth-
ers have only four. | [
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Some
automobiles come with disc brakes, others (in the past, at least) with drums.
Some automobiles have eight cylinders, others run on six cylinders, and still oth-
ers have only four. Some are turbocharged, some are not. Some automobiles can
travel 60 miles on one gallon of gasoline, others are lucky to travel from one gas
station to the next without running out of gas. Some automobiles cost 6000 US
dollars, others cost 200,000 US dollars. | [
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] |
Some automobiles can
travel 60 miles on one gallon of gasoline, others are lucky to travel from one gas
station to the next without running out of gas. Some automobiles cost 6000 US
dollars, others cost 200,000 US dollars. In each case, the microarchitecture
of the specic automobile is a result of the automobile designers decisions
regarding the tradeos of cost and performance. The fact that the micro-
architecture of every model or make is dierent is a good reason to take ones
Honda, when it is malfunctioning, to a Honda repair person, and not to a Buick
repair person. | [
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] |
In each case, the microarchitecture
of the specic automobile is a result of the automobile designers decisions
regarding the tradeos of cost and performance. The fact that the micro-
architecture of every model or make is dierent is a good reason to take ones
Honda, when it is malfunctioning, to a Honda repair person, and not to a Buick
repair person | [
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] |
Some automobiles cost 6000 US
dollars, others cost 200,000 US dollars. In each case, the microarchitecture
of the specic automobile is a result of the automobile designers decisions
regarding the tradeos of cost and performance. The fact that the micro-
architecture of every model or make is dierent is a good reason to take ones
Honda, when it is malfunctioning, to a Honda repair person, and not to a Buick
repair person. | [
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] |
In each case, the microarchitecture
of the specic automobile is a result of the automobile designers decisions
regarding the tradeos of cost and performance. The fact that the micro-
architecture of every model or make is dierent is a good reason to take ones
Honda, when it is malfunctioning, to a Honda repair person, and not to a Buick
repair person.
In the previous section, we identied ISAs of several computer manufactur-
ers, including the x86 (Intel), the PowerPC (IBM and Motorola), and THUMB
(ARM). | [
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] |
The fact that the micro-
architecture of every model or make is dierent is a good reason to take ones
Honda, when it is malfunctioning, to a Honda repair person, and not to a Buick
repair person.
In the previous section, we identied ISAs of several computer manufactur-
ers, including the x86 (Intel), the PowerPC (IBM and Motorola), and THUMB
(ARM). Each has been implemented by many dierent microarchitectures. | [
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0.01212170161306858,
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-0.0027883299626410007,
-0.013719870708882809
] |
In the previous section, we identied ISAs of several computer manufactur-
ers, including the x86 (Intel), the PowerPC (IBM and Motorola), and THUMB
(ARM). Each has been implemented by many dierent microarchitectures. For | [
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example, the x86s original implementation in 1979 was the 8086, followed by the
80286, 80386, and 80486 in the 1980s. More recently, in 2001, Intel introduced
the Pentium IV microprocessor. Even more recently, in 2015, Intel introduced
Skylake. Each of these x86 microprocessors has its own microarchitecture.
The story is the same for the PowerPC ISA, with more than a dozen dierent
microprocessors, each having its own microarchitecture. | [
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] |
Each of these x86 microprocessors has its own microarchitecture.
The story is the same for the PowerPC ISA, with more than a dozen dierent
microprocessors, each having its own microarchitecture.
Each microarchitecture is an opportunity for computer designers to make dif-
ferent tradeos between the cost of the microprocessor, the performance that the
microprocessor will provide, and the energy that is required to power the micro-
processor. | [
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] |
The story is the same for the PowerPC ISA, with more than a dozen dierent
microprocessors, each having its own microarchitecture.
Each microarchitecture is an opportunity for computer designers to make dif-
ferent tradeos between the cost of the microprocessor, the performance that the
microprocessor will provide, and the energy that is required to power the micro-
processor. Computer design is always an exercise in tradeos, as the designer
opts for higher (or lower) performance, more (or less) energy required, at greater
(or lesser) cost. | [
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] |
Each microarchitecture is an opportunity for computer designers to make dif-
ferent tradeos between the cost of the microprocessor, the performance that the
microprocessor will provide, and the energy that is required to power the micro-
processor. Computer design is always an exercise in tradeos, as the designer
opts for higher (or lower) performance, more (or less) energy required, at greater
(or lesser) cost.
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] |
Computer design is always an exercise in tradeos, as the designer
opts for higher (or lower) performance, more (or less) energy required, at greater
(or lesser) cost.
1.7.6 The Logic Circuit
The next step is to implement each element of the microarchitecture out of simple
logic circuits. Here also there are choices, as the logic designer decides how to
best make the tradeos between cost and performance. | [
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] |
6 The Logic Circuit
The next step is to implement each element of the microarchitecture out of simple
logic circuits. Here also there are choices, as the logic designer decides how to
best make the tradeos between cost and performance. So, for example, even for
an operation as simple as addition, there are several choices of logic circuits to
perform the operation at diering speeds and corresponding costs. | [
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] |
Here also there are choices, as the logic designer decides how to
best make the tradeos between cost and performance. So, for example, even for
an operation as simple as addition, there are several choices of logic circuits to
perform the operation at diering speeds and corresponding costs.
1.7.7 The Devices
Finally, each basic logic circuit is implemented in accordance with the require-
ments of the particular device technology used. | [
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] |
7.7 The Devices
Finally, each basic logic circuit is implemented in accordance with the require-
ments of the particular device technology used. So, CMOS circuits are dierent
from NMOS circuits, which are dierent, in turn, from gallium arsenide
circuits.
The Bottom Line
In summary, from the natural language description of a prob-
lem to the electrons that actually solve the problem by moving from one voltage
potential to another, many transformations need to be performed. | [
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] |
So, CMOS circuits are dierent
from NMOS circuits, which are dierent, in turn, from gallium arsenide
circuits.
The Bottom Line
In summary, from the natural language description of a prob-
lem to the electrons that actually solve the problem by moving from one voltage
potential to another, many transformations need to be performed. If we could
speak electron, or if the electrons could understand English, perhaps we could just
walk up to the computer and get the electrons to do our bidding. | [
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] |
The Bottom Line
In summary, from the natural language description of a prob-
lem to the electrons that actually solve the problem by moving from one voltage
potential to another, many transformations need to be performed. If we could
speak electron, or if the electrons could understand English, perhaps we could just
walk up to the computer and get the electrons to do our bidding. Since we cant
speak electron and they cant speak English, the best we can do is this systematic
sequence of transformations. | [
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] |
If we could
speak electron, or if the electrons could understand English, perhaps we could just
walk up to the computer and get the electrons to do our bidding. Since we cant
speak electron and they cant speak English, the best we can do is this systematic
sequence of transformations. At each level of transformation, there are choices as
to how to proceed. Our handling of those choices determines the resulting cost
and performance of our computer. | [
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] |
At each level of transformation, there are choices as
to how to proceed. Our handling of those choices determines the resulting cost
and performance of our computer.
In this book, we describe each of these transformations. We show how tran-
sistors combine to form logic circuits, how logic circuits combine to form the
microarchitecture, and how the microarchitecture implements a particular ISA. | [
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] |
In this book, we describe each of these transformations. We show how tran-
sistors combine to form logic circuits, how logic circuits combine to form the
microarchitecture, and how the microarchitecture implements a particular ISA.
In our case, the ISA is the LC-3. We complete the process by going from the
English-language description of a problem to a C or C++ program that solves the
problem, and we show how that C or C++ program is translated (i. | [
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] |
In our case, the ISA is the LC-3. We complete the process by going from the
English-language description of a problem to a C or C++ program that solves the
problem, and we show how that C or C++ program is translated (i.e., compiled)
to the ISA of the LC-3.
We hope you enjoy the ride. | [
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] |
, Data Types, and
rations
2.1 Bits and Data Types
2.1.1 The Bit as the Unit of Information
We noted in Chapter 1 that the computer was organized as a system with several
levels of transformation. A problem stated in a natural language such as English
is actually solved by the electrons moving around inside the components of the
computer.
Inside the computer, millions of very tiny, very fast devices control the move-
ment of those electrons. | [
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] |
A problem stated in a natural language such as English
is actually solved by the electrons moving around inside the components of the
computer.
Inside the computer, millions of very tiny, very fast devices control the move-
ment of those electrons. These devices react to the presence or absence of voltages
in electronic circuits. They could react to the actual values of the voltages, rather
than simply to the presence or absence of voltages. | [
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] |
These devices react to the presence or absence of voltages
in electronic circuits. They could react to the actual values of the voltages, rather
than simply to the presence or absence of voltages. However, this would make
the control and detection circuits more complex than they need to be. It is much
easier to detect simply whether or not a voltage exists at a point in a circuit than
it is to measure exactly what that voltage is. | [
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] |
However, this would make
the control and detection circuits more complex than they need to be. It is much
easier to detect simply whether or not a voltage exists at a point in a circuit than
it is to measure exactly what that voltage is.
To understand this, consider any wall outlet in your home. You could measure
the exact voltage it is carrying, whether 120 volts or 115 volts, or 118. | [
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] |
To understand this, consider any wall outlet in your home. You could measure
the exact voltage it is carrying, whether 120 volts or 115 volts, or 118.6 volts,
for example. However, the detection circuitry to determine only whether there is
a voltage or whether there is no voltage is much simpler. Your nger casually
inserted into the wall socket, for example, will suce.
We symbolically represent the presence of a voltage as 1 and the absence
of a voltage as 0. | [
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0.030373988673090935,
-0.00486762635409832,
0.005257036536931992,
0.002563616493716836
] |
Your nger casually
inserted into the wall socket, for example, will suce.
We symbolically represent the presence of a voltage as 1 and the absence
of a voltage as 0. We refer to each 0 and each 1 as a bit, which is a shortened
form of binary digit. Recall the digits you have been using since you were a
child0, 1, 2, 3, , 9. There are ten of them, and they are referred to as decimal
digits. | [
0.003321046009659767,
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0.029454171657562256,
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] |
Recall the digits you have been using since you were a
child0, 1, 2, 3, , 9. There are ten of them, and they are referred to as decimal
digits. In the case of binary digits, there are two of them, 0 and 1.
To be perfectly precise, it is not really the case that the computer dieren-
tiates the absolute absence of a voltage (i.e., 0) from the absolute presence of
a voltage (i.e., 1). | [
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] |
e., 1). Actually, the electronic circuits in the computer dierentiate
voltages close to 0 from voltages far from 0. So, for example, if the computer
expects either a voltage of 1.2 volts or a voltage of 0 volts (1.2 volts signifying
1 and 0 volts signifying 0), then a voltage of 1.0 volts will be taken as a 1 and
0.2 volts will be taken as a 0. | [
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] |
honewire,onecandifferentiateonlytwothings.Oneofthemcanbeassigned
e 0, the other can be assigned the value 1. But to get useful work done by
puter, it is necessary to be able to differentiate a large number of distinct
and to assign each of them a unique representation. We can accomplish
ombining many wires, that is, many bits. For example, if we use eight bits
(corresponding to the voltage present on each of eight wires), we can represent one
particularvalueas01001110,andanothervalueas11100111. | [
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] |
We can accomplish
ombining many wires, that is, many bits. For example, if we use eight bits
(corresponding to the voltage present on each of eight wires), we can represent one
particularvalueas01001110,andanothervalueas11100111.Infact,ifwearelimited
toeightbits,wecandifferentiateatmostonly256(i.e., 28) differentthings.Ingeneral,
with k bits, we can distinguish at most 2k distinct items. | [
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] |
, 28) differentthings.Ingeneral,
with k bits, we can distinguish at most 2k distinct items. Each pattern of these k bits
is a code; that is, it corresponds to a particular item (or value).
2.1.2 Data Types
There are many ways to represent the same value. For example, the number ve
can be written as a 5. This is the standard decimal notation that you are used to.
The value ve can also be represented by someone holding up one hand, with all
ngers and thumb extended. | [
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] |
This is the standard decimal notation that you are used to.
The value ve can also be represented by someone holding up one hand, with all
ngers and thumb extended. The person is saying, The number I wish to com-
municate can be determined by counting the number of ngers I am showing. A
written version of that scheme would be the value 11111. This notation has a name
alsounary. The Romans had yet another notation for vethe character V. | [
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] |
This notation has a name
alsounary. The Romans had yet another notation for vethe character V. We
momentarily that a fourth notation for ve is the binary representation
01.
s not enough simply to represent values; we must be able to operate on
alues. We say a particular representation is a data type if there are oper-
n the computer that can operate on information that is encoded in that
ntation. | [
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] |
s not enough simply to represent values; we must be able to operate on
alues. We say a particular representation is a data type if there are oper-
n the computer that can operate on information that is encoded in that
ntation. Each instruction set architecture (ISA) has its own set of data types
own set of instructions that can operate on those data types. In this book,
mainly use two data types: 2s complement integers for representing posi-
tive and negative integers that we wish to perform arithmetic on, and ASCII codes
for representing characters that we wish to input to a computer via the keyboard or
output from the computer via a monitor. | [
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] |
Each instruction set architecture (ISA) has its own set of data types
own set of instructions that can operate on those data types. In this book,
mainly use two data types: 2s complement integers for representing posi-
tive and negative integers that we wish to perform arithmetic on, and ASCII codes
for representing characters that we wish to input to a computer via the keyboard or
output from the computer via a monitor. Both data types will be explained shortly. | [
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] |
In this book,
mainly use two data types: 2s complement integers for representing posi-
tive and negative integers that we wish to perform arithmetic on, and ASCII codes
for representing characters that we wish to input to a computer via the keyboard or
output from the computer via a monitor. Both data types will be explained shortly.
There are other representations of information that could be used, and indeed
that are present in most computers. | [
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] |
Both data types will be explained shortly.
There are other representations of information that could be used, and indeed
that are present in most computers. Recall the scientic notation from high
school chemistry where you were admonished to represent the decimal num-
ber 621 as 6.21102. There are computers that represent numbers in that form,
and they provide operations that can operate on numbers so represented. | [
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] |
21102. There are computers that represent numbers in that form,
and they provide operations that can operate on numbers so represented. That
data type is usually called oating point. We will examine its representation in
Section 2.7.1.
2.2 Integer Data Types
2.2.1 Unsigned Integers
The rst representation of information, or data type, that we shall look at is the
unsigned integer. As its name suggests, an unsigned integer has no sign (plus or
minus) associated with it. | [
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0.025303658097982407,
-0.011507675051689148,
0.007843736559152603,
-0.0019543205853551626,
0.004073981661349535,
-0.00996009074151516,
-0.0001708170457277447,
-0.016229789704084396,
0.005737303290516138,
-0.02437775209546089,
0.0076453289948403835,
-0.0036705515813082457,
-0.02296244166791439,
0.017340876162052155,
0.0126848965883255,
0.0138356639072299,
-0.03007868118584156,
-0.007063331548124552,
0.015899108722805977,
-0.0020402974914759398,
-0.018571006134152412,
0.015991700813174248,
-0.024906842038035393,
-0.00250325002707541,
-0.016335606575012207,
-0.004331911914050579,
0.0038524256087839603,
0.01773769222199917,
0.05439029633998871,
0.03476111590862274,
-0.0040045385248959064,
0.01718214899301529,
-0.012281467206776142,
0.01870327815413475,
0.005866268649697304,
0.005459532141685486,
-0.0017046569846570492,
-0.0279094185680151,
0.027380330488085747,
-0.008835777640342712,
-0.034073300659656525,
0.011269585229456425,
0.004034299869090319,
0.016891149803996086,
-0.020488951355218887,
0.002589226933196187,
-0.03153367340564728,
-0.004090515431016684,
0.007274966686964035,
0.008941595442593098,
0.03558120131492615,
0.016653060913085938,
-0.030766496434807777,
0.009206139482557774,
0.004586535971611738,
-0.0017459921073168516,
-0.04137472063302994,
-0.033411938697099686,
-0.005677781067788601,
0.003971470519900322,
-0.022499488666653633,
-0.022697895765304565,
0.005542201921343803,
-0.010389975272119045,
-0.02025086246430874,
-0.03367648273706436,
0.03584574535489082,
-0.0015649446286261082,
0.010264316573739052,
0.005942325107753277,
-0.023174075409770012,
-0.0034192344173789024,
-0.0021758764050900936,
-0.006408584304153919,
-0.005499213468283415,
-0.0269041508436203,
-0.030713587999343872
] |
1 Unsigned Integers
The rst representation of information, or data type, that we shall look at is the
unsigned integer. As its name suggests, an unsigned integer has no sign (plus or
minus) associated with it. An unsigned integer just has a magnitude. Unsigned | [
0.0006672894232906401,
-0.0027873492799699306,
0.03159652277827263,
-0.03164905309677124,
-0.0039626979269087315,
-0.006743480917066336,
-0.03157025948166847,
-0.012764680199325085,
-0.0016842286568135023,
-0.028287163004279137,
0.013828404247760773,
0.028576074168086052,
-0.03217434883117676,
-0.011477706953883171,
-0.0001227057509822771,
-0.008627978153526783,
0.008115814998745918,
0.0005737211904488504,
0.024938402697443962,
0.017150897532701492,
0.00512163108214736,
0.007984491065144539,
0.003274888964369893,
-0.005620661657303572,
-0.00612625852227211,
0.0013526359107345343,
0.028628604486584663,
-0.03138640522956848,
0.02208867482841015,
-0.04535926505923271,
0.010387718677520752,
-0.01736101508140564,
-0.028313426300883293,
-0.04178725555539131,
-0.025056594982743263,
-0.0001464055967517197,
-0.0057880994863808155,
-0.0339340902864933,
0.012843474745750427,
-0.01684885285794735,
0.023152397945523262,
0.015246701426804066,
0.0028398786671459675,
-0.013867801055312157,
0.013473829254508018,
0.021484585478901863,
-0.012180289253592491,
-0.015982115641236305,
-0.00009905718616209924,
0.019107623025774956,
0.008148645982146263,
0.017505472525954247,
-0.02629103884100914,
-0.019882434979081154,
0.009310862980782986,
0.0008585298201069236,
-0.0037000500597059727,
0.021418923512101173,
0.002619911218062043,
-0.010184166021645069,
0.017203427851200104,
0.00845725741237402,
-0.022692766040563583,
-0.02080170065164566,
-0.014393096789717674,
-0.008161778561770916,
-0.013592020608484745,
0.000994778354652226,
-0.008890626020729542,
0.01190450880676508,
0.0062050530686974525,
0.012607092037796974,
-0.0020946157164871693,
0.012876305729150772,
0.006615439895540476,
-0.015220437198877335,
-0.006848540157079697,
-0.026080921292304993,
0.011057469993829727,
0.01560127642005682,
0.017387280240654945,
-0.012784378603100777,
-0.016047777608036995,
-0.01856919564306736,
-0.009547245688736439,
0.004153117537498474,
0.004011944402009249,
0.011957038193941116,
0.003140282118692994,
-0.04168219864368439,
0.00577496737241745,
-0.012751547619700432,
0.01921268180012703,
0.01107060257345438,
0.004839284811168909,
0.019974360242486,
0.01374960970133543,
0.01388093363493681,
-0.017531737685203552,
-0.010545306839048862,
-0.012265649624168873,
-0.0007300786674022675,
-0.024596961215138435,
-0.00003908937287633307,
-0.007840035483241081,
-0.0009898536372929811,
0.009199237450957298,
-0.01011193823069334,
-0.0008326754323206842,
-0.019987493753433228,
-0.012817209586501122,
0.031176287680864334,
-0.017269089818000793,
-0.034170471131801605,
0.014353699050843716,
0.006960165221244097,
0.012764680199325085,
0.027210306376218796,
-0.015246701426804066,
-0.015049715526401997,
0.024084798991680145,
0.016376087442040443,
0.04204990342259407,
-0.008444124832749367,
0.03629791736602783,
0.015154775232076645,
-0.015496216714382172,
-0.020525921136140823,
-0.00684197386726737,
-0.01388093363493681,
0.002943296218290925,
0.03049340285360813,
-0.012876305729150772,
0.023257458582520485,
0.015194172039628029,
0.018332812935113907,
0.0032896630000323057,
0.026067789644002914,
-0.01921268180012703,
-0.018647989258170128,
0.02482021227478981,
0.0076890126802027225,
-0.03747983276844025,
-0.005335032474249601,
0.008956287987530231,
-0.009987180121243,
0.02910136990249157,
0.022574573755264282,
-0.004806453827768564,
-0.019751111045479774,
-0.0016275952802971005,
0.013933463022112846,
0.024596961215138435,
0.01908135786652565,
0.010315489955246449,
0.015286099165678024,
-0.0057487026788294315,
0.0194096677005291,
0.01755800098180771,
0.012140892446041107,
0.01673066057264805,
0.007544556632637978,
-0.005036270711570978,
0.013178350403904915,
0.01678319089114666,
0.016822587698698044,
0.00826683733612299,
-0.005131480284035206,
-0.018595460802316666,
0.006037615239620209,
0.004619317129254341,
0.03319867327809334,
-0.006513664033263922,
0.016284160315990448,
-0.0007994340849108994,
0.0316753163933754,
0.010716027580201626,
0.010624101385474205,
-0.026698144152760506,
-0.009580076672136784,
0.026080921292304993,
-0.01977737434208393,
0.007964792661368847,
0.01665186695754528,
-0.026461759582161903,
0.030834846198558807,
0.017269089818000793,
0.011215059086680412,
0.008056719787418842,
0.0036278220359236,
0.01608717441558838,
-0.011996435932815075,
0.01190450880676508,
-0.0040743229910731316,
-0.6454830765724182,
-0.03527359291911125,
-0.018963167443871498,
-0.016546808183193207,
0.03380276635289192,
0.015246701426804066,
0.018280282616615295,
0.0022045995574444532,
0.017150897532701492,
0.027840660884976387,
0.009264899417757988,
-0.010315489955246449,
0.004015227314084768,
-0.028287163004279137,
-0.012718716636300087,
-0.012587393634021282,
-0.011379214003682137,
-0.028418486937880516,
-0.011221624910831451,
-0.008293102495372295,
0.002311300253495574,
0.014091051183640957,
-0.01703270711004734,
0.0010842427145689726,
0.014524420723319054,
-0.0070455255918204784,
0.0012500390876084566,
0.018070165067911148,
-0.028418486937880516,
0.0010325339389964938,
-0.018647989258170128,
-0.011806015856564045,
0.002695422386750579,
-0.017886310815811157,
0.02629103884100914,
-0.01477393601089716,
0.00636592460796237,
0.015929585322737694,
-0.007879432290792465,
0.02417672425508499,
-0.007780939340591431,
-0.040027517825365067,
0.03183290734887123,
-0.01562754064798355,
-0.00708492286503315,
0.014012257568538189,
-0.007334438152611256,
-0.0024196424055844545,
0.01793884113430977,
-0.030230754986405373,
0.021602777764201164,
-0.001096554333344102,
0.0004081299703102559,
0.005512319505214691,
0.02597586251795292,
-0.0290225762873888,
0.014340566471219063,
0.003716465551406145,
0.01959352195262909,
-0.006480833049863577,
0.0029974672943353653,
-0.004422331228852272,
-0.02661934867501259,
-0.006313395220786333,
0.00982959195971489,
0.007853168062865734,
-0.015259834006428719,
-0.0005142150330357254,
0.0016875118017196655,
-0.015614408068358898,
0.0029974672943353653,
0.04541179537773132,
0.011320117861032486,
0.0056337942369282246,
0.004494559485465288,
0.0066515542566776276,
0.018214620649814606,
-0.02763054333627224,
0.004806453827768564,
0.014747670851647854,
-0.008719905279576778,
-0.0036278220359236,
-0.027578013017773628,
-0.008765868842601776,
0.007748108357191086,
0.008319367654621601,
0.000013645370927406475,
-0.0048557003028690815,
0.006933900527656078,
0.020578451454639435,
0.009914952330291271,
0.025187918916344643,
0.001119535998441279,
-0.0473291240632534,
-0.011786317452788353,
0.027551747858524323,
-0.021734101697802544,
0.002477096626535058,
-0.022824089974164963,
0.010991808027029037,
0.0022308642510324717,
-0.0014683650806546211,
0.0038477894850075245,
0.03375023603439331,
0.01403852179646492,
0.0018730066949501634,
0.030966170132160187,
-0.0025460415054112673,
0.01895003393292427,
-0.01767619326710701,
0.002805406227707863,
-0.009947783313691616,
-0.004264742601662874,
0.020512789487838745,
0.007459195796400309,
-0.032515790313482285,
0.021720968186855316,
0.0019222531700506806,
0.012607092037796974,
-0.000019288194380351342,
0.03902945667505264,
0.009599775075912476,
0.012396973557770252,
-0.02462322637438774,
-0.0032847383990883827,
0.0028677850496023893,
-0.001141696935519576,
0.015167906880378723,
-0.0010341755114495754,
-0.0015208945842459798,
-0.0028710681945085526,
0.007879432290792465,
-0.0029071823228150606,
-0.017452942207455635,
0.010098805651068687,
-0.009468451142311096,
0.008135514333844185,
-0.02068351022899151,
0.0070258271880447865,
-0.01939653605222702,
-0.024938402697443962,
-0.00392330065369606,
0.008174911141395569,
-0.01666499860584736,
-0.0016062550712376833,
-0.04874742031097412,
-0.015246701426804066,
-0.005062535405158997,
0.0070455255918204784,
0.026277907192707062,
-0.01286317314952612,
0.008693640120327473,
-0.024084798991680145,
0.01564067415893078,
-0.0070258271880447865,
-0.014248640276491642,
-0.0011252814438194036,
-0.03057219833135605,
0.01889750547707081,
0.001777796889655292,
-0.011221624910831451,
0.03853042423725128,
-0.03989619389176369,
-0.006763179320842028,
-0.02240385301411152,
-0.02462322637438774,
-0.01594271883368492,
0.027289099991321564,
-0.009323994629085064,
-0.0075970860198140144,
0.013329372741281986,
0.003407854586839676,
0.0004822048358619213,
0.006835407577455044,
-0.008831530809402466,
0.013762742280960083,
-0.02878619357943535,
0.019869301468133926,
0.023756489157676697,
-0.018976299092173576,
0.005236539524048567,
-0.002030595438554883,
-0.022574573755264282,
0.003176396246999502,
-0.001713776495307684,
0.02973172441124916,
-0.014419361017644405,
-0.00033056680695153773,
-0.00470467796549201,
-0.01464261207729578,
0.003535895375534892,
0.024715153500437737,
-0.012003001756966114,
0.023717092350125313,
-0.021839160472154617,
0.03763742372393608,
0.012528297491371632,
-0.014314302243292332,
-0.0076890126802027225,
0.02661934867501259,
0.007872866466641426,
-0.0008913608035072684,
0.00684197386726737,
-0.023244325071573257,
0.046042148023843765,
-0.02380901761353016,
0.02053905464708805,
-0.014760803431272507,
0.013828404247760773,
-0.0019682166166603565,
0.019606653600931168,
-0.016034644097089767,
0.006408604793250561,
-0.016494277864694595,
-0.0038839036133140326,
0.014485022984445095,
0.009146708063781261,
0.04036895930767059,
0.015561878681182861,
-0.012193421833217144,
-0.0025542492512613535,
-0.002989259548485279,
0.02991557866334915,
0.00695359893143177,
-0.007629917003214359,
0.020827965810894966,
0.011799450032413006,
-0.001749890623614192,
-0.013605153188109398,
-0.01895003393292427,
0.01780751720070839,
0.003201019484549761,
0.014340566471219063,
-0.009960915893316269,
0.0354837104678154,
0.02686886489391327,
0.01052560843527317,
-0.024793947115540504,
0.0006796010420657694,
0.003496498102322221,
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0.026435496285557747,
0.004146551247686148,
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0.019304608926177025,
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0.0172953549772501,
0.017439810559153557,
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0.006933900527656078,
0.017636796459555626,
0.00970483385026455,
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0.01273184921592474,
0.005032987333834171,
-0.005771683994680643,
0.008378462865948677,
0.009258332662284374,
0.010893315076828003,
0.02030267007648945,
0.008536051958799362,
0.013033894822001457,
0.013066725805401802,
0.006769745610654354,
0.01620536670088768,
0.01004627626389265,
-0.010926146060228348,
-0.010919580236077309,
-0.012521731667220592,
0.011267588473856449,
-0.0004407557426020503,
-0.024281784892082214,
-0.01633669063448906,
0.019002564251422882,
-0.0045241075567901134,
0.006861672271043062,
0.013710211962461472,
-0.002191467210650444,
0.036455508321523666,
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0.012659621424973011,
0.03721718490123749,
0.002368754241615534,
-0.046042148023843765,
0.010341755114495754,
0.010072541423141956,
0.00012978492304682732,
-0.012199987657368183,
-0.012410106137394905,
0.01927834376692772,
0.03146519884467125,
-0.011819148436188698,
0.00982302613556385,
0.007754674647003412,
0.04480770602822304,
0.008509786799550056,
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0.025936465710401535,
0.024807078763842583,
0.01990869827568531,
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0.019737977534532547,
0.040237635374069214,
0.022233132272958755,
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0.008943155407905579,
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0.008017322048544884,
0.008890626020729542,
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0.008424426428973675,
0.020762303844094276,
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0.004235194995999336,
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0.022285660728812218,
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0.0025082859210669994,
0.00048015289939939976,
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0.013027328066527843,
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] |
integers have many uses in a computer. If we wish to perform a task some spe-
cic number of times, unsigned integers enable us to keep track of this number
easily by simply counting how many times we have performed the task. Unsigned
integers also provide a means for identifying dierent memory locations in the
computer in the same way that house numbers dierentiate 129 Main Street from
131 Main Street. | [
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] |
If we wish to perform a task some spe-
cic number of times, unsigned integers enable us to keep track of this number
easily by simply counting how many times we have performed the task. Unsigned
integers also provide a means for identifying dierent memory locations in the
computer in the same way that house numbers dierentiate 129 Main Street from
131 Main Street. I dont recall ever seeing a house number with a minus sign in
front of it. | [
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] |
Unsigned
integers also provide a means for identifying dierent memory locations in the
computer in the same way that house numbers dierentiate 129 Main Street from
131 Main Street. I dont recall ever seeing a house number with a minus sign in
front of it.
We can represent unsigned integers as strings of binary digits. To do this, we
use a positional notation much like the decimal system that you have been using
since you were three years old. | [
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] |
We can represent unsigned integers as strings of binary digits. To do this, we
use a positional notation much like the decimal system that you have been using
since you were three years old.
You are familiar with the decimal number 329, which also uses positional
notation. The 3 is worth much more than the 9, even though the absolute value of
3 standing alone is only worth 1/3 the value of 9 standing alone. | [
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] |
You are familiar with the decimal number 329, which also uses positional
notation. The 3 is worth much more than the 9, even though the absolute value of
3 standing alone is only worth 1/3 the value of 9 standing alone. This is because,
as you know, the 3 stands for 300 (3102) due to its position in the decimal string
329, while the 9 stands for 9 100.
Instead of using decimal digits, we can represent unsigned integers using just
the binary digits 0 and 1. | [
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] |
This is because,
as you know, the 3 stands for 300 (3102) due to its position in the decimal string
329, while the 9 stands for 9 100.
Instead of using decimal digits, we can represent unsigned integers using just
the binary digits 0 and 1. Here the base is 2, rather than 10. So, for example, if
we have ve bits (binary digits) available to represent our values, the number 5,
which we mentioned earlier, is represented as 00101, corresponding to
0 24 + 0 23 + 1 22 + 0 21 + 1 20
With k bits, we can represent in this positional notation exactly 2k integers, rang-
ing from 0 to 2k 1. | [
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] |
Here the base is 2, rather than 10. So, for example, if
we have ve bits (binary digits) available to represent our values, the number 5,
which we mentioned earlier, is represented as 00101, corresponding to
0 24 + 0 23 + 1 22 + 0 21 + 1 20
With k bits, we can represent in this positional notation exactly 2k integers, rang-
ing from 0 to 2k 1. Figure 2.1 shows the ve-bit representations for the integers
from 0 to 31. | [
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] |
Figure 2.1 shows the ve-bit representations for the integers
from 0 to 31.
2.2.2 Signed Integers
To do useful arithmetic, however, it is often (although not always) necessary to
be able to deal with negative quantities as well as positive. We could take our 2k
distinct patterns of k bits and separate them in half, half for positive integers and
half for negative integers. In this way, with ve-bit codes, instead of representing
integers from 0 to +31, we could choose to represent positive integers from +1
to +15 and negative integers from 1 to 15. | [
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] |
We could take our 2k
distinct patterns of k bits and separate them in half, half for positive integers and
half for negative integers. In this way, with ve-bit codes, instead of representing
integers from 0 to +31, we could choose to represent positive integers from +1
to +15 and negative integers from 1 to 15. There are 30 such integers. Since
25 is 32, we still have two 5-bit codes unassigned. | [
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] |
There are 30 such integers. Since
25 is 32, we still have two 5-bit codes unassigned. One of them, 00000, we would
presumably assign to the value 0, giving us the full range of integer values from
15 to +15. That leaves one 5-bit code left over, and there are dierent ways to
assign this code, as we will see momentarily.
We are still left with the problem of determining what codes to assign to what
values. | [
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] |
That leaves one 5-bit code left over, and there are dierent ways to
assign this code, as we will see momentarily.
We are still left with the problem of determining what codes to assign to what
values. That is, we have 32 codes, but which value should go with which code?
Positive integers are represented in the straightforward positional scheme.
Since there are k bits, and we wish to use exactly half of the 2k codes to represent
the integers from 0 to 2k1 1, all positive integers will have a leading 0 in their
representation. | [
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] |
That is, we have 32 codes, but which value should go with which code?
Positive integers are represented in the straightforward positional scheme.
Since there are k bits, and we wish to use exactly half of the 2k codes to represent
the integers from 0 to 2k1 1, all positive integers will have a leading 0 in their
representation. In our example of Figure 2.1 (with k = 5), the largest positive
integer +15 is represented as 01111. | [
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0.01352661196142435,
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-0.0341513492166996
] |
In our example of Figure 2.1 (with k = 5), the largest positive
integer +15 is represented as 01111.
Note that in all three signed data types shown in Figure 2 | [
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] |
Since there are k bits, and we wish to use exactly half of the 2k codes to represent
the integers from 0 to 2k1 1, all positive integers will have a leading 0 in their
representation. In our example of Figure 2.1 (with k = 5), the largest positive
integer +15 is represented as 01111.
Note that in all three signed data types shown in Figure 2.1 , the represen-
tation for 0 and all the positive integers start with a leading 0. | [
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] |
Note that in all three signed data types shown in Figure 2.1 , the represen-
tation for 0 and all the positive integers start with a leading 0. What about the
representations for the negative integers (in our ve-bit example, 1 to 15)? | [
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] |
11111
31
15
0
1
Figure 2.1
Four representations of integers.
The rst thought that usually comes to mind is: If a leading 0 signies a positive
integer, how about letting a leading 1 signify a negative integer? The result is
the signed-magnitude data type shown in Figure 2.1. A second thought (which
was actually used on some early computers such as the Control Data Corpora-
tion 6600) was the following: Let a negative number be represented by taking the
representation of the positive number having the same magnitude, and ipping
all the bits. | [
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] |
1. A second thought (which
was actually used on some early computers such as the Control Data Corpora-
tion 6600) was the following: Let a negative number be represented by taking the
representation of the positive number having the same magnitude, and ipping
all the bits. That is, if the original representation had a 0, replace it with a 1; if
it originally had a 1, replace it with a 0. | [
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] |
A second thought (which
was actually used on some early computers such as the Control Data Corpora-
tion 6600) was the following: Let a negative number be represented by taking the
representation of the positive number having the same magnitude, and ipping
all the bits. That is, if the original representation had a 0, replace it with a 1; if
it originally had a 1, replace it with a 0. For example, since +5 is represented as
00101, we designate 5 as 11010. | [
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] |
That is, if the original representation had a 0, replace it with a 1; if
it originally had a 1, replace it with a 0. For example, since +5 is represented as
00101, we designate 5 as 11010. This data type is referred to in the computer
engineering community as 1s complement and is also shown in Figure 2.1. | [
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] |
At this point, you might think that a computer designer could assign any bit
pattern to represent any integer he or she wants. And you would be right! Unfor-
tunately, that could complicate matters when we try to build an electronic circuit
to add two integers. In fact, the signed-magnitude and 1s complement data types
both require unnecessarily cumbersome hardware to do addition. Because com-
puter designers knew what it would take to design a circuit to add two integers,
they chose representations that simplied the circuit. | [
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