The Physics of Computing

261 Pages·2017·11.404 MB·English

by  Marilyn Wolf

The Physics of Computing
Marilyn Wolf
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MorganKaufmannisanimprintofElsevier
Preface
This bookisanattempttotakeastepback andprovide alonger,morefoundational
view of computer engineering. While a lot of software design proceeded from the
theoreticaltotheexperimentaldthinkaboutsorting,forexampledcomputersystem
design has long taken an example-driven approach. Studying particular computer
systemswasusefulintheearlydayswhenwewerenotquitesurewhatmajorconcepts
undergirded the design of these systems. But today we are much more capable of
making generalized statements about many topics in computer engineering. Those
foundational topics should formthe core ofour approach tocomputerengineering.
Afoundationalapproachtodigitalsystemsisparticularlyimportantbecauseitis
sohardtodaytotouchandseelogicinoperation.WhenIwasastudent,mostsystems
were boardsmadeofSSIandMSI logic. Wehadnochoice buttodeal withcircuits
andwaveforms.Today,allthatishiddeninsideachip;evenboardshavesmallerwires
and are harder to analyze. Many students today think that 1s and 0s float through
chipsdtheyhave noconception ofvoltagesand currents incomputers.
This book does not ask students to design anything. Instead, we walk students
through the principles that define the computer system design space. I like to think
of the concepts inthis course as knobs and meters on a control panel. Changing the
settingsofknobschangethevaluesonthemeters;thetwistofoneknobmaychange
severalmeters.Consider,forexample,thecascadingeffectsofreducingMOSdielec-
tric thickness: transistor transconductance changes, which in turn affects gate delay
for the better andleakage current for theworse.
Engineersdonotdesignsystemsinavacuum.Instead,theydesigntoasetofgoals
orrequirements.Thetraditionalgoalforcomputerarchitectsisperformance,ormore
preciselythroughput.Butcomputersareactuallydesignedwithseveralothergoalsin
mind, with energy/power and reliability paramount. Performance, energy, and reli-
abilityallhavetheirrootsinphysicalphenomenon.Andtheyareinextricablylinked
by physics: improving one metric incurs costs inthe othermetrics. As in the rest of
life, thereis no free lunch incomputer design.
Computer engineering is a relatively young field. Introductory courses have
concentrated on building and taxonomydbuild something, see the different ways
to buildsomething. As the field matures, it is time tostart thinking about new ways
to present the basics. The biologist E.O. Wilson said, “A field is initially defined by
thequestionsitasksandeventuallydefinedbytheanswersitprovides.”After70years
ofelectroniccomputerengineering,itistimetostartthinkingofthefieldintermsof
answers.
Ihavebeenthinkingaboutcomputerdesignforalongtime.Performancewasfor
manyyearstheparamountmetricforcomputerdesign,althoughtheASICworldwas
always interested in area as a proxy for cost. I started to think more seriously about
other fundamental limits, particularly power, for the class on pervasive information
systems taught by Perry Cook and myself. A new course at Georgia Tech gave me
the impetusto take thistrain ofthoughttoits logical conclusion.
ix
x Preface
Thiscoursetakesabroadviewofbothcomputerengineeringandphysics.Someof
the most basic phenomena in computer architecture and even software designdthe
memory wall, the power wall, the race to darkdare due to fundamental physics.
But the physics required to understand these major computational issues is much
more than classical Shockleysemiconductortheory. We need tounderstand thermo-
dynamics, electrostatics, andgood deal of circuit theory.
As I thought about this material, I came to regard Boltzmann’s constant is a key
concept. k pops up everywhere: the diode equation, Arrhenius’s equation, tempera-
ture, and the list goes on. Boltzmann’s constant links temperature and energy, so it
shouldnot bea surprisethat it is sotightly woven intothe topics of thisbook.
Some of the material in this book is unique to modern CMOSdleakage mecha-
nisms. But some of the topics can be applied to a wide range of circuit and device
technologies. Delay through logic networks, metastability, and the fundamentals of
reliability are examples of foundational concepts that computer engineers should
understand evenif CMOS is swept off the map by some other technology.
Partsofthis bookwill probablystrike some readers ashopelesslysimplified and
compressed.Ihopethatthosesamereaderswillfindotherpartsofthebookdenseand
hardtofollow.Theonlywaytounderstandhowcomputersworkistounderstandthe
relationships between an entire collection of topics that do not always seem at first
glancetoberelated.Weknowthoseknobsonthedesignprocessarelinkedbecause
a change to one parameter that we think will help our design often results in side
effects that negate much of the benefit we sought. I worked very hard to find the
simplest possible description for a lot of concepts. Hopefully they are presented in
awaythatgivesabasicunderstanding.Thereaderwhoisinterestedinadeeperunder-
standing of one of these topics can pursue each one in more depth. But the singular
goalofthisbookistoprovideaunifieddescriptionofthefundamentalphysicalprin-
ciples ofcomputingmachines.
Bothcomputerengineersandelectricalengineersarepotentialaudiencesforthis
book. These two groups come to the material with very different backgrounds.
Computer engineers often have limited experience in circuit design. While they
may have some knowledge of ideas like Kirchhoff’s laws, they usually are not
extremely comfortable with circuit analysis. Electrical engineers may not always
have a detailed understanding of computer architecture. One of my challenges in
writingthisbookwastoprovideenoughbackgroundforeachaudiencewithoutover-
loadingthem.
I have mentioned a number of historical discoveries and inventions for several
reasons.First,goingthroughthesequenceofideasthatledtotoday’sdesignpractices
helpsbothtoremindusthatthereisoftenmorethanonewaytodothingsandtohigh-
light the true advantages of the methods that were settled upon by history. Second,
semiconductor physics and computer engineering have produced some of the most
importantinventionsofthe20thcentury.Theseinventionswillbeusedforcenturies
to come. We should not let ourselves become so accustomed to these ideas that we
lose all capacity tomarvelat them and at their inventors.
Preface xi
RichardFeynman’sLecturesonComputingwasanearlyinspirationforthisclass,
butmuchofthatbookisdevotedtoquantumcomputing.Thatbookdoesnotconsider
many topics in traditional computing. For example, metastability is a fundamental
physicalconceptincomputersystemdesignthatFeynmandoesnottouch.Wesalute
himforhisearlyrecognitionofthephysicalnatureofcomputing.Wealsothankhim
fortheLecturesonPhysics,whichprovidedaclear,concisewaytothinkaboutmany
of the basic physical phenomena that underlie computing.
Severaltipsofthehatareinorder.MyfriendandcolleagueSaibalMukhopodhyay
proposed the Physical Foundations of Computer Engineering course and provided
many concrete suggestions, particularly on reliability and leakage. My thanks go
outtohimforhispatienceandinsight.DaveCoelhograciouslyprovidedinformation
on his power distribution system. Kees Vissers invented thewelder current compar-
ison. Alec Ishii advised me on clock distribution. Kevin Cao suggested how to
make best use of the Predictive Technology Models. Bruce Jacob gave insight into
DRAM.SriniDevadas’ssuggestionsledtotheadvancedtopicsappendix.TomConte
providedthecorememoryandPentiumProaswellasmanydiscussionsonthepresent
state and future of computing. Thanks to the reviewers for their helpful comments.
And many thanks to my editor Nate McFadden for guiding this book through the
long development and production process. Any faults in this book can be traced
entirelyand solely tome.
Marilyn Wolf
Atlanta, GA
The Physics of Computing
1st Edition
Author: Marilyn Wolf
eBook ISBN: 9780128096161
Paperback ISBN: 9780128093818
Published Date: 2nd November 2016
Page Count: 276
Table of Contents
Preface
Chapter 1. Electronic Computers
1.1. Introduction
1.2. The long road to computers
1.3. Computer system metrics
1.4. A tour of this book
1.5. Synthesis
Chapter 2. Transistors and Integrated Circuits
2.1. Introduction
2.2. Electron devices and electronic circuits
2.3. Physics of materials
2.4. Solid-state devices
2.5. Integrated circuits
2.6. Synthesis
Chapter 3. Logic Gates
3.1. Introduction
3.2. The CMOS inverter
3.3. Static gate characteristics
3.4. Delay
3.5. Power and energy
3.6. Scaling theory
3.7. Reliability
3.8. Synthesis
Chapter 4. Sequential Machines
4.1. Introduction
4.2. Combinational logic
4.3. Interconnect
4.4. Sequential machines
4.5. Synthesis
Chapter 5. Processors and Systems
5.1. Introduction
5.2. System reliability
5.3. Processors
5.4. Memory
5.5. Mass storage
5.6. System power consumption
5.7. Heat transfer
5.8. Synthesis
Chapter 6. Input and Output
6.1. Introduction
6.2. Displays
6.3. Image sensors
6.4. Touch sensors
6.5. Microphones
6.6. Accelerometers and inertial sensors
6.7. Synthesis
Chapter 7. Emerging Technologies
7.1. Introduction
7.2. Carbon nanotubes
7.3. Quantum computers
7.4. Synthesis
Appendix A. Useful Constants and Formulas
Appendix B. Circuits
Appendix C. Probability
Appendix D. Advanced Topics
References
Index
CHAPTER
1
Electronic Computers
1.1 Introduction
Wetakecomputersforgranted.Butwhatisacomputer?Thecomputersweuseevery
daycanbesummarizedasEBT:electronic,binary,Turingmachines.Thiscombina-
tion oftechnologieshas allowed us toconquerproblems asdiverseas weather fore-
casting, self-driving vehicles, andshopping.
But the path that led us to today’s computers is long, and the EBTapproach to
computing is surprisingly recent. Some of the history helps us understand why we
build computers the way we do. Machines that could computedcalculate with
numbers and perform other multistep tasksdwere originally conceived of and built
withtheonlydevicesavailable,namelymechanicaldevices.Thesemechanicalcom-
putershadseverelimitationsthatwereovercomeonlywiththecreationofelectronic
devices.
Wewill startwith abriefintroduction tothehistoryofcomputing machines. We
willthendiscussthetheoryofcomputingthatwasdevelopedbasedonthisearlyexpe-
rienceandwhichunderpinsourmodernideasofcomputers.Wethendiscussthemet-
ricsweusetoevaluatecomputerdesignsandthetrade-offsbetweenthesegoalsthat
physicsimposesonus.Wewillwrapupwithasurveyoftheremainderofthisbook.
1.2 The long road to computers
Mechanicalcomputationwasinspiredinlargepartbytheneedtocontrolmachines.
Peoplecouldnotreactquicklyandreliablyenoughtomaintaintheproperoperationof
the equipment that appeared during the Industrial Revolution. Early mechanical
computingdeviceswereanalogdtheyoperatedoncontinuousvalues.Butmachines
that manipulated discrete values arrived surprisingly early. Eventually, theory was
developed to describe these types of machines. One of those theories, the Turing
machine, is the blueprint for theway inwhich we design computers today.
1
ThePhysicsofComputing.http://dx.doi.org/10.1016/B978-0-12-809381-8.00001-8
Copyright©2017ElsevierInc.Allrightsreserved.
2 CHAPTER 1 Electronic Computers
1.2.1 Mechanical computing devices
Mechanical devices are much older than electrical devices. The subtlety required to
makemachineswithcomplexbehaviorsshouldnotbeminimized.Thoseearlyinven-
tors lacked hardened metals with which to make both the machines themselves and
the tools required to shape the parts. They also lacked machine tools that we take
for granted today. Even relatively simple machines needed to be controlled without
humanintervention.Theinventionofthesteamenginespurreddemandforautomatic
control ofmachines.
Control Thegovernorisaprimeexampleofanearlyanalogcomputerbuiltfrommechan-
icalcomponents.JamesWatt,theinventorofthefirstpracticalsteamengine,designed
agovernortocontrolthespeedofthesteamengine,andsimilardeviceshadbeenused
before.Hebuilthisgovernorin1788.Fig.1.1showstheoperationofWatt’sgovernor.
The central shaft is rotated and is connected to the steam engine’s crankshaft. Two
shaftsarehingedatthetop,withaweightattheendofeach.Asetofleversconnect
theweightedshaftstotheengine’sthrottledthehighertheweights,themoreclosed
the throttle. As the central shaft (and the engine’s crankshaft) rotates at higher
speed, theweights lift themselves up due to centrifugal force, causing the engine to
be throttled down. This mechanism implements negative feedback, a fundamental
principle incontrol.
Memory The Jacquard loom demonstrates an important concept, built with mechanical
elements, which would be fundamental to our modern conception of computers:
discrete memory. The loom, which was created in 1801, was invented to automate
theweavingofcomplexpatternsinfabrics.Itcreatedahugemassmarketforsophis-
ticatedfabricsthatpreviouslyhadbeenavailableonlytotheverywealthy.AsFig.1.2
shows,afabricconsistsofthreadsinbothx,knownastheweftthread,andthewarp
threadiny.Theloom’sshuttlemovesthewarpthreadbackandforth.Liftingtheweft
threadswithsmallhooksknownasbolushooksselectivelycausesthewarpthreadto
beeitheraboveorbelowtheweft,selectingwhenitwillbevisible.Themorecomplex
thepattern,themorecomplexthepatternsofthreadliftings;acomplexpatterncould
lifthundredsofthreadsinadifferentpatternoneachrow.TheJacquardloomstored
that complex pattern in punched card: a hole in the card allowed the bolus hook to
throttle
FIGURE1.1
Amechanicalgovernor.
1.2 The long road to computers 3
Warp
Weft
FIGURE1.2
OperationofaJacquardloom.
descend and grab its weft thread; no hole meant that the weft was not lifted at that
point. Not only could the card represent complex two-dimensional patterns, but the
entire fabric’s patterncould bechanged simply by replacing the card.
Babbagemachines Charles Babbage started work in 1822 on a difference machine to calculate
numbers, specifically to compute polynomial functions. His work was motivated by
the need to tables of functions that were more accurate than those compiled by
hand calculation, an error-prone process. At the heart of this machine’s operation is
the use of gears to count; this principlewas also used in the mechanical calculators
thatwerewidelyusedwellintothesecondhalfofthe20thcentury.Thebasicprinciple
behindmechanicalcountingissimpleandelegant,asshowninFig.1.3.Weuseashaft
whosepositionrepresentsthevalueofadigitinthecountingsum.Wecanputaradial
mark on the end of each shaft, then a dial around the shaft with a position for each
digit; the mark points thevalue of the shaft’s digit. To builda two-digit counter, we
connect the two shafts with gears. In this figure, the small gear has 5 teeth and the
largegearhas15teeth,givingagearingratioof3:1.Threefullrotationsofthesmall
gear produce one complete rotation of the largegear. The largegear remembers the
number of teeth turned against it by the small gear up to a limit of 15. If we want
to count in base 10, we gear the shafts at a 10:1 ratio: 10 rotations of the ones-digit
5 teeth
15 teeth
FIGURE1.3
Usinggearstocount.
4 CHAPTER 1 Electronic Computers
shaftresultinonerotationofthetens-digitshaft.Now,asweturntheones-digitshaft,
we can count either up ordown.
Babbage later went on to design an analytical engine that had the essential ele-
ments of a modern computer but in mechanical form: input and output in the form
of punched cards (and even a plotter for output); a program memory that could
performwhatwenowknowasbranchesandloops.Butheneverfinishedtheconstruc-
tion ofeither his difference machineor the analyticalengine.
Hollerithpunchcards HermanHollerithcombinedtheideaofpunchedcardsasmemorywithcounting
machines.Histabulatingmachine[Hol88]punchedholesatvariouslocationsinpaper
cardstorecorddata;thecardsweresimilartothecardsoftheJacquardloom.Hethen
scanneddecks ofcardsthrough electromechanical readers thatcountedthe numbers
ofholesatvariouslocations.Hismachineswereusedtotabulatedataforthe1890US
Census. His company became one of the building blocks for the modern IBM
Corporation.
Allthesemachinesweregreatadvances.TheJacquardloomandHollerith’stabu-
lation machines provided huge increases in productivity for important tasks. But in
retrospect, we can see some inherent problems with the use of mechanical devices
forcomputingthatwouldultimatelylimithowfarthislineofdevelopmentcouldgo:
(cid:129) Mechanical components are relativelyheavyand introducenoticeable friction.
Both these properties mean that we haveto use substantialamounts ofenergyto
makethemwork.Evenwithtoday’snanometer-scaleelectroniccomputers,energy
is a prime enemy.
(cid:129) Mechanical components are also subject towear, which introduces slop inthe
connectionsbetween components.In the case of mechanical analogcomputers
such as the Watt regulator,the accuracyof the control lawis limited bythe
accuracy with which the mechanism can move. Inthe case ofdiscretesystems
such as the Babbage engines, the mechanical componentshad tobe accurately
aligned, andthe complex organization ofthesedevices meantthat tolerances in
one partof the machineaffect the tolerances elsewhere.
1.2.2 Theories of computing
Mathematicallogic Mathematicians spent several centuries developing mathematical notation and
theories that freed them from the imprecision of written language. George Boole
introducedanalgebraforlogicalexpressionsthatwenowknowasBooleanalgebra.
He developed laws for basic logical operations such as AND, OR, and NOT. One
simple way to describe a logical function is a truth table as shown in Fig. 1.4: the
left-hand columns enumerate the possible arguments to the function, and the right-
hand column gives the result for each. Boole’s mathematics is an algebra because
its rules are analogous tothose oftraditional numerical arithmetic.
Lambdacalculus Oneoftheimportantquestionsinmathematicsatthestartofthe20thcenturywas
thenatureofcomputingdwhatfunctionscouldbecalculated?Mathematiciansdevel-
opedmorethanoneanswertothisquestion.Theiranswersturnedouttobeimportant
notjust for theorybutalso toshape the organization of computing machines.