cs 61c: great ideas in computer architecture lecture 2 ...cs61c/fa17/lec/02/02 numrep, c...

CS61C:GreatIdeasinComputerArchitecture

Lecture2:Numbers&CLanguage

KrsteAsanović &RandyKatz

http://inst.eecs.berkeley.edu/~cs61c

Agenda• Numberswrap-up• Thisisnotontheexam!• Break• CPrimer• Administrivia,Break• CTypedeclarations• AndinConclusion,…CS61c Lecture2:CProgrammingLanguage 2

Recap:BinaryNumberConversion

Binaryà Decimal

1001010two = ?ten

Decimalà Binary

74ten = ?two

9/6/17 3Fall2017 - Lecture#1

BinaryDigit

DecimalValue

0 0 x 20 = 0

1 1 x 21 = 2

0 0 x 22 = 0

1 1 x 23 = 8

0 0 x 24 = 0

0 0 x 25 = 0

1 1 x 26 = 64

S = 74ten

Decimal Binary(odd?)74 0

/2 = 37 1

/2 = 18 0

/2 = 9 1

/2 = 4 0

/2 = 2 0

/2 = 1 1

Collect à 1001010two

SignedIntegerRepresentationHowtorepresent-5?Sign&magnitude(8-bitexample):

Rulesforaddition,a+b:• If(a>0andb>0):addb toa• If(a>0andb<0):subtractb froma• …• +0,-0à aretheyequal?Ifso,comparatormusthandlespecialcase!(Ifnotequal???)

Cumbersome• ”Complicated”hardware:reducedspeed/increasedpower• Isthereabetterway?

9/6/17 4Fall2017 - Lecture#1

sign 7-bitmagnitude (0…127)

Goingbackwardsbygoingforwards• Howtoadd-1toafour-bitnumber?

9/6/17 5Fall2017 - Lecture#1

0111two = 7ten????two + = -1ten0110two = 6ten

Goingbackwardsbygoingforwards• Add10000two andthrowawayfifthbit,resultunchanged

– Resultwrapsaroundtosamevalue

9/6/17 6Fall2017 - Lecture#1

0111two = 7ten10000two + = 16ten10111two = 7ten+16ten0111two = 7ten

Goingbackwardsbygoingforwards• Add(10000two – 1two = 01111two)andthrowawayfifthbit– Onelessthanoriginalvalue

9/6/17 7Fall2017 - Lecture#1

0111two = 7ten01111two + = 16 - 1ten10110two = 16 + 6ten0110two = 6ten

4-bitExample

7+ -3

4

9/6/17 8

7+ -3 +16

4 +16

7+ 13

4 +16

0111+ 1101

10100 0100 +10000

Decimal Binary

• Mapnegativeà positivenumbers§ ExampleforN=4-bit:-3à 24– 3=13§ “Two’scomplement”§ Nospecialrulesforaddingpositiveandnegativenumbers

-8 -7 … -1 0 1 … 70 1 … 7 8 9 … 15

+24 =16

Extrabitisignoredasdoesn’tfitin4bits.

Two’sComplement(8-bitexample)

9/6/17 9Fall2017 - Lecture#1

AsSignedDecimal AsUnsignedDecimal

BinaryNumber

-128 128 1 0 0 0 0 0 0 0-127 129 1 0 0 0 0 0 0 1… … …-2 254 1 1 1 1 1 1 1 0-1 255 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 01 1 0 0 0 0 0 0 0 1… … . . .127 127 0 1 1 1 1 1 1 1

Most-significantbit(MSB)equalssignwheninterpretedasasignednumber

+256

+0

SignedversusUnsignedBinaryNumbers

• Botharestoredasacollectionofbits• Thesamesetofbitscanbeusedtorepresentasignednumberoranunsignednumber(orastring,orapicture,ora….)

• It’suptotheoperationinterpretingthebits

9/6/17 10Fall2017 - Lecture#1

1101two =+13ten (asanunsignednumber)1101two =-3ten(asasignednumber)1101two =orange(asacolor)1101two =cat(asatypeofanimal)1101two =whateveryouwantittomean…

UnaryNegation(Two’sComplement)4-bitExample(-8ten …+7ten)

BruteForce&Tedious Clever&Elegant

16ten 10000two- 3ten - 0011two13ten 1101two

16ten 10000two- 13ten - 1101two

3ten 0011two

”largest”4-bitnumber+1

9/6/17 Fall2017 - Lecture#1 11

15ten 01111two- 3ten - 0011two12ten 1100two invert

+1ten +0001two13ten 1101two

YourTurn

• Whatisthedecimalvalueofthefollowingbinary8-bit2’scomplementnumber?

11100001two

9/6/17 12Fall2017 - Lecture#1

Answer ValueRED 33ten

ORANGE -31tenGREEN 225tenYELLOW -33ten

Addition4-bitExample

Unsigned Signed(Two’sComplement)

9/6/17 13Fall2017 - Lecture#1

3ten 0011two+4ten +0100two

7ten 0111two


14ten 1110two


7ten 0111two

3ten 0011two+-5ten +1011two

-2ten 1110two

Nospecialrulesfortwo’scomplementsignedaddition

Overflow4-bitExample

Unsignedaddition Signedaddition(Two’sComplement)

9/6/17 14Fall2017 - Lecture#1


27ten 1 1011two


8ten 0 1000two

-3ten 1101two+-2ten +1110two

-5ten 1 1011two

7ten 0111two+1ten +0001two-8ten 01000two

Carry-outà Overflow Carry-outà Overflow

carry-outbutnooverflowcarry-outandoverflow

nocarry-outbutoverflownocarry-outandnooverflow

AdditionOverflowDetection4-bitExample

Unsignedaddition• Carry-outindicatesoverflow

Signedaddition(Two’sComplement)• Overflowif

– SignsofoperandsareequalAND

– Signofresultdiffersfromsignofoperands

• Nooverflowispossiblewhensignsofoperandsdiffer

9/6/17 15Fall2017 - Lecture#1

Overflowrulesdependontheoperation(signedvs unsignedaddition)

AddingNumbersofDifferentBitWidths

• Whatshouldweassumeforupperfourbitsoffirstoperand?• Treataszeros!• “Zero-extension”

9/6/17 16Fall2017 - Lecture#1

1101 (4-bit,13ten)10100101 + (8-bit,165ten)????0010 (8-bit,???ten)

Unsignedaddition

00001101 (4-bit,13ten)10100101 + (8-bit,165ten)10110010 (8-bit,178ten)

Zero extension

AddingSignedNumbersofDifferentBitWidths

• Whatshouldweassumeforupperfourbitsoffirstoperand?• Copysignbit(MSB)ofoperandintoupperbits– Ifsignis1,copy1s,ifsignis0copy0s

• “Sign-extension”

9/6/17 17Fall2017 - Lecture#1

1101 (4-bit,-3ten)10100101 + (8-bit,-91ten)????0010 (8-bit,???ten)

Signedaddition

11111101 (4-bit,-3ten)10100101 + (8-bit,-91ten)10100010 (8-bit,-94ten)

SignextensionSignbit

SignExtensionDecimal Binary

4-bit 8-bit 32-bit3ten 0011two 00000011two 0000000000000011two-3ten 1101two 11111101two 1111111111111101two

9/6/17 18Fall2017 - Lecture#1

• Whenisthisrelevant?• Anytimeyouneedawiderversionofanarroweroperand

e.g.,addingtwointegersofdifferentwidths

YourTurn

• Whichrangeofdecimalscanbeexpressedwitha6-bittwo’scomplementnumber?

9/6/17 19Fall2017 - Lecture#1

Answer RangeRED -32…32

GREEN -64…63ORANGE -31…32YELLOW -32…31

Agenda

• Numberswrap-up• Thisisnotontheexam!• Break• CPrimer• Administrivia,Break• CTypedeclarations• AndinConclusion,…

CS61c Lecture2:CProgrammingLanguage 20

HotChips 2017:Brains&Dinosaurs• Topconferenceintroducingnewprocessorchips

CS61c

Lecture2:CProgrammingLanguage

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CS61c


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Z14,IBMMainframe,50+yearson

CS61c


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CS61c


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Break!

9/6/17 25Fall2017 - Lecture#2

LevelsofRepresentation

lw t0,0(s2)lw t1,4(s2)sw t1,0(s2)sw t0,4(s2)

HighLevelLanguageProgram(e.g.,C)

AssemblyLanguageProgram(e.g.,RISC-V)

MachineLanguageProgram(RISC-V)

HardwareArchitectureDescription(e.g.,blockdiagrams)

Compiler

Assembler

MachineInterpretation

temp=v[k];v[k]=v[k+1];v[k+1]=temp;

0000 1001 1100 0110 1010 1111 0101 10001010 1111 0101 1000 0000 1001 1100 0110 1100 0110 1010 1111 0101 1000 0000 1001 0101 1000 0000 1001 1100 0110 1010 1111

LogicCircuitDescription(CircuitSchematicDiagrams)

ArchitectureImplementation

Anythingcanberepresentedasanumber,

i.e.,dataorinstructions

27

CurrentFocus

IntroductiontoC“TheUniversalAssemblyLanguage”

• Languagesusedin61C:• C• Assembly• Pythonusedintwolabs

• Priorprogrammingexperiencehelpful,e.g.• Java• C++

28CS61c Lecture2:CProgrammingLanguage

Survey

WhohasneverwrittenaprograminJavaor

C,C++,Objective-C?


HelloWorldC

Java


Compilation&Running$ gcc HelloWorld.c$ ./a.outHello World!$


CCompilationSimplifiedOverview(morelaterincourse)

32

foo.c bar.c

Compiler Compiler

foo.o bar.o

Linker lib.o

a.out

Csourcefiles(text)

Machinecodeobjectfiles

Pre-builtobjectfilelibraries

Machinecodeexecutablefile

Compiler/assemblercombinedhere

CS61c Lecture2:CProgrammingLanguage

CompilationversusInterpretationC(compiled)

• Compiler(&linker)translatessourceintomachinelanguage• MachinelanguageprogramisloadedbyOSanddirectlyexecutedbythehardware

Python(interpreted)

• Interpreteriswritteninsomehigh-levellanguage(e.g.C)andtranslatedintomachinelanguage• LoadedbyOSanddirectlyexecutedbyprocessor• Interpreterreadssourcecode(e.g.Python)and“interprets”it


Java“ByteCode”• Javacompiler(javac)translatessourceto“bytecode”• “Bytecode”isaparticularassemblylanguage

- Justlikei86,RISC-V,ARM,…- Canbedirectlyexecutedbyappropriatemachine

§ implementationsexist(ed),notcommerciallysuccessful- Moretypically,“bytecode”is

§ interpretedontargetmachine(e.g.i86)byjavaprogram§ compiledtotargetmachinecode(e.g.byJIT)

- Programrunsonanycomputerwitha“bytecode”interpreter(moreorless)


Compilation• Excellentrun-timeperformance:

- Muchfasterthaninterpretedcode(e.g.Python)- UsuallyfasterthanJava(evenwithJIT)

• Note:Computersonlyrunmachinecode- Compiledapplicationprogram,or- Interpreter(thatinterpretssourcecode)


Compilation:Disadvantages• Compiledfiles,includingtheexecutable,are

- architecture-specific,dependingonprocessortype§ e.g.,RISC-Vvs.ARM

- andtheoperatingsystem§ e.g.,Windowsvs.Linux

• Executablemustberebuiltoneachnewsystem- I.e.,“portingyourcode”toanewarchitecture

• “Change® Compile® Run[repeat]”iterationcyclecanbeslowduringdevelopment- Recompileonlypartsofprogramthathavechanged- Tools(e.g.make)automatethis


CDialects$ gcc x.c

$ gcc –ansi –Wpedantic x.c


CPre-Processor(CPP)

• Csourcefilespassthroughmacroprocessor,CPP,beforecompilation• CPPreplacescommentswithasinglespace• CPPcommandsbeginwith“#”• #include “file.h” /* Inserts file.h */• #include <stdio.h> /* Loads from standard loc */• #define M_PI (3.14159) /* Define constant */• #if/#endif /* Conditional inclusion of text */• Use–save-tempsoptiontogcc toseeresultofpreprocessing• Fulldocumentationat:http://gcc.gnu.org/onlinedocs/cpp/

38

foo.c CPP foo.i Compiler


Administratrivia• Notifyusofallknownvariances

- DSPspecialaccommodations:EmailheadTA(StevenHo)- Examconflicts:FillouttheformonPiazza(specialaccommodationscanbemadeonlyinexceptionalcases)

- Ifyoucannotgetaninstructionalaccount,emailheadTA

•NotifyheadTAbyTuesday,9/5/2017- seehttp://www-inst.eecs.berkeley.edu/~cs61c/fa17/


Break!

9/6/17 41Fall2017 - Lecture#2

TypedVariablesinCint a = 4;float f = 1.38e7;char c = ‘x’;


• Declarebeforeuse• Typecannotchange• LikeJava

Type Description Examplesint integers,positiveornegative 0,82,-77,0xAB87unsignedint ditto, nonegatives 0,8, 37float (single precision)floatingpoint 3.2,-7.9e-10char textcharacterorsymbol ’x’,‘F’,‘?’double highprecision/range float 1.3e100long integerwithmorebits 427943

ConstantsandEnummerations inC• Constants

- Assignedintypeddeclaration,cannotchange- E.g.

§ const float pi = 3.1415;§ const unsigned long addr = 0xaf460;

• Enumerations

44

Integers:Pythonvs.Javavs.C

• C:int- integertypethattargetprocessorworkswithmostefficiently

• Onlyguarantee:- sizeof(longlong)≥sizeof(long)≥sizeof(int)≥sizeof(short)- Also,short >=16bits,long >=32bits- Allcouldbe64bits

• Impactsportabilitybetweenarchitectures45

Language sizeof(int)Python >=32bits(plainints),infinite (longints)Java 32bitsC Dependsoncomputer;16 or32or64


VariableSizes:MachineDependent!sizeof ... (bytes) char: 1short: 2int: 4unsigned int: 4long: 8long long: 8float: 4double: 8


Boolean• Noboolean datatypeinC

- Declareifyouwish:typedef int boolean;const boolean false = 0;const boolean true = 1;

• WhatevaluatestoFALSEinC?- 0(integer)- NULL(aspecialkindofpointer:moreonthislater)

• WhatevaluatestoTRUEinC?- Anythingthatisn’tfalseistrue- SimilartoPython:

only0’soremptysequencesarefalse,everythingelseistrue!CS61c Lecture2:CProgrammingLanguage 47

FunctionsinCint number_of_people() {

return 3;

}

void news() {

printf(”no news”);

}

int sum(int x, int y) {

return x + y;

}


• LikeJava• Declarereturn&argumenttypes• void fornovaluereturned• FunctionsMUSTbedeclaredbeforetheyareused

UninitializedVariablesCode Output

$ gcc test.c

$ ./a.outx = 0x = 16807x = -4x = 282475249x = -16


Struct’s inC• Struct’s arestructuredgroupsofvariables• AbitlikeJavaclasses,butnomethods• E.g.


MoreC…• LecturedoesnotcoverCcompletely

- You’llstillneedyourCreferenceforthiscourse- K&R,TheCProgrammingLanguage- &otherreferencesonthecoursewebsite

• Nextfewlectures’focus:- Pointers &Arrays- Memorymanagement


AndInConclusion,…• Signedintegersrepresentedin2’scomplement• CProgrammingLanguage

- Popular(still!)- SimilartoJava,but

§ noclasses§ explicitpointers(nextlecture)

- Beware§ variablesnotinitialized§ variablesize(#ofbits)ismachine&compilerdependent

• Ciscompiledtomachinecode- UnlikePythonorJava,whichareinterpreted- Compilationisfasterthaninterpretation


cs 61c: great ideas in computer architecture lecture 2 ...cs61c/fa17/lec/02/02 numrep, c...

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