Where are we? - University of...
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Where are we? Instruction set architecture (e.g., MIPS) Compiler Memory system I/O system Processor Datapath & Control Digital logic translating source code (C or Java) Programs to assembly language And linking your code to Library code How the software talks To the hardware How a processor runs MIPS Programs! How switches (1 or 0) can be used to build Interesting functions: from integer arithmetic to programmable computers
Transcript of Where are we? - University of...
Wherearewe?
Instructionsetarchitecture(e.g.,MIPS)
Compiler
Memorysystem I/OsystemProcessor
Datapath &Control
Digitallogic
translatingsourcecode(CorJava)ProgramstoassemblylanguageAndlinkingyourcodetoLibrarycode
HowthesoftwaretalksTothehardware
HowaprocessorrunsMIPSPrograms!
Howswitches(1or0)canbeusedtobuildInterestingfunctions:fromintegerarithmetictoprogrammablecomputers
CS2630ComputerOrganization
Meeting2:Bits,bytes,andmemoryBrandonMyers
UniversityofIowa
Arithmeticonnumbers
StoringnumbersNumbertotrackthecurrentlineintheprogram
Caveat…wewillbuildeverythingfromswitches(onoroff)• Abinarydigit(or,bit) hastwopossiblevalues0or1• Justlikeadecimaldigithas10possiblevalues0-9
Hundreds|tens|ones19310 =193
fours|twos|ones1012 =101
digitisapowerof10
digitisapowerof2
Peerinstruction
• Translatethefollowingbinarynumberstodecimal• 102 =____10• 1112=____10• 101012=____10
• Bonus,translatethisfractionalnumber• 11.012
Bits:formorethanjustnumbers
Bitscanbeusedtoencode(represent)ANYkindofdata,yesanydata
https://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Microphone.svg/2000px-Microphone.svg.png
http://www.billboard.com/charts/hot-100
https://upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Desktop_computer_clipart_-_Yellow_theme.svg/2000px-Desktop_computer_clipart_-_Yellow_theme.svg.png
Sampleanalogsignal(displacementofmicrophonediaphragm)onceevery23us(44.1KHz)– storeitdigitally asan8-bitnumber
Peerinstruction
Howmanyuniquevaluescanyourepresentwith3bits?
Peerinstruction
• Howmanybitsareneededtorepresentthenumberπ?a) 1bitb) infinitebitsc) 3bitsd) 8 bitse) Can’tbedone
CountingwithNbits(N=3)
000001
010
011
100101
110
111
Whataboutnegativeintegers?
000001
010
011
100101
110
111
Positiveintegersonly(“unsigned”)
01
2
345
6
7
000001
010
011
100101
110
111
Positive&negativeintegers(“signed”)
01
2
3-4-3
-2
-1
Makesomespaceforthem!
Two’scomplementjustworks!
• 11001=(-1)*16+(1)*8+(0)*4+(0)*2+1*1=-16+9=-7
• 1001=(-1)*8+(0)*4+(0)*2+1*1=-7
Ortheinvertandadd1trick-7=11001->00110->00111=7
invert +1
Peerinstructions:Two’scomplementandHex
1. Whatis-1110 inbinary(usingtwo’scomplementencodingforintegers)?
2. A116 =____10
Anothercommonbase:16Binary(2) Decimal(10) Hexadecimal (16)
00000 0 0
00001 1 1
00010 2 2
00011 3 3
00100 4 4
00101 5 5
00110 6 6
00111 7 7
01000 8 8
01001 9 9
01010 10 A
01011 11 B
01100 12 C
01101 13 D
01110 14 E
01111 15 F
10000 16 10
10001 17 11
… …
Anoteonconventions
• Sometimesweindicateabinarynumberwithprefix0b• 101012 or 0b10101
• Sometimesweindicateahexnumberwithprefix0x• FA4116 or 0xFA41
WherewearegoingnextBitsstorewhateveryouwant,includingintegers.Howdowemanipulatesequencesofbits?
Q:Howdowearrangebitsinthememoryofthecomputer?(whydowecare?wewantthecomputertostoremanyindividualnumbers)A:bytes andwords
Q:Howdowenameorrefertoallthoseindividualnumbersinmemory?A:addresses andpointers
10110000
10110000 00001110 01000010 11110001
10110000 00001110 01000010 11110001
0 1 2 3
Arithmeticonnumbers
StoringnumbersNumbertotrackthecurrentlineintheprogram
Instructionmemory
Executionengine
Datamemory
Arithmeticonnumbers
StoringnumbersNumbertotrackthecurrentlineintheprogram
Instructionmemory
Executionengine
Datamemory
organizesitsbitsasbytes andwords
candobitwiseoperations(andotherstuff)
Backtobitssoon,butfirst…memory!
Organizingbits
• Byte:aunitofdata• IntheMIPSarchitecture,bytesare8-bitslongandarethesmallestunitofdatathearchitecturegivesanameto (moreonnamessoon)• Trueofmostothermodernarchitectures,too
00011010 1byte,perhapsstoringtheinteger2610
1A Wealsoliketowritethevalueofabyteastwohexdigits
Memoryorganization
1A …
Wethinkofmemoryasonebigarrayofbytes
AnalogyinJava?byte[] memory = new byte[NUM_BYTES];
• Justlikeeveryelementinanarrayhasanindex,everybyteinmemoryhasanindex,calleditsaddress.
• Usetheaddresstofindthebytetoreadorwriteit
1A …
http://www.publicdomainpictures.net/view-image.php?image=2759
Whattodonow
• HW1andQuiz1• Newreadingsareup• Buyyourclickerlicense(ifyoudon’tyethaveone)andgothroughgettingstarteddoc• linkedfromthesyllabus• We’lltryitMonday/WedandstartkeepingtrackFriday
• Takealookatsyllabusforofficehours/DebugYourBrain
Organizebytesintomachinewords
1A
0000000100020003000400050006000700080009000A000B000C000D000E000F
(noteaddressinhex)
32-bitwords 64-bitwords
PeerInstruction
1A
0000000100020003000400050006000700080009000A000B000C000D000E000F
(noteaddressinhex)
32-bitwords 64-bitwords
MIPShas32-bitaddresses
WhatisthelargestnumberofbytesthememoryofaMIPScomputercanhave?
Lookingatmemoryaswords000000040008000C001000140018001C002000240028
Storingvalues
• storethevalue integer1510 ataddress 0x0008 00 00 00 0F
000000040008000C001000140018001C002000240028
Storingvalues
• storethevalue integer1510 ataddress 0x0014• storethevalue integer2010ataddress 0x0000
00 00 00 14
00 00 00 0F
000000040008000C001000140018001C002000240028
Addressescanbevalues,too!
• storethevalue integer1510 ataddress 0x0014• storethevalue integer2010 ataddress 0x0000• storethevalue address0x0014 ataddress 0x001C
00 00 00 14
00 00 00 0F
00 00 00 14
000000040008000C001000140018001C002000240028
Addressescanbevalues,too!• storethevalue integer1510 ataddress 0x0014• storethevalue integer2010 ataddress 0x0000• storethevalue address0x0014 ataddress 0x001C• wesaythewordataddress0x001Cisapointertotheintegerataddress0x0014
00 00 00 14
00 00 00 0F
00 00 00 14
000000040008000C001000140018001C002000240028
Addressescanbevalues,too!• storethevalue integer1510 ataddress 0x0014• storethevalue integer2010 ataddress 0x0000• storethevalue address0x0014 ataddress 0x001C• wesaythewordataddress0x001Cisapointertotheintegerataddress0x0014
• storethevalue address0x001C ataddress 0x0028• wesaythewordataddress0x0028 isapointer toapointer toaninteger
00 00 00 14
00 00 00 0F
00 00 00 14
00 00 00 1C
000000040008000C001000140018001C002000240028
int[] arr = new int[3];
Howarrayslookinmemory000000040008000C001000140018001C002000240028
int[] arr = new int[3];arr[0] = 13;
Howarrayslookinmemory
00 00 00 0D
000000040008000C001000140018001C002000240028
int[] arr = new int[3];arr[0] = 13;arr[1] = 10;
Howarrayslookinmemory
00 00 00 0D00 00 00 0A
000000040008000C001000140018001C002000240028
int[] arr = new int[3];arr[0] = 13;arr[1] = 10;arr[2] = 16;
Howarrayslookinmemory
00 00 00 0D00 00 00 0A00 00 00 10
000000040008000C001000140018001C002000240028
Peerinstruction• Supposeweallocatethisarray:int[] arr = new int[7];andJavadecidedtoputthefirstbyteofthearray(firstbyteofarr[0])ataddress0x04
Whatistheaddressofarr[5]?a. 0x04b. 0x14c. 0x09d. 0x54e. 0x05f. 0x18
address=baseaddress+index*element_size
Sizeofdatatypes(inbytes)Javadatatype sizein32-bit
architecturesizein64-bitarchitecture
boolean 1 1byte 1 1short 2 2int 4 4long 8 8float(later!) 4 4reference (storesamemoryaddress)
4 8
slideinspiredbyUWCSE351
Administrivia:Moreofficehours!
• Xin’sofficehoursnowscheduled!• Monday4:30pm- 6:00• Friday9:30am– 11• 101NinMacleanHall(MLH)
Aside:namingpowersoftwo• Oneofourfavoriteformulas:howmanyuniquethingscanyourepresentwithNbits?2Nthings• NamingconventionsN =? name Close (butnotequal!)to
powerof10
10 Kibi (Ki) 103 orKilo (K)20 Mebi (Mi) 106orMega (M)30 Gibi (Gi) 109orGiga (G)40 Tebi (Ti) 1012orTera (T)50 Pebi (Pi) 1015orPeta (P)60 Exbi (Ei) 1018orExa (E)
Namethesenumbersofbytes:
211 bytes=_____
232 bytes=_____
259 bytes=_____
Wherewearegoing(today)Bitsstorewhateveryouwant,includingintegers.Howdowemanipulatesequencesofbits?
Q:Howdowearrangebitsinthememoryofthecomputer?(whydowecare?wewantthecomputertostoremanyindividualnumbers)A:bytes andwords
Q:Howdowenameorrefertoallthoseindividualnumbersinmemory?A:addresses andpointers
10110000
10110000 00001110 01000010 11110001
10110000 00001110 01000010 11110001
0 1 2 3
DONE(fornow)
DONE(fornow)
NEXT
Changingthenumberofbits• Oftenweneedtochangethenumberofbitsweareusingtostoreanumber(why?)
• 1210 using4bitsis11002• Ifwestoreitin8bits:000011002
• -510 using4bitsis:1011• Ifwestoreitin8bits:____________2
Wecallthisoperationsignextension: copytheleftmostbitin4-bitnumbertothenew4leftmostbitsinthe8-bitnumber
Representingsetswithbits• 4-bitvectorrepresentssubsetsof{3,2,1,0}• 1meansintheset,0meansnotintheset
• Aistheset{1,0},encodedas0011• Bistheset{2,0},encodedas0101
• Setoperationsusingbitwiseoperators• A&BIntersection0001(1iff bothare1)• A|BUnion0111(1iff atleastone1)• A^Bsymmetricdifference0110(1iff exactlyone1)• ~Bcomplement1010(1iff 0)
slideinspiredbyUWCSE351
Shift
• shift:movebitsleftorright
• Leftshift:5<<2
• Rightshift:5>>1
0 0 1 0 1
1 0 1 0 0
0 0 1 0 1
0 0 0 1 0
PeerinstructionWhatistheintegerresultfromevaluatingthisexpression?(assumeintegersare32bits)
(7<<2)&15
Let’splayacardgame
• Comeupwithabinaryencodingfora52-carddeck
SlideinspiredbyCSE351Spring2016
Operationsonapairofcards
• Wewantthefollowingoperationstobeeasytoimplement• Comparetwocards,whichishighervalue?• Comparetwocards,aretheythesamesuit?
Whereweareheadednext
Instructionmemory
Executionengine
Datamemory
organizesitsbitsasbytes andwords
Storesprograms!
candobitwiseoperations(andotherstuff)
Whattodonow
• HW1isouttoday:duenextThursday• Buyyourclickerlicense(ifyoudon’tyethaveone)andgothroughgettingstarteddoc• VoteonDebugYourBrainavailabilityifyouhaven’tyet• <30postsonthe“Introduceyourself…”discussionthread;godoit
