ManywaystobuildlogicoutofMOSFETs
passtransistorlogic(mostsimilartothefirstswitchlogicwesaw)
staticCMOSlogic(whatwesawlasttime)
dynamicCMOSlogic• Clock=0precharges X
throughthepMOS• clock=1givesthetwo
nMOS timetodrainchargeonXtoground(ifAandBturnthemon)
Wikimediacommons
Switchesotherthantransistors
relays(electro-mechanical)
diodes
ORgate
Wikimediacommons
CS2630ComputerOrganization
CombinationallogicforarithmeticBrandonMyers
UniversityofIowa
Peerinstruction• Drawthecircuitforthefollowingtruthtable(thisonehas2inputs,2outputs)
In0 In1 Out0 Out1
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Answerthenumberoflogicgatesusedwhenfinished;workinpairs
Wherewearegoing
Instructionsetarchitecture(e.g.,MIPS)
Compiler
Memorysystem I/OsystemProcessor
Datapath&Control
Digitallogic
translatingsourcecode(CorJava)ProgramstoassemblylanguageAndlinkingyourcodetoLibrarycode
HowthesoftwaretalksTothehardware
HowaprocessorrunsMIPSPrograms!
Howswitches(1or0)canbeusedtobuildInterestingfunctions:fromintegerarithmetictoprogrammablecomputers
Ingredientsforaprocessor• Combinationallogic• arithmeticandbitwiseoperations• multiplexors(pick1outofofNinputs)• controllogic• branchcalculation• addresscalculation
• Synchronouslogic(we’llgettotheselater)• registers• programcounter,orPC• datamemory• instructionmemory
startlearninghowtobuildthesecombinationallogiccircuits
Howdoweaddtwonumbersaddu $t0,$t1,$t2
Weknow:Thenumbersarephysicallystoredinregistersasbits
Thesumoftwonumbersisafunctionwecanimplementusingcombinationallogic
Startwitha1-bitadder
+
Sum
Carryout
A BCarryin
Peerinstruction:2-bitadder
+2-bit
Sum0
Carryout
A0B0Carryin
Sum1
A1B1
NumberofrowsoftruthtableforSum1outputof2-bitadder?
Howmanyrowsinthistruthtable?
4GBmemoryx8bit/byte=32Gbits
32registersx4Bytex8bit/byte=1Kbit
PCregisterx4Bytex8bit/byte=32bits
processortakesonestepfromcurrentstatetonewstate.Howmanyrowsinthetruthtableofbit0?
https://commons.wikimedia.org/wiki/File:Performance_PIPER_die.JPG
currentstate(theinput)
newstate(theoutput)
Administrivia• 2MidtermpracticesareonICON• takethemlikearealexamandthen checkyouranswerswiththesolutions
• DebugYourBrainnextWednesdaywillbededicatedtoreview• extraofficehour4-5pmonMonday2/27,tobededicatedtoHW3
• Reminder:Midterm3/6• opennotesopenbook,nodevices
https://en.wikipedia.org/wiki/Field-programmable_gate_array
Lookuptable(LUT)– aprogrammabletruthtableinhardware!
“3-LUT”means3inputs(somustprogram8rows)
Field-programmablegatearray(FPGA)
1-bitadder
programmableMUXselectsinputs
analternativetomanufacturingyourownsiliconchip
CS2630ComputerOrganization
AddersandtimingBrandonMyers
UniversityofIowa
Howhumansaddtwonumbers• compute65210 +36710 onpaper
• compute110102 +010112 onpaper
Buildinglargercircuitsoutofcomponents:2-bitadderbuiltfrom1-bitadders
+
Sum0
C1
A0 B00
+
Sum1
C2
A1 B1individualcomponentshavetheirownsmalltruthtables;thenwejustcombinethecomponents
32-bitadder
+
Sum0
A0 B00
+
Sum1
A1 B1
+
Sum2
A2 B2
+
Sum31
A31 B31
…
Reflect:WenowhaveacircuitforA+B.WhatisasmallchangewecanmaketogetA-B?
Undertherugofcombinationallogic:computationtime
PropagationdelaythroughlogicgatesResistor-capacitor(RC)modelofNOTgatewhengiveninput0
1à0 0à1
inputchanges
R
C
1à0 0à1
ChargingacapacitorinanRCcircuit
https://www.quora.com/How-does-a-RC-circuit-work-especially-the-charges-on-the-capacitor
PropagationdelaythroughlogicgatesResistor-capacitor(RC)modelofNOTgatewhengiveninput0
1à0 0à1
inputchanges
R
C
Whentheinputchangesfrom1to0,thereisadelaybeforetheoutputoftheNOTgatereaches1
drainingthecapacitorwheninputgoes0à1
0à1
1à0 0à1
Backuptotheleveloflogicgates• InCS2630,whenwethinkaboutdelay,we’llusethefollowingsimplifiedmodel• propagationdelayishigherformorecomplexgates• propagationdelayincreaseswiththenumberofinputstoagate
• e.g.,2-inputORgateisfasterthana3-inputORgate• propagationdelayofasequenceofgatesisadditive• allinputsmustbeavailablebeforelogicgatebeginscomputing
T=0 T=0.5 T=1 T=1.5
Example:assumedelayofinverteris0.5ns
Delayofaddercircuit
+
Sum0
A0 B00
+
Sum1
A1 B1
+
Sum2
A2 B2
+
Sum31
A31 B31
…
1-bitadderdelay:sum=21-bitadderdelay:carry=1
Peerinstruction:delaytogetSum31?
Delayofaddercircuit
+
Sum0
A0 B00
+
Sum1
A1 B1
+
Sum2
A2 B2
+
Sum31
A31 B31
…
1-bitadderdelay:sum=21-bitadderdelay:carry=1
Thisadderiscalled“ripplecarryadder”
Next…• Wenowknowhowonekindofadderworksandhowlongittakestocomputetheresult• Canwebuildfasteradders?Yes!Usehierarchy/trees
Administrivia• Reminders:• extraofficehour4-5pmtodayforHW3• DYBthisweekdedicatedtoreview• MidtermonMonday3/6:opennoteopenbook,nodevices
Carry-selectadder
Peerinstruction
WhatisthedelayfromthetimeAandBareavailabletowhenSumisavailable?
delays:sum:1carry:1mux:1
Administrivia• Reminders:• DYBtonight6-7pmdedicatedtoreview
• bringyourprioritizedlistofspecificproblemsorquestionsthatyou’dliketoreview
• itwillbemostusefulifyoutakethepracticeexam(s)first• MidtermonMonday3/6:opennoteopenbook,nodevices
Peerinstruction
WhatisthedelayfromthetimeAandBareavailabletowhenSumisavailable?
delays:sum:1carry:1mux:1
1
1
22
3
3
1
1
11
2
4
4
timesignalisavailableshowninred/bold
http://www-inst.eecs.berkeley.edu/~cs150/sp13/agenda/lec/lec20-adders.pdf
computecarries
usecarriestofinishthesums
Bestcasedelayofadders?O(logn)pmeans“propagateacarry”gmeans“generateacarry”
important:pandgarenotfunctionsofc
Bestcasedelayofadders?O(logn)
http://www-inst.eecs.berkeley.edu/~cs150/sp13/agenda/lec/lec20-adders.pdf
computecarries
usecarrys tofinishthesums
criticalpath
Multiplication• Evaluate50110 x42210 onpaper
• Evaluate11002 x10012 onpaper
Aside:usefullogiccircuitnotation
Shiftingbyaconstant
Variableshifter:firstattemptwith1-bitmuxes
Variableshifter,similardesignwith8-bitmux
Canyouthinkofadesignthatavoidsusingahuge8-bitx8-choicemux?
e.g.,usingonly8-bitx2-choicemuxes andhardwiredshifters?
hardwiredshiftsbyeachpossibleshiftamount
pickwhichoneusingtheshiftamount
Multi-stageshifterusingthemagicofbinarydecision-making• Hint:RecalltheenvelopesfromHW1
anothersolution(butusesmore2-inputMUXs)istobuildthe8-inputMUXonthepreviousslideusing2-inputMUXs,likeasoccertournamentwith8teamsandonechampion
Peerinstruction• Builda2-bitmultiplier(4-bitoutput)• youmayuseanynumberof
• exampletestcases:• 01*01=0001• 10*01=0010• 10*11=0110• 11*11=1001
