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Although the first half of this module is about analogue circuits and signals, we will nevertheless introduce the topic of digital representations and signals in this lecture. We will come back to digital in later lectures.

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Bywayofintroductiontodigitalelectronics,Iwillspendthenextperiodjustgoingthroughsomeofthebasicideasindigitalcircuits.Ifyouknowthisalready,justbepatient.Someofyourclassmatesmaynotbefamiliarwithatleastsomeaspectsofthis.Iwillbecoveringinthiscoursequiteabitofdigitalelectronics,butnotdowntotransistorlevel.However,youwillbelearningsomethingaboutwhat’sinsideadigitalcircuits,theideaofcombinationalandsequentialcircuits;somethingaboutdigitalcounters,microprocessors.Youwillalsolearnhowtogetdigitalhardwareandcomputersoftwareworkingtogethertodosomethinginteresting.

Althoughthislectureintroducesyoutodigitalcircuits,Iwillnotcomebacktodigitalagainuntilthesecondpartofthecourse.

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Itisimportantforyoutoappreciatethehigh-levelviewofanelectronicsystem,end-to-end.Shownhereisamobilephonelinkedtoanothermobilephone.Thespeechsignal,likemanyelectricalsignalinthephysicalworld,areanalogueinnature.Thatis,thesignalvariescontinuouslyintimeandinamplitude.Amodernelectronicsystemconvertstheanaloguesignalintodigitalformintwosteps.Itsamplesthedataintodiscretetime,aprocessknownas“sampling”.Itthendigitizeeachsampleintodiscretelevels,aprocessknownas“quantization”.

YouwilllearninthesecondyearcourseinEEEthatthesamplingprocessingdoesNOTdestroyinformation.Weknowhowtorecovertheoriginalsignalwithoutloosinganyinformation.However,quantizationwillalwayslooseinformation–wewillonlyhaveanapproximationoftheoriginalsignal.

Oncethespeechisindigitalform,itgoesthroughmanydigitalcircuitswhichcompressesthespeechsignalsothatyoutrytosendaslittleinformationaspossible,thesearethenturnintoelectricalsignalsthataresuitablefortransmissionthroughair,cableoropticalfibre.Thisprocessiscalledmodulation.Formodernphones,thetransmissioncouldverywellbeviatheinternet(knownasVoiceoverIPorVoIP).Atthereceivingend,thereversehappens.

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Digitalinformationarehandledinelectronicsabinarybits,i.e.0’sand1’s.Inelectricalsignalsforms,thesearerepresentedbyelectricalvoltageVLandVH.

Verycommoninelectronicsaretwostandardsofvoltagelevels:TTL(standsfortransistor-transistor-logic)and3.3VLowVoltage(3.3LV).ForTTL,thesupplyvoltage(VCC)is5Vwith0Vasthereference.For3.3Vlogic,thesupplyis3.3V.Inbothcases,thereferencevoltageis0VorGround(GND).

Forthiscourse,wewillexclusivelyuse3.3Vlogic.Thatmean

Logic0(False)is0Vandlogic1(True)is3.3V.

Inlogiccircuitswedefinefour“threshold”voltages:VOHistheguaranteedminimumvoltageFROMANOUTPUTNODEwhichisalogicHIGH.VIHistherequiredminimumvoltagebeforeANINPUTNODEwouldregardthesignaltobelogicHIGH.Similarlyforthelowthresholdvoltages.

ThereforeifyouareusingTTLlogic,thegapbetweenVOHandVIHis0.7V.Inotherwords,ahighoutputsignalcouldbe“corrupted”bynoiseupto0.7Vandthelogiccircuitshouldstillinterpretthesignalaslogicalhigh(or‘1’).Thisdifferenceiscalled“noiseimmunity”.

Theshadedregioninthevoltagescaleareillegal“no-man”zone.Alogicsignalnodeshouldnevertakeavoltagevalueinthisregion.

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Adigitalwaveformisrealitydonothaveinfinitelyfastrisingandfallingedges.Shownhereisarealdigitalwaveformwiththemostimportantcharacteristics.

Oftenusedare:therisetime(timeittakestorisefrom10%to90%ofthefinalvalue)andthefalltime.Inrepetitivedigitalsignals,wealsoareinterestedinitsfrequency,periodanddutycycle.Dutycycleistheratiobetweenthetimethesignalishightothatoftheperiod.

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ThebasiclogicelectroniccomponentsaretheNOTgate(outputistheinverseoftheinput),ANDgate(outputis1onlyifALLtheinputsare1’s),andtheORgate(outputis1ifANYoftheinputsare1).

Interestinglyitcanbeproventhatgiventhesethreegates,onecouldintheorybuildANYdigitalcircuits,includingaPentiumCPU!Wewillcomebacktothislateronthecourse.

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Allelectronicintegratedcircuitscomeindifferentpackages,particularlyfordigitalelectronics.YouwillbeusingtheDualin-linepackagesinthelaboratory.However,ontheproject,youwillbeusingasmallmicrocontrollerboard(knownasthePyboard)whichcomesasprinted-circuitboard(PCB)withotherpackagessuchastheSOIC,FPandPLCC.

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Wewillnowconsiderdigitalsignalsrepresenting“data”orinformation.1’sand0’saremeaninglessunlesswehaveawayofinterpretingwhattheymean.Forthat,weneedcontext.

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Dataorinformationisactuallyquiteacomplexthing.Forexample,thecurrenthottopicforresearchiscalled“BigData”.Thisword,data,couldmeanmanythings:yourname(i.e.alphabets),yourage(i.e.numbers),yourpicture(imagedata),yourvoice(speech)orencodedsignalofyourspeechetc.

Indigitalelectronics,weusevoltagestorepresentsuchinformation.Thebasicdigitalbuildingblockisaswitchasimplementedinatransistor.Hereisasimpleschematicofaswitchwhichcanbeusedtopresentadigital1(switchopen)ordigital0(switchclosed).

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Howtousesuchsimplecircuittorepresentorstoreinformation?Toanswerthis,weneedtoundernumbersystem.Hereisafamiliardecimalnumbersystemwithadecimalpointinthemiddle.Itsinterpretationisstraightforward.

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Inthebinarysystem,wesimplyusebinaryinsteadofdecimalweighting.Notethatthebinarypointisalsointhemiddle.Allbinarydigits(bits)ontheleftofthebinarypointhaveweightinginincreasingpositivepowersof2(i.e.20,21…28etc.Ontherightofthebinarypoint,thepowerarenegative.

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Convertingabinaryintegertodecimalissimplebuttedious.Anyonecandoit.

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Hereisafractionalbinarynumberwith3bitsAFTERthebinarypoint.Thewholenumberishas8bits.ThisisknownasQ3format.Thisbinarynumberhasadecimalvalueof19.375.

Ifyouwanttorepresent19.376inthesame8-bitformat,youhaveaproblem.Youcan’t.19.375istheclosestyoucanuse.Thisisanexamplewhydigitalrepresentationofananaloguequantitymaygeneratequantizationerror.

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Simple – no need to explain.

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This is somewhat tedious. We will see how we can make this easier with hexadecimal (instead of binary) representation.

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Onereasonwhydigitalcircuitisusefulisthatitcandocomputationsuchasadditionveryquickly.Binaryadditionissimilartodecimaladditionwithslightdifference.Inbinaryaddition,thecarryandthetwooperands(whichyouadd)arethesame–theyareallBINARY.Soinbinaryaddition,youhavethreeinputs(A,BandCarry)andtwobinaryoutputs(SUMandCarry).

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In binary addition, the carry and the two operands (which you add) are the same – they are all BINARY. So in binary addition, you have three inputs (A, B and Carry) and two binary outputs (SUM and Carry).

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Handlinglargebinarynumberistediousandpronetoerror.Wethereforeusuallyhandlebinarynumbersingroupsoffour,withvaluesgoingfrom0todecimal15.Werepresentthevalues10to15insinglealphabetAtoF.ThisisthehexadecimalnumbersystemorHEXforshort.Itisworthwhiletomemorisethat10102isdecimal1010andA16,and11112isdecimal1510andF16.Forallotherpatterns,youjustcountupfromA16ordownfromF16.

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Thisisusing4-bitunitofbinaryrepresentationtorepresentdecimaldigits.Sincea4-bitbinarynumberhasarangeof0to15,anddecimaldigitonlygoesupto9,weareeffectivelyNOTusingtherange10102to11112.

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Codes representing letters of the alphabet, punctuation marks, and other special characters as well as numbers are called alphanumeric codes. The most widely used alphanumeric code is the American Standard Code for Information Interchange(ASCII). The ASCII (pronounced “askee”) code is a seven-bit code.