Electronics notes (Digital)

Electronicsnotes(Digital)(pmsomething3009ondiscordifthereareanyerrors)Chapter Content Examples Chapter10:IntroductiontoDigitalElectronics AnaloguequantitiesvarycontinuouslywhileDigitalquantitiesvaryinsteps Howtodifferentiatebetweenanalogueanddigitalsignals:Analoguesignals:HascontinuouslyvaryingVoltagelevelsDigitalsignals:Onlyhas2distinctvoltagelevels(HIGHorLOWonly)(HIGHreferstoLogic1state(+5V),LOWreferstoLogic0state(0V)) Analoguesignals Digitalsignals LogicSwitches Pull-Upswitch: (Pull-Upresistorwithaswitchbelow)Whenswitchisclosed,outputisLogic0(0V)Whenswitchisopen,outputisLogic1(+5V) Pull-Upswitchwhenclosed: Pull-Upswitchwhenopened:

Pull-Downswitch: (Pull-Downresistorwithaswitchabove)Whenswitchisclosed,outputisLogic0(0V)Whenswitchisopen,outputisLogic1(+5V) *ResistorinPull-Up/Pull-Downswitchareusually10㏀ Resistorisneededifnotthelogicswitchwillproducean‘floating’outputwhenopen(BadasitcanpickupunwantedelectricalsignalsandtakeonLogic0orLogic1inaunpredictableway) Pull-Downswitchwhenclosed: Pull-Downswitchwhenopened: Advantages/DisadvantagesofusingDigitalsystemsoverAnaloguesystems Advantages:- Lessaffectedbyelectricalinterference(duetofairlylargedifferencebetweenvoltagelevels),cantellLogic1apartfromLogic0aslongasitisnottoobadlydistorted- Signalscanberestoredtooriginalconditionviarepeaters(cantraveloverlongdistancesandismorereliable)- Easiertodesignduetoonlyhaving2voltagelevels- Easiertostoreinformation(asitisstoredasaseriesof0sand1s)

- Largenumberofdigitalcomponentscanbesqueezedintosmallareaofsemiconductormaterial(savecosts) Disadvantages:- AdditionalstepsareneededtoconvertbetweenAnalogueandDigitalsignals(manyquantitiesinourdailylivessuchastemperatureandlightintensityareanaloguequantities) HowtorepresentanddisplayvaluesinDigitalForm DecimalSystem:Madeupof10digits(0-9)Positionofadigitdeterminesitsplacevalue BinarySystem:Madeupof2digits(bits)(0and1)PositionofabitdeterminesitsplacevalueHighestplacevalue-MostSignificantBit(MSB)Lowestplacevalue-LeastSignificantBit(LSB) *youcanpresscalculatortoskipthecalculationpartsinconvertingdecimaltobinaryandViceVersa Binary-codeddecimal(BCD):Usesgroupsof4-bitbinarycodetorepresentthedigitsofadecimalnumber(Codingsystem)Decimalnumber BCDequivalent 4 0100 98 10011000 163 000101100011 ConvertingbetweenBinary,DecimalsystemsandBCD BinarytoDecimal:11002 =(1x )+(1x)+(0x)+(0x)2 3 2 2 2 1 2 3 =8+4+0+0=1210 DecimaltoBinary:1210 R0(LSB)12÷ 2 = 6R06 ÷ 2 = 3R13 ÷ 2 = 1R1(MSB)12÷ 2 = 61210 =11002 DecimaltoBCD:=00111000011138710 𝐵𝐶𝐷 BCDtoDecimal:010101101001 =𝐵𝐶𝐷 56910

Advantages/DisadvantagesofconvertingbetweenDecimalandBCDAdvantages:- MorestraightforwardtoconvertlargerdecimalnumbertoBCDthantoBinary- Usefulfordisplayingdecimalnumbers Disadvantages:- MorebitsareneededtostorethesamenumberinBinary BCDto7-SegmentDisplay:TodisplaybinarynumbersindecimalformInsertBCDinputinto7-segmentdecodertoconvertBCDtoa7-segmentcode BCDto7-SegmentcodeTruthTable Chapter11:BasicLogicGates LogicGatesComponentswith1ormoreinputsand1outputofeitherLogic1orLogic0dependingontheLogicgate TruthTableAwaytoshowtheoutputsofaLogicgateforallpossibleinputcombinations(Inputcombinationsarearrangedinbinaryfromsmallesttobiggest) TruthtableofaNOTGateA X 0 1 1 0 CommonLogicGates NOTGate BooleanExpression:𝑋 =𝐴(InvertstheInput)TruthTableA X 0 1 1 0

ANDGate BooleanExpression:𝑋 = 𝐴 · 𝐵(ProducesaLogic1outputonlyifbothinputsareLogic1)TruthTableA B X 0 0 0 0 1 0 1 0 0 1 1 1 ORGate BooleanExpression:𝑋 = 𝐴 + 𝐵(ProducesaLogic1outputwheneitherorbothinputsareLogic1)TruthTableA B X 0 0 0 0 1 1 1 0 1 1 1 1 NANDGate(UniversalGate) (AND+NOTgate)BooleanExpression:𝑋 =𝐴 · 𝐵(OppositeofANDgate;ProducesLogic1ifonlyoneinputisLogic1orbothinputsareLogic0)

TruthTableA B X 0 0 1 0 1 1 1 0 1 1 1 0 NORGate(UniversalGate) (OR+NOTgate)BooleanExpression:𝑋 =𝐴 + 𝐵(OppositeofORgate;ProducesLogic1onlyifbothinputsareLogic0)TruthTable:A B X 0 0 1 0 1 0 1 0 0 1 1 0 UniversalGates:Gatesthatcanbeusedtomakeanyothertypeofgates(NAND,NOR) NOT,AND,ORusingNANDgates:

NOT,AND.ORusingNORgates: Dual-In-Line(DIL)ICsIdentifyingpins: Pin1-BesideDotandNotch*RefertoDatasheetforDILICconnections,ratingsandcharacteristics KeyDILICs:74LS00-2inputNANDgate74LS02-2inputNORgate74LS04-NOTgate74LS08-2inputANDgate74LS11-3inputANDgate74LS32-2inputORgate74LS47-BCDto7-Segmentdecoder74LS390-DecadeCounterNE555-555TimerLM311-VoltageComparator Chapter12:CombinationalLogicCircuits DescribingaLogicCircuit TocreateTruthTable:1.DeterminenumberofRows(Numberofpossibleinputcombinations)andColumns(Numberofinputs,intermediatesignalsandoutputs)2.DrawandfilluptheinputsoftheTruthTable3.Workouttheintermediatesignalsandoutputs BooleanExpressionToexpresstheoutputsofanTruthTable(sum-of-productexpression)(SOP)-Product(multiply)· -Sum(addup)+-Inverse𝑋 WhenA=1.B=1,X=1WhenA=0,C=1,X=1TruthTable:A B C X 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1

SOPexpression:𝑋 =𝐴· 𝐵· 𝐶 +𝐴· 𝐵 · 𝐶+ 𝐴 · 𝐵 · 𝐶+ 𝐴 · 𝐵 · 𝐶 ConvertingBooleanexpressionintoLogicCircuit Step1:DrawaLogiccircuitforeachANDtermStep2:ConnecttheoutputstotheinputsofanORGate 𝑋 =𝐴· 𝐶 + 𝐵 + 𝐴 · 𝐵· 𝐶 KarnaughMap(K-map)TosimplifySOPexpressionstoreducenumberofgatesrequired,savingcostsandreducingerrors Step1.PrepareK-Map2-Input: 3-Input: (NotethatthenumbersforBCarearrangedas00011110) Step2:InputinformationintoK-Map Step3:Loopthe1sintheK-Map- Loopingroupsof2or4orindividually- Onlyloop1sthatareadjacenttoeachother- FirstandLastcolumnareconsideredadjacenttoeachother Step4:ObtainthesimplifiedBooleanexpressionbyidentifyingthecommoninputs 𝑋 =𝐴· 𝐵 · 𝐶 + 𝐴 · 𝐵· 𝐶+ 𝐴 · 𝐵 · 𝐶 A3-inputK-Mapwillbeused SimplifiedSOPexpression:𝑋 =𝐵+ 𝐴 · 𝐶 (p.s.K-Mapiseasierinmyopinion)

BooleanAlgebraTosimplifySOPexpressionstoreducenumberofgatesrequired,savingcostsandreducingerrors BooleanLaws*LawsgiveninDatasheet OneVariable:Law Explanation 𝐴= 𝐴 If𝐴 = 0, 0=1= 0andviceversa 𝐴 + 0 = 𝐴 Addinga0 𝐴 + 1 = 1 Answerwillalwaysbecome1 𝐴 + 𝐴 = 𝐴 IfA=1,resultis1IfA=0,resultis0 𝐴 +𝐴= 1 Eitheror =1𝐴 𝐴 𝐴 · 0 = 0 Multiplyby0 𝐴 · 1 = 𝐴 Multiplyby1 𝐴 · 𝐴 = 𝐴 IfA=1,resultis1IfA=0,resultis0 𝐴 · 𝐴= 0 Eitheror =0,hence𝐴 𝐴multiplyby0 Twoormorevariables:Law Type 𝐴 + 𝐵 = 𝐵 + 𝐴 ORcommutativelaw 𝐴 · 𝐵 = 𝐵 · 𝐴 ANDcommutativelaw 𝐴 + (𝐵 + 𝐶)= (𝐴 + 𝐵) + 𝐶 ORassociativelaw 𝐴 · (𝐵 · 𝐶)= (𝐴 · 𝐵) · 𝐶 ANDassociativelaw 𝑋 =𝐴· 𝐵 · 𝐶 + 𝐴 · 𝐵· 𝐶+ 𝐴 · 𝐵 · 𝐶 UsingBooleanAlgebra, (SameanswerasK-Map)

𝐴 · (𝐵 + 𝐶)= 𝐴 · 𝐵 + 𝐴 · 𝐶 (𝐴 + 𝐵) · (𝐶 + 𝐷)= 𝐴 · 𝐶 + 𝐴 · 𝐷+ 𝐵 · 𝐶 + 𝐵 · 𝐷 DistributiveLaws 𝐴 + 𝐴 · 𝐵 = 𝐴𝐴 · (𝐴 + 𝐵) = 𝐴 𝐴 +𝐴· 𝐵= 𝐴 + 𝐵 𝐴 · (𝐴+ 𝐵)= 𝐴 · 𝐵 AbsorptionLaws 𝐴 · 𝐵=𝐴+𝐵𝐴 + 𝐵=𝐴· 𝐵 DeMorgan’sTheorem justdoK-Mapitseasiertrustme UsingCombinationalLogictosolvereal-lifeproblems Step1:CreateTruthTableandcreateanunsimplifiedbooleanexpression Step2:UseK-MapORBooleanAlgebratogetasimplifiedbooleanexpression Step3:Createthecircuitusingthesimplifiedbooleanexpression Repeattheaboveexamplesusingthecontextgivenwithinthequestion * ONLYPICKONEMETHODWHENSIMPLIFYINGSOP Chapter13:Set-ResetLatches AnS-RLatchisadevicethatcanstoreaLogicstate(1or0) S-RLatchsymbol