CS 278Course PreliminariesSlide 3Slide 4Slide 5Slide 6Slide 7Digital System DesignDigital Logic DesignExample of Digitization BenefitImplementing Digital Systems: Using mprocessors Vs. Designing Digital CircuitsDigital Design: When mprocessors Aren’t Good EnoughIntroductionSwitchesSlide 15Moore’s LawThe Power of MiniaturizationThe CMOS TransistorBoolean Logic Gates Building Blocks for Digital Circuits (Because Switches are Hard to Work With)Boolean Algebra and Digital CircuitsSlide 21Evaluating Boolean EquationsConverting to Boolean EquationsSlide 24Building Circuits with GatesRelating Boolean Algebra to Digital DesignNOT/OR/AND Logic Gate Timing DiagramsBuilding Circuits Using GatesExample: Converting a Boolean Equation to a Circuit of Logic GatesExample: Seat Belt Warning Light SystemSome Circuit Drawing ConventionsBoolean AlgebraSlide 33Operator PrecedenceBoolean Algebra TerminologyBoolean Algebra Properties Textbook pg 30-31Examples Using PropertiesAdditional PropertiesBoolean Function RepresentationsTruth Table RepresentationConverting among RepresentationsRepresentation: Truth TableCanonical Form -- Sum of MintermsCanonical S-O-P ExampleMultiple-Output CircuitsMultiple-Output Example: BCD to 7-Segment ConverterCombinational Logic Design ProcessCS 278Digital System DesignCourse PreliminariesTeaching StaffProfessor Dan Ernst Office Hours: Weds. 9-11am, Fri. 1-3pm… or by appointmentPhillips 139[email protected]Course web page accessCourse notes are posted online athttp://www.cs.uwec.edu/~ernstdj/courses/cs278/All assignments and labs will be posted there as wellTextbook:Grading policiesAssignments/Quizzes ( 15% )Three exams ( 15% each – 45% total )2 midterms + 1 finalLabs ( 25% )Project ( 15% )More info laterAttendance not directly counted towards gradeThere will be turn-ins during lab timeLab room is P122!Hardware Boards (1)The Altera UP2 Development BoardHandle with care, and leave them in the lab!Hardware Boards (2)The IDL-800 Digital Logic Trainer with solderless breadboard isn’t cheap eitherThese must stay in the lab, along with all of the suppliesDigital System DesignDigital Logic DesignExample of Digitization BenefitAnalog signal (e.g., audio) may lose qualityVoltage levels not saved/copied/transmitted perfectlyDigitized version enables near-perfect save/cpy/trn. “Sample” voltage at particular rate, save sample using bit encodingVoltage levels still not kept perfectlyBut we can distinguish 0s from 1stimeVolts0123original signallengthy transmission(e.g, cell phone)time0123received signalHow fix -- higher, lower, ?lengthy transmission(e.g, cell phone)01 10 11 10 11sametime01 10 11 10 11Voltsdigitized signaltime01a2dVolts0123d2aLet bit encoding be: 1 V: “01” 2 V: “10” 3 V: “11”timeCan fix -- easily distinguish 0s and 1s, restore01Digitized signal notperfect re-creation,but higher sampling rate and more bits per encoding brings closer.aImplementing Digital Systems:Using processors Vs. Designing Digital CircuitsMicroprocessors a common choice to implement a digital systemEasy to programCheap (as low as < $1)Available nowI3I4I5I6I7I2I1I0P3P4P5P6P7P2P1P0void main(){ while (1) { P0 = I0 && !I1; // F = a and !b, }}0Fba101016:00 7:057:06 9:009:01 timeDesired motion-at-night detectorProgrammedmicroprocessorCustom designeddigital circuitmicroprocessorDigital Design: When processors Aren’t Good EnoughWith microprocessors so easy, cheap, and available, why design a digital circuit?Microprocessor may be too slowOr too big, power hungry, or costly(a)Micro-processor(Read,Compress,and Store)MemoryImage Sensor(b)(c)Sample digital camera task execution times (in seconds) on a microprocessor versus a digital circuit:Q: How long for each implementation option?a5+8+1=14 sec.1+.5+.8=1.4 sec.1+.5+1=1.6 secGood compromiseReadcircuitCompresscircuitMemoryStorecircuitImage SensorCompresscircuitMicroprocessor(Store)MemoryImage SensorReadcircuitTask MicroprocessorCustom Digital CircuitRead 5 0.1Compress8 0.5Store 1 0.8IntroductionCombinationaldigital circuit1ab1F01ab?F0Let’s learn to design digital circuitsWe’ll start with a simple form of circuit:Combinational circuitA digital circuit whose outputs depend solely on the present combination of the circuit inputs’ valuesDigital circuitSequentialdigital circuitSwitchesSwitches are the basis of binary digital circuitsElectrical terminologyVoltage: Difference in electric potential between two pointsAnalogous to water pressure Current: Flow of charged particlesAnalogous to water flowResistance: Tendency of wire to resist current flowAnalogous to water pipe diameterV = I * R (Ohm’s Law)4.5 A4.5 A4.5 A2 ohms9V0V9V+–SwitchesA switch has three partsSource input, and outputCurrent wants to flow from source input to outputControl inputVoltage that controls whether that current can flow The amazing shrinking switch1930s: Relays1940s: Vacuum tubes1950s: Discrete transistor1960s: Integrated circuits (ICs)Initially just a few transistors on ICThen tens, hundreds, thousands... “off”“on”outputsourceinputoutputsourceinputcontrolinputcontrolinput(b)relayvacuum tubediscrete transistorICquarter(to see the relative size)aMoore’s LawThe Power of MiniaturizationEDSAC 1 (1949)~ 500 OPsPentium 4 (2002)~ 12 GFLOPs24,000,000 times fasterThe CMOS TransistorCMOS transistorBasic switch in modern ICsgatesource drainoxideA positivevoltage here......attracts electrons here,turning the channelbetween source and draininto aconductor.(a)IC packageICdoes notconduct0conducts1gatenMOSdoes notconduct1gatepMOSconducts0Silicon -- not quite a conductor or insulator:SemiconductoraBoolean Logic GatesBuilding Blocks for Digital Circuits (Because Switches are Hard to Work With)“Logic gates” are better digital circuit building blocks than switches (transistors)Why?...AbstractionBoolean Algebra and Digital CircuitsTo understand the benefits of “logic gates” vs. switches, we should first understand Boolean algebra“Traditional” algebraVariable represent real numbersOperators operate on variables, return real numbersBoolean AlgebraVariables represent 0 or 1 onlyOperators return 0 or 1 onlyBasic operatorsAND: a AND b returns 1 only when both a=1 and b=1OR: a OR b returns 1 if either