CSC 110 -Intro. to ComputingLecture 5:Gates, Circuits, & Transistors

AnnouncementsHomework available on BlackboardHomework due Friday at 4:00PMHand to me or put in my box in Wehle 207Quiz on this material next ThursdayQuiz last week went fairly wellTop was 100; Mean was 77 ( = 20.7)Scores available on BlackboardCome to my office to pick up your quiz

AnnouncementsCSC tutors are now availableHours posted outside Wehle 208Also come to my office hours, make an appointment, or call/e-mail me questions

Circuit DesignIn your group, complete work with circuitsCompute the truth tables for circuitsDraw the diagrams for these equations

Truth Table

Sheet1

abcc'a+bc'+b(a+b) * (c' + b)

0001010

0010000

0101111

0110111

1001111

1010100

1101111

1110111

Truth Table

Sheet1

abca'(a'+b)(a+c)'(a'+b) * (a+c)'

0001111

0011100

0101111

0111100

1000000

1010000

1100100

1110100

Circuit Design

Circuit Design

Algebraic PropertiesLaw of Double Negation: a = a

Sheet1

PropertyANDOR

Commutativeab = baa + b = b + a

Associative(ab)c = a(bc)(a + b) + c = a + (b + c)

Distributivea(b + c) = ab + aca + (bc) = (a + b)(a + c)

Identitya1 = aa + 0 = a

Complementa(a') = 0a + a' = 1

DeMorgan(ab)' = a' + b'(a + b)' = a'b'

Idempotencyaa = aa + a = a

Improving Circuit Design

Improving Circuit Design

Circuit Propagation DelayTime taken for signal to get through circuitImportant measure when building processorGate cannot generate results until it has all of its inputsEach gate starts at the time of the latest input Each gate requires a set amount of time to completeCould be specific amount of time (e.g., 10 ps)Or state result as multiple of gate delays

How are these improved?How long will this circuit need to complete?

How are these improved?How long will it take for the signal to propagate through?

Circuit Delay PropagationWhat is the propagation delay for this circuit?

Circuit Delay PropagationWhat about this circuit?

TransistorsTransistors used to implement gatesUses a semiconductive materialMaterial can serve as both conductor and insulatorSilicon is the preferred semiconductor because of cost. Why is it so cheap?

TransistorsOriginally invented by Bell Labs in 1947Have been improved since thenCan switch on-and-off in nanosecondsEach transistor dissipates energyWhy is this be a problem?

My View of TransistorSource

My View of TransistorGround

My View of TransistorOutput

My View of CircuitInput: Franklin off flying a kite

My View of CircuitInput: Franklin on poking key

Engineers View of a CircuitSource connects system powerAlways at +5V (e.g. high state or 1)Ground drains transistors energyLeaves transistor at +1V (e.g. 0)When Vin controls baseActs like on-off switchWhen on, source drains into groundWhen off, source signal sent to Vout

Transistor DesignTurns out NOT, NAND, and NOR are easiest gates to turn into transistorsHow do these work?

Transistor DesignApple wanted NAND-based memory (rather than NOR-based) for iPod Nano. Why?

Combinatorial CircuitsSo far, all circuits have been combinatorialOutput is determined only by input valuesWhy would we need other circuits?

Sequential CircuitsSequential circuits include another featureOutput determine by inputs AND current stateUsed when current state is important detailE.g., Memory

S-R LatchS-R latch stores single binary digit (1 or 0)Result is value of X

Inputs stand for Set and ResetCould also be implemented with NOR gatesAdapted from Computer Science Illuminated, Dale and Lewis, p. 112

S-R LatchNormally, S & R = 1Maintains value of X

S = 1, R = 0 X = 0Called the set stateS = 0, R = 1 X = 1Called the reset state

Latches also called flip-flops

For next lectureStart doing the homeworkStart reading Section 5Be ready to discuss:What Individual Computer Component Descriptions MeanSizesDisksSpeed