CSC 110 -Intro. to Computing

Lecture 5:

Gates, Circuits, & Transistors

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Circuit Design

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

)()( caba )()( bcba

Truth Table

)()( bcba a b c c' a+b c'+b (a+b) * (c' + b)0 0 0 1 0 1 00 0 1 0 0 0 00 1 0 1 1 1 10 1 1 0 1 1 11 0 0 1 1 1 11 0 1 0 1 0 01 1 0 1 1 1 11 1 1 0 1 1 1

Truth Table

a b c a' (a'+b) (a+c)' (a'+b) * (a+c)'0 0 0 1 1 1 10 0 1 1 1 0 00 1 0 1 1 1 10 1 1 1 1 0 01 0 0 0 0 0 01 0 1 0 0 0 01 1 0 0 1 0 01 1 1 0 1 0 0

)()( caba

Circuit Design

)()( bcba

Circuit Design

)()( caba

Algebraic Properties

Property AND ORCommutative ab = ba a + b = b + aAssociative (ab)c = a(bc) (a + b) + c = a + (b + c)Distributive a(b + c) = ab + ac a + (bc) = (a + b)(a + c)Identity a1 = a a + 0 = aComplement a(a') = 0 a + a' = 1DeMorgan (ab)' = a' + b' (a + b)' = a'b'Idempotency aa = a a + a = a

Law of Double Negation: a’’ = a

Improving Circuit Design

Circuit Property Used in this Step

Identity

Commutative

Distributive

)()( bcba

)()( cbab

)( cab

Improving Circuit DesignCircuit Property Used in this Step

Identity

DeMorgan’s Law

Associativity

Commutativity

Distributive

Identity

Distributive

Identity

Identity

)()( caba )()( caba caba ))((cbaa ))((

cbaaa ))()((

cbaa ))((cba ))1((

ca )1(ca

Circuit Propagation Delay

Time taken for signal to get through circuit Important measure when building processorGate cannot generate results until it has all of its

inputs Each gate starts at the time of the latest input

Each gate requires a set amount of time to complete

Could 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?

)( cab

How are these improved?

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

Circuit Delay Propagation

What is the propagation delay for this circuit?

Circuit Delay Propagation

What about this circuit?

Transistors

Transistors used to implement gatesUses a semiconductive material

Material can serve as both conductor and insulator Silicon is the preferred semiconductor because of

cost. Why is it so cheap?

Transistors

Originally invented by Bell Labs in 1947Have been improved since then…

Can switch on-and-off in nanoseconds Each transistor dissipates energy

Why is this be a problem?

My View of Transistor

Source

My View of Transistor

Ground

My View of Transistor

Output

My View of Circuit

Input:Franklin “off”flying a kite

My View of Circuit

Input:Franklin “on”poking key

Engineer’s View of a Circuit

Source connects system power Always at +5V (e.g. “high” state or 1)

Ground drains transistor’s energy Leaves transistor at +1V (e.g. 0)

When Vin controls “base” Acts like on-off switch When on, source drains into ground When off, source signal sent to Vout

Transistor Design

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

Transistor Design

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

Combinatorial Circuits

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

Sequential Circuits

Sequential circuits include another featureOutput determine by inputs AND current stateUsed when current state is important detail

E.g., Memory

S-R Latch S-R latch stores single

binary digit (1 or 0) Result is value of X

Inputs stand for Set and Reset

Could also be implemented with NOR gates

Adapted from Computer Science Illuminated, Dale and Lewis, p. 112

X’

S-R Latch

X’

Normally, S & R = 1 Maintains value of X

S = 1, R = 0 X = 0 Called the “set state”

S = 0, R = 1 X = 1 Called the “reset state”

Latches also called “flip-flop”s

For next lecture

Start doing the homework Start reading Section 5 Be ready to discuss:

What Individual Computer Component Descriptions Mean

Sizes Disks Speed