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