how computers work lecture 9 page 1 how computers work lecture 9 the static discipline + regular...

How Computers Work Lecture 9

How Computers WorkLecture 9

The Static Discipline + Regular Logic

The Statistical Nature of the Universe, and how we make computers work despite it.


Analog vs. Digital Noise Tolerance


CMOS Inverter

In Out

In Out


MOS (“Metal” Oxide Semiconductor)Transistors

G

S D

G

S D

P Channel

N Channel

H

L

H

L


Inverter

HH

LL


Inverter


CMOS Buffer

In Out

In OutL

H

H

L


Buffer

HH

LL


Buffer


The Digital Abstraction Part 1:The Static Discipline

Noise

Tx

Rx

Vol Voh

VihVil


Noise Marginsand the Forbidden Zone

Data

Flow


Consequences of theStatic Discipline

Vil Vih

Vol

Voh

= Disallowed

In

Out

Transfer Curve of a single input, single output device:

Device Musthave

_______________and be

_______________

GainGain

Non-LinearNon-Linear


Recall that the probability of asynchronous arbitration metastability after a finite Tpd is non-

zero

• So What about the Static Discipline?– A: It, like many abstractions you learn about in

computer design is really a probabilistic one.– Parts fail too.

• Reliability typically follows a “bathtub” curve

– If the probability of the static discipline failing is much less than the probability of any part failing,

we can basically ignore the problem.


Other things in life are probabilistic too...

In the February ‘97 issue of Scientific American, Richard E. Crandall, MIT Ph.D. Course 8 ‘73, chief scientist at NeXT,writes in “The Challenge of Large Numbers” :

1) The age of the universe is about _________________ years.

2) It would take a bird, pecking randomly on a keyboard, about10 3,000,000 years to write “The Hound of the Baskervilles”

3) A full beer can, sitting on a level, steady table, will spontaneously topple due to quantum fluctuations about once every 10 1033 years.

4) The probability of a mouse living on the surface of the sun for a week is about 1 in 10 1042.

5) The probability of you suddenly dematerializing on earth, materializing on Mars, then re-materializing on earth is about 1 in 10 1051.

10^1010^10


CMOS NOR

A

B

Q

A B QL L

LL

H

HH

H

H

L

LL


CMOS NAND

A

B Q

A B QL L

LL

H

HH

H

H

H

HL


A Systematic Approach

k

Q0Q1

QN-1

k SELECT inputs

N = 2k OUTPUTs.

Selected Qj HIGH

All other Qj LOW

The ROM


Lookup Table Implementation(1-Dimensional ROM)

Ci

00001111

A00110011

B01010101

S01101001

Co

00010111


NMOS NOR

A

B

Q

C


The Expandable Wire-NOR

Pulldown Notation:

HIGH horiz. input

causes vertical output LOW

Passive Pullup makes vertical line HIGH by default


ROM ArchitectureCo = ABCi + ABCi + ABCi + ABCi


General PLA ArchitectureAND Plane OR Plane


NMOS AND

A

B

Q

?


PLA Implementation of Co

= AB + BCi + ACi


PALS

• PLA with fixed OR plane

• Usually contain memory devices as well


22V10 PAL


Tree Structure

N-input TREE has O(log (n)) levels...

Signal propagation takes O(log (n)) gate delays.

O(n) gates.

A2

A1

A4

A3

AN


FPGAs• Recognition that PLA 2-Level Architecture is

poor match to many functions• Network of many small programmable logic

elements– ROMs– PLAs– Gates

• Programmable Interconnection Network


Xilinx 4000 FPGA CLB


FPGA Interconnect per CLB


FPGA Interconnect Matrix

how computers work lecture 9 page 1 how computers work lecture 9 the static discipline + regular...

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