Midterm Review

1
Midterm Review

• October 23, 2001

2
Administrivia The Midterm

• Problem solving
• What logic gates do
• How to build circuits that realize truth tables
• Addition circuitry
• Memory
• State machines to model situations
• Building the logic for state machines
• Putting it together to build a computer
• Programming the computer using machine language
• Representing information
• Understanding key ideas
• Von Neumann machine
• Moores law

3
Extra Midterm help

• DPD office hours Wednesday 24
• My office, CS 219
• Check with qlv and wtcorrea for other hours

4
More for Less --Moores Law

• Everything doubles every 18 months
• Memory/dollar
• Disk/dollar
• Transistors per inch
• Processor speed
• Network bandwidth

5
Practical Details

• Problem sets 20
• Lab reports 10
• Midterm exam 25
• Final exam 25
• Class Participation 20

6
Building a computer
7
Layers of Abstraction

• Build more and more powerful tools out of simpler
  ones.

Really Simple Stuff
Computers
8
A Simple Logic Puzzle

• Frank will go to the party if Ed goes
  AND Dan does NOT.
• Dan will go if Bob does NOT go OR if Carole goes.
• Ed will go to the party if Alice AND Bob go.
• Alice and Bob decide to go,but Carol stays home.
• Will Frank go to the party?

9
Using 0s and 1s

• What do 0s and 1s mean?
• For now, well take Natural meanings
• For example, if we have a variable Alice
  forwhether Alice goes to the party,
• If Alice goes, we write Alice 1
• If Alice doesnt, we write Alice 0

0 False
1 True
10
Logic Gates

• Computers are circuits made of Logic Gates.
• Logic gates manipulate 0s and 1s (False and
  True) by letting electrons flow or not.
• Well look at three types of Logic Gates
• AND are all inputs true?
• OR is one input true?
• NOT flip the truth value

11
AND Gate
W X Y Z 0 0 0 0 0 0 1 0 0 1 0 0 0 1
1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1
12
OR Gate
W
Z
W X Y Z 0 0 0 0 0 0 1 1 0 1 0 1 0 1
1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1
X
Y
13
NOT Gate

• Yanni will go to the party if Xena does NOT go.

Y
X
Shorthand
X
Y
X Y 0 1 1 0
Truth Table
14
Logic Puzzle Circuit
Alice
Ed
Frank
Bob
Dan
Carole
Dan will go if Bob does NOT go OR if Carole goes.
15
Given Any Truth Table
A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1
1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0
16
Given Any Truth Table
A B C F 0 0 0 0 0 0 1 1 0 1 0 1 0 1
1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 0
A
B
C
A
B
C
A
B
C
Build AND gate for each output 1
17
Given Any Truth Table
A
Finally, combine ANDswith an OR gate.
B
C
A
F
B
C
A
Can build logic for any Truth table this way
B
C
18
Universality

• Note same idea works no matter how manyinput
  variables. So for ANY Truth Table we can write
  down,we can make a circuit for it using only 3
  Logic Gates AND, OR, NOT
• This gives us a very powerful tool !
• But, in practice, we are limited in size we can
  realize numeracy exercise.

19
Our First Abstract Tool
Universal Method Circuits for ANY Truth Table
0s 1s
Universal Method
Computers
We are here
20
Powers of 2 (cont.)

• Some rough numbers
• 210 ? 1,000 (103 ) kilo
• 220 ? 1,000,000 (106 ) mega RAM
• 230 ? 109 giga disk
• 240 ? 1012 tera BIG disk
• 250 ? 1015 peta
• 260 ? 1018 exa knowledge

21
Representing Information

• We represent information with 0s and 1s
• Numbers
• Use binary or hexadecimal
• Letters
• Use ASCII
• Sounds
• Use samples
• Images
• Use pixels

22
Adding Binary Numbers
X
Y
sum
X
Y
X
carry


Y
23
Addition
We can use 1 building block to add numbers of any
length. Black box operation
ith bit of X
ith bit of Z
ith bit of Y
carry bit out
carry bit
Abstraction in action -- This is a piece of a
carry-ripple adder
24
Carry-Ripple Adder
Z1
Z2
Universal Circuit For Z2 and carry
X2
Z0
Universal Circuit For Z2 and carry
X1
Universal Circuit
X0
C2
Y2
Y0
Y1
C1
C0
0
Fixed at 0
X2 X1 X0 Y2 Y1
Y0 C2 Z2 Z1 Z0
25
Memory
26
Enter Rita

• Matt doesnt like Rita
• Matt decides to go to the party if Sue decides to
  go OR
• If he (Matt) already feels like going AND Rita
  decides NOT to go.

Sue
Matt
Rita
Feedback Wire
27
The Flip-Flop
Set
M
Reset

• M becomes 1 if Set is turned on
• M becomes 0 if Reset is turned on
• Otherwise (if Set and Reset are both 0), M just
  remembers its value

28
The Flip-Flop
S
M
R

• M becomes 1 if Set is turned on
• M becomes 0 if Reset is turned on
• Otherwise (if Set and Reset are both 0), M just
  remembers its value

29
The Data Flip-Flop
D
M
Write

• If Write 0, M just keeps its value.(It ignores
  D.)
• If Write 1, then M becomes set to D

30
RAM

• Group 8 of them together.
• 8 bits (b)is called abyte (B).
• Most RAMis arrangedin bytes.

31
RAM (cont.)

• We want a HUGE number of such 1 byte memory
  cells.
• Problem How do we indicate which byte ofmemory
  we want to use at any given time?

32
RAM (cont.)
20 bits of address
Address
Data Output
Data input
Write
8 bits (1 byte)of data
33
Review
On our way to building a computer
Represent Info with 0s 1s (aka bits)
Logic Circuits Universal Method
0s 1s
Memory Circuits
Computers
We are here
34
The System Clock

• 500 Mhz Pentium III computer
• What does 500 Mhz mean?
• It refers to the speed of the System
  Clock. (actually this is only one of the
  clocks)
• All digital systems have such Clocks, even
  traffic lights and elevator control systems.

35
Our System A Traffic Light
36
A Traffic Light

• Intersection of two one-way roads

A
B
Car Sensors
37
Traffic Light Behavior
Otherwise
NoteClock beats every 4 sec.So Light is
Yellow for 4 sec.
IF A1 AND B0
Light A
Always
Always
IF A0 AND B1
Otherwise
Light B
38
Traffic Light State Machine
Otherwise
NoteClock beats every 4 sec.So Light is
Yellow for 4 sec.
IF A1 AND B0
Light A
Always
Always
IF A0 AND B1
Otherwise
Light B
39
Traffic Light States
Otherwise
IF A1 AND B0
01
00
Light A
Always
Always
IF A0 AND B1
11
10
Otherwise
Light B
40
Traffic Light Behavior
Build A Truth Table for next state / Output
41
Traffic Light Design
Current State
2-bit Memory Register
Logic For Next State Output
Clock
Sensor A
6 Outputs for eachLight
Sensor B
42
Design for Any State Machine
Manybits
Current State
Memory Register
Logic For Next State Output
Clock
Inputs
Outputs
43
State Machinesin Real Life

• Elevator control systems
• Car control systems
• VCRs
• Alarm Clocks
• Personal Computers
• Just about everything!

44
Computers
45
Computer Architecture
CPU
Keyboard
Display
Bus
Hard Disk
CD-ROM
RAM
46
The Bus

• Communication on the bus is via postcards
• CPU puts Keyboard, did the user type anything?
  (represented in some way) on the Bus.

CPU
Keyboard
Display
Bus
Keyboard, did the user type anything?
47
The Bus

• Each device (except CPU) is a State Machine that
  constantly checks to see whats on the Bus.

CPU
Keyboard
Display
Bus
Keyboard, did the user type anything?
48
The Bus

• Keyboard notices that its name is on the Bus,and
  reads info. Other devices ignore the info.

CPU
Keyboard
Display
Bus
Keyboard, did the user type anything?
49
The Bus

• Keyboard then writes CPU Yes, user typed a.
  to the Bus.

CPU
Keyboard
Display
Bus
CPU Yes, user typed a.
50
The Bus

• At some point, CPU reads the Bus, and getsthe
  Keyboards response.

CPU
Keyboard
Display
Bus
CPU Yes, user typed a.
51
The CPU (cont.)
Memory Registers
Control Unit(State Machine)
52
Important Point

• One of the important features of the von Neumann
  model is the fact that
• The instructions themselves
• And
• The data the instructions manipulate
• are all stored in the same RAM.
• This was one of the revolutionary features of the
  modern computer, totally unlike Punch-Card
  computers proposed in the past.

53
Important Point

• This innovation is crucial to modern computing.
• It even allows for the possibility of programs
  that change themselves as they are executed.
• With great power comes great risk
• Computer Viruses!

54
Machine Language

• We now have a machine that can execute
  instructions.
• Basic Questions
• What instructions?
• How do computers understand these instructions?
  (Representation)
• What does software look like to acomputer?

55
Instructions

• 16 possible Op-Codes

0 halt 1 add 2 subtract 3 multiply 4 bus
output 5 jump 6 jump if positive 7 jump
count 8 bus input 9 load A store B load
direct/addr. C NAND D AND E Shift Right F
Shift Left
56
Adding Numbers

• Simple Program to calculate1 2 3 4 5 6
  21 15 (hex)

10 Load R0 ? 0001 (always 1) 11 Load R2 ?
0000 (running total) 12 Load R1 ? 0001
(current number) 13 Add R2 ? R2 R1
(R21) 14 Add R1 ? R1 R0 (R12) 15 Add
R2 ? R2 R1 (R23) 16 Add R1 ? R1 R0
(R13) 17 Add R2 ? R2 R1 (R26) 18 Add
R1 ? R1 R0 (R14) 19 Add R2 ? R2 R1
(R2A) 1A Add R1 ? R1 R0 (R15) 1B Add
R2 ? R2 R1 (R2F) 1C Add R1 ? R1 R0
(R16) 1D Add R2 ? R2 R1 (R215) 1E halt
57
Adding Numbers

• Alternate Loop using Jump Count for1 2 3
  4 5 N

10 Load R1 ? 0006 (N) 11 Load R2 ?
0000 (running total) 12 Add R2 ? R2
R1 (add in N) 13 Jump to 12 and
(If N isnt 0 yet, decrease R1 if (R1gt0)
Let NN-1, and go back) 14 halt
(N is now 0, and R2 12N)
58
Sound is a waveform
59
Sampling the waveform
60
The approximation
61
Even finer sampling
62
Digital vs. Analog

• A sound file is just a sequence of bytes
• On a CD, the sampling rate is 44,100 samples per
  second. Each sample is quantized into a number in
  the range from 0 to 65,535, So a CD has 44,100
  numbers (each 2 bytes) per channel per second of
  music.
• A graphic image is just a sequence of bytes
• An image is made up of pixels
• Each pixel might be represented by 3 bytes giving
  color intensities.
• Manipulating sounds or images just involves
  manipulating numbers

63
Numeracy

• CD has 44,100 2 byte samples per second.
• 44,100 x 2 x 60 x 2 (channels) 10.09 megabytes
  per CD minute
• A CD is 74 minutes (746 megabytes) long.
• MP3 players typically use memory 32 or 64
  megabytes in size. (or 3-6 minutes)
• Compression is needed

64
The need for compression

• A CD is 746 megabytes long
• A printed page requires 86.4 Megabytes of storage

65
Simple compression

• Simple compression
• Use redundancy
• More complex compression
• Lossy vs. lossless
• Ideas for lossy
• Drop frequencies you cant hear
• Drop small differences you wont notice

66
More complex compression

• Lossy compression
• Can save space by eliminating parts of the
  image/sound that dont matter very much
• Big savings compared to lossless, but the signal
  cannot be fully recovered.
• Ideas
• Dropping frequencies you cant hear
• Dropping small differences you wont notice
• Generally large savings compared to lossless

67
Pause for experiment