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
Moore’s law

3. Extra Midterm help DPD office hours Wednesday 2—4
My office, CS 219
Check with qlv and wtcorrea for other hours

4. More for Less --Moore’s 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 0’s and 1’s 0 = False 1 = True What do 0’s and 1’s mean?
For now, we’ll take “Natural meanings:”
For example, if we have a variable Alice for whether Alice goes to the party,
If Alice goes, we write Alice = 1
If Alice doesn’t, we write Alice = 0
0 = False
1 = True

10. Logic Gates Computers are circuits made of Logic Gates.
Logic gates manipulate 0’s and 1’s (False and True) by letting electrons flow or not.
We’ll 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
AND W Y Z X
W X Y Z

12. OR Gate W OR Z
W X Y Z X Y

13. NOT Gate Shorthand: Truth Table
“Yanni will go to the party if Xena does NOT go.” X
NOT Y
Shorthand: X Y
X Y
0 1
1 0
Truth Table

14. Logic Puzzle Circuit AND AND OR 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

16. Given Any Truth Table AND AND AND A B C F A 0 0 0 0 0 0 1 1 B 0 1 0 1 A
AND B C A
AND B C A
AND B C
Build AND gate for each output 1

17. Given Any Truth Table Finally, combine ANDs with an OR gate. AND F AND
Can build logic for any
Truth table this way
AND B C

18. Universality
Note same idea works no matter how many input 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
0’s
&
1’s
Universal
Method
Computers
We are here

20. Powers of 2 (cont.) 210  1,000 (103 ) kilo
Some rough numbers:
210  1,000 (103 ) kilo
220  1,000,000 (106 ) mega RAM
230  giga disk
240  tera BIG disk
250  peta
260  exa knowledge

21. Representing Information
We represent information with 0’s and 1’s
Numbers
Use binary or hexadecimal
Letters
Use ASCII
Sounds
Use samples
Images
Use pixels

22. Adding Binary Numbers AND sum OR AND carry AND X X Y sum 0 0 0 0 1 1 Y Y
sum OR X
AND Y
X Y carry X
carry
AND 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 X2 Universal Circuit For Z2 and carry Z0 X1
Fixed at 0
X2 X1 X0
Y2 Y1 Y0
============
C2 Z2 Z1 Z0

25. Memory

26. Enter Rita Matt doesn’t 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 OR
Matt
AND
Rita
Feedback Wire

27. The Flip-Flop OR AND M becomes 1 if Set is turned on
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 a byte (B).
Most RAM is arranged in bytes. D M W D M W

31. RAM (cont.) We want a HUGE number of such 1 byte memory cells.
Problem: How do we indicate which byte of memory we want to use at any given time? 1B 1B

32. RAM (cont.) 220 bytes of RAM (1 Mega-byte) 20 bits of address Address
Data input
Data Output
Write
8 bits (1 byte) of data

33. On our way to building a computer…
Review
On our way to building a computer…
Logic
Circuits:
Universal
Method
Represent
Info with
0’s & 1’s
(aka bits)
0’s
&
1’s
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. Light A Light B Traffic Light Behavior Otherwise Note: Clock beats
every 4 sec. So Light is Yellow for 4 sec.
IF A=1
AND B=0
Light A
Always
Always
IF A=0
AND B=1
Otherwise
Light B

38. Light A Light B Traffic Light State Machine Otherwise
Note: Clock beats
every 4 sec. So Light is Yellow for 4 sec.
IF A=1
AND B=0
Light A
Always
Always
IF A=0
AND B=1
Otherwise
Light B

39. Light A Light B Traffic Light States 00 01 11 10 Otherwise IF A=1
AND B=0 00 01
Light A
Always
Always
IF A=0
AND B=1 11 10
Otherwise
Light B

40. Traffic Light Behavior
Build A Truth Table
for next state / Output
M1 M2 A B D1 D2 Light A Red Light B Red …
0 1 * *
1 1 * *
… … … … … … …

41. Traffic Light Design Current State 2-bit Memory Logic Register For
Next
State
&
Output
Clock
Sensor A
6 Outputs:
for each Light
Sensor B

42. Design for Any State Machine
Many bits
Current State
Memory
Register
Logic
For
Next
State
&
Output
Clock
Inputs
Outputs

43. State Machines in Real Life
Elevator control systems
Car control systems
VCR’s
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 Keyboard Display
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 what’s 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.
Display
Bus
“CPU: Yes, user typed ‘a’.”

50. The Bus
At some point, CPU reads the Bus, and gets the Keyboard’s response.
CPU
Keyboard
Display
Bus
“CPU: Yes, user typed ‘a’.”

51. The CPU (cont.) Memory Registers Register 0 Arithmetic / Logic Unit
Control Unit (State Machine)
Instruction Register
Instr. Pointer (IP)

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 a computer?

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 calculate = 21 = 15 (hex)
10: Load R0  (always 1)
11: Load R2  (running total)
12: Load R1  (current number)
13: Add R2  R2 + R1 (R2=1)
14: Add R1  R1 + R0 (R1=2)
15: Add R2  R2 + R1 (R2=3)
16: Add R1  R1 + R0 (R1=3)
17: Add R2  R2 + R1 (R2=6)
18: Add R1  R1 + R0 (R1=4)
19: Add R2  R2 + R1 (R2=A)
1A: Add R1  R1 + R0 (R1=5)
1B: Add R2  R2 + R1 (R2=F)
1C: Add R1  R1 + R0 (R1=6)
1D: Add R2  R2 + R1 (R2=15)
1E: halt

57. Adding Numbers
Alternate Loop using Jump & Count for … + N
10: Load R1  (N)
11: Load R2  (running total)
12: Add R2  R2 + R (add in N)
13: Jump to 12 and (If N isn’t 0 yet, decrease R1 if (R1>0) Let N=N-1, and go back)
14: halt (N is now 0, and R2 = 1+2+…+N)

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) = 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 More complex compression
Use redundancy
More complex compression
Lossy vs. lossless
Ideas for lossy
Drop frequencies you can’t hear
Drop small differences you won’t notice

66. More complex compression
Lossy compression
Can save space by eliminating parts of the image/sound that don’t matter very much
Big savings compared to lossless, but the signal cannot be fully recovered.
Ideas
Dropping frequencies you can’t hear
Dropping small differences you won’t notice
Generally large savings compared to lossless

67. Pause for experiment