[PPT] - Chapte Chapter 1: Nuts and ts and Bolts CS105: Great Insights in PowerPoint Presentation

SLIDE 1

Chapte Nuts and

CS105: Great Insights in Com

Chapter 1: ts and Bolts

ights in Computer Science

SLIDE 2

Comput

Design: a hierarchy of par
Interactions between par

well-defined

They are dependent not

technology as on ideas

These ideas have almos

the electronics out of w built

mputers

hy of parts een parts are simple and e dependent not so much on

n ideas

e almost nothing to do with

ut of which computers are

SLIDE 3

From thinking

George Boole:
logic of human thought

thinking to bits

an thought -> math operations

SLIDE 4

From thinking

George Boole:
logic of human thought
invented a language

manipulating logical determining whether true (Boolean Algeb

thinking to bits

an thought -> math operations anguage for describing and

gical statements and

hether or not they were Algebra)

SLIDE 5

From thinking

George Boole:
logic of human thought
invented a language

manipulating logical determining whether true (Boolean Algeb

Claude Shannon: Build

equivalent to expressions

thinking to bits

an thought -> math operations anguage for describing and

gical statements and

hether or not they were Algebra) hannon: Build electrical circuits pressions in Boolean Algebra

SLIDE 6

The Low

Chemistry has its molec
Physics has its elementar
Math has its sets.
Computer science has
They are the smalles
True (1, on)
False (0, off)

he Lowly Bit

molecules. elementary particles. e has its bits. allest unit of information.

SLIDE 7

What’s a

Like “ginormous” (giganti

“motel” (motor + hotel); More?

It’s a contraction of “b

Claude Shannon, attributed

In our decimal (base ten)

digit can be any of the ten v

In the binary (base 2) num

can be any of the two v

What’s a “Bit”?

(gigantic + enormous) or hotel); it is a portmanteau. binary digit”, used by hannon, attributed to John Tukey. base ten) number system, a

f the ten values 0,...,9.

e 2) number system, a digit

f the two values 0 or 1.

SLIDE 8

Why a

Bits have the property
simple: There’s no s

distinction to be made.

powerful: sequences

seemingly anything!

Why a Bit?

perty of being...

s no smaller discrete to be made. equences of bits can represent thing!

SLIDE 9

0/1, Black/

Escher created

spectacular images with just a single distinction.

“...God divided the

light from the darkness.” (Genesis Chapter 1)

Black/White

SLIDE 10

Bits Abound

Nearly everything has gone di
Digital sound: groups

acoustic intensity at di

Digital images: groups

color at each particular location: pixel.

ts Abound

ng has gone digital.

und: groups of bits represent the

ity at discrete time points. groups of bits represent the h particular discrete image

SLIDE 11

“Regular” A

Variables stand for num
x = 3, p = 22/7, a = −2
Binary operations (two
addition: 2 + 3 = 5; subtraction: 1 − 4 = −3
multiplication: 2/3 x 7/4 =
Unary operations (one num
negation: −(11) = −11, square root: √16 = 4

egular” Algebra

tand for numbers. = −2 (two numbers in, one out) addition: 2 + 3 = 5; subtraction: 1 − 4 = −3 2/3 x 7/4 = 7/6 (one number in, one out) negation: −(11) = −11, square root: √16 = 4

SLIDE 12

Boolean A

Variables stand for bits
x = True, p = False,
Binary operations (two
and (“conjunction”): T
or (“disjunction”): True
Unary operations (one num
not (“negation”): not (
olean Algebra

tand for bits (True/False). alse, z = x and p (two bits in, one out)

n”): True and False = False

): True or False = True (one number in, one out) : not (False) = True

SLIDE 13

Follow the R

When is it ok to be in an R m
lder than 16 or you hav

with you.

x: Person is older than
y: Person is accompani

guardian.

x or y: Person can see

the Rules #1

to be in an R movie? You are

u have an adult guardian

der than 16 .

mpanied by an adult

an see an R-rated movie.

SLIDE 14

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = ?

” Examples

eeing the movie with his

= ?

SLIDE 15

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T

” Examples

eeing the movie with his

= True

SLIDE 16

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = ?

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= ?

SLIDE 17

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = T

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= True

SLIDE 18

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = T
Seth is 16 and is there w
x = False, y = True, x or y = ?

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= True

there with both of his parents.

= ?

SLIDE 19

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = T
Seth is 16 and is there w
x = False, y = True, x or y = T

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= True

there with both of his parents.

= True

SLIDE 20

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = T
Seth is 16 and is there w
x = False, y = True, x or y = T
Jessica is 13 and is ther

school.

x = False, y = False, x or y

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= True

there with both of his parents.

= True

and is there with friends from

= ?

SLIDE 21

“OR” Exampl

Bill is 22 and is seeing the m

stepdad.

x = True, y = True, x or y = T
Samantha is 17 and is s
x = True, y = False, x or y = T
Seth is 16 and is there w
x = False, y = True, x or y = T
Jessica is 13 and is ther

school.

x = False, y = False, x or y

” Examples

eeing the movie with his

= True

17 and is seeing the movie alone.

= True

there with both of his parents.

= True

and is there with friends from

= False

SLIDE 22

Follow the R

All vehicles parked on Un

must be registered and Rutgers permit.

x: Car is registered.
y: Car displays a valid Rutger
x and y: Car can be park

the Rules #2

ked on University property and display a valid alid Rutgers permit. be parked at Rutgers.

SLIDE 23

“AND” Exampl

Bill’s car is registered and di
x = True, y = True, x and y = ?

” Examples

ed and displays a valid permit.

= ?

SLIDE 24

“AND” Exampl

Bill’s car is registered and di
x = True, y = True, x and y = T
Samantha’s is registered, but the per
x = True, y = False, x and y =

” Examples

ed and displays a valid permit.

= True

stered, but the permit fell off.

= ?

SLIDE 25

“AND” Exampl

Bill’s car is registered and di
x = True, y = True, x and y = T
Samantha’s is registered, but the per
x = True, y = False, x and y =
Al’s registration expired,
x = False, y = True, x and y =

” Examples

ed and displays a valid permit.

= True

stered, but the permit fell off.

= False

pired, but his permit is still ok.

= ?

SLIDE 26

“AND” Exampl

Bill’s car is registered and di
x = True, y = True, x and y = T
Samantha’s is registered, but the per
x = True, y = False, x and y =
Al’s registration expired,
x = False, y = True, x and y =
Jessica is visiting with no r
x = False, y = False, x and y

” Examples

ed and displays a valid permit.

= True

stered, but the permit fell off.

= False

pired, but his permit is still ok.

= False

ith no registration or permit.

y = ?

SLIDE 27

“AND” Exampl

Bill’s car is registered and di
x = True, y = True, x and y = T
Samantha’s is registered, but the per
x = True, y = False, x and y =
Al’s registration expired,
x = False, y = True, x and y =
Jessica is visiting with no r
x = False, y = False, x and y

” Examples

ed and displays a valid permit.

= True

stered, but the permit fell off.

= False

pired, but his permit is still ok.

= False

ith no registration or permit.

y = False

SLIDE 28

Follow the R

It is not allowed by feder

provide tobacco produc persons under 18 year

x: Person is under 18.
not x: Person can buy tobac

the Rules #3

by federal law to

products to

18 years of age. under 18. an buy tobacco

SLIDE 29

“NOT” Exampl

Samantha is 17 and is
x = True, not x = ?

T” Examples

17 and is buying cigarettes.

SLIDE 30

“NOT” Exampl

Samantha is 17 and is
x = True, not x = False

T” Examples

17 and is buying cigarettes.

SLIDE 31

“NOT” Exampl

Samantha is 17 and is
x = True, not x = False
Seth is 21 and purchas
x = False, not x = ?

T” Examples

17 and is buying cigarettes. 21 and purchased a cigar.

SLIDE 32

“NOT” Exampl

Samantha is 17 and is
x = True, not x = False
Seth is 21 and purchas
x = False, not x = True

T” Examples

17 and is buying cigarettes. 21 and purchased a cigar.

SLIDE 33

And, Or,

The most important logi
r, and not.
x and y is True only if
x or y is True only if
not x is True only if x
A lot like their English m

unambiguous.

nd, Or, Not

tant logical operations are and, ue only if both x and y are True. ue only if either x or y are True. ue only if x is False. nglish meanings, but

SLIDE 34

A B A and B

False False False False True False True False False True True True

A

False F False True F True

Order of operations: Parenthes

And, Or,

B A or B

False False True True False True True True

A not A

False True True False

: Parentheses, not, and, or

nd, Or, Not

SLIDE 35

Relating And/

Note: not (not x) = x
DeMorgan’s Law: not fl
not (x and y) = (not
not (x or y) = (not x) and (

ng And/Or/Not

: not flips ands and ors (not x) or (not y) ) and (not y)

SLIDE 36

DeMorgan’s Law

x: Car is registered.
y: Car displays a valid R
accepted = x and y
not (accepted) if
either Car is not regist
r Car does not displa
not (x and y) = (not x) or

eMorgan’s Law Example

alid Rutgers permit. registered (not x) display a valid permit (not y) t x) or (not y)

SLIDE 37

More Exampl

x = True, y= False, z = F
not x = ? not z = ?
x and y = ? y or z = ?
y or (x and not z) = ?

e Examples

= False

SLIDE 38

Implementing

Clearly, our brains can handl

expressions.

But, can we automate them

ementing Logic

ns can handle these sorts of automate them?

SLIDE 39

Implementing

Clearly, our brains can handl

expressions.

But, can we automate them
Yes, obviously, but let’s

simple way to do it befor fancier stuff.

ementing Logic

ns can handle these sorts of automate them? , but let’s start with a really to do it before we move on to

SLIDE 40

lightOn = A = False lightOn = A = True

http://scratch.mit.edu/projects/cs105/35907

Simple C

False

tOn = True

Switch A is either

n or off making

the light either on

r off: lightOn=A.

Symbols: battery switch bulb ground (completes circuit)

105/35907

mple Circuit

SLIDE 41

Multiple Sw

A = False B = True D = False C = True

http://scratch.m

jects/cs105/

iple Switches

Switches A and B are wired in parallel: either will light the bulb. Switches C and D are wired in series: both are needed to light the bulb.

http://scratch.mit.edu/pr

jects/cs105/35905

tch.mit.edu/pr s105/35909

SLIDE 42

Multiple C

A B

tiple Circuits

light1 = A or B light2 = A and B

SLIDE 66

miniN

There’s a pile of objects
On her turn, a player can tak
ne or two objects.
Players alternate.
The player to take the l

miniNim

f objects, say 10.

ayer can take away either e the last object wins.

SLIDE 67

Ideas?

The Strategy?

Ideas?

SLIDE 68

Nim5Bot: Game

Let’s start by considering

the 5-object version.

We’ll design a strategy for

the computer “C” to beat the user “U”.

t: Game Tree

beat the

SLIDE 69

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

SLIDE 70

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

SLIDE 71

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

??

SLIDE 72

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

C takeOne

SLIDE 73

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

SLIDE 74

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

SLIDE 75

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

SLIDE 76

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

??

SLIDE 77

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

??

SLIDE 78

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

C takeOne

SLIDE 79

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

2 left

SLIDE 80

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

2 left

takeOne takeTwo

SLIDE 81

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

2 left

takeOne takeTwo

C

SLIDE 82

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

2 left

takeOne takeTwo

C

SLIDE 83

Nim5Bot: Game

Let’s start by

considering the 5-

bject version.
We’ll design a

strategy for the computer “C” to beat the user “U”.

t: Game Tree

5 left

takeOne takeTwo

3 left

takeOne takeTwo

C C

2 left

takeOne takeTwo

C U

SLIDE 84

Nim5Bot: Game

Let’s start by considering

the 5-object version.

We’ll design a strategy for

the computer “C” to beat the user “U”.

t: Game Tree

5 left 3 left

takeOne takeTwo

2 left

takeOne takeTwo takeOne takeTwo

C C C U

beat the

SLIDE 85

Backwards I

There’s a powerful idea
Many decision making

solved optimally by reas from the end of the gam

We know how to win
We use this to win from
We use this to win from
Chess: removed pieces

ards Induction

ful idea here: making problems can be y by reasoning backwards the end of the game. to win from 1 or 2. to win from 4 or 5. to win from 7 or 8. pieces don’t return.

SLIDE 86

Further Consi

To win miniNim: if poss

leave opponent with a m

Why does it work? W

3; if opponent has a m her with next smaller

What if goal is to not
What if we can take 1, 2, or

round? 2 or 3? 1 or 3? Is rule?

her Considerations

if possible, remove pieces to ith a multiple of 3.

rk? We win if opponent has

has a multiple of 3, can leave aller multiple of 3. take the last object? take 1, 2, or 3 objects per 3? 1 or 3? Is there a general

SLIDE 87

Complete Ni

fiveLeft = True
threeLeft = fiveLeft and takeOne
twoLeft = fiveLeft and takeTwo1
C-Win = (threeLeft and (takeOne
r takeTwo2)) or (twoLeft and

takeOne2)

U-Win = twoLeft and takeTwo2

ete Nim5 Logic

5 left 3 left

takeOne1 takeTwo1

2 left

takeOne2 takeTwo2 takeOne2 takeTwo2

C C C U

One1 One2

SLIDE 88

tw

Nim5 Ci

takeOne1 takeTwo1 fiveLeft U-Win twoLeft threeLeft

m5 Circuit

C-Win takeTwo2 takeOne2

http://scratch.mit.edu/pro jects/cs105/35736

SLIDE 89

What a Headache!

Encoding Nim10 with s

Why?

Since some switches

places, needs more than a doubl switch.

Since values are reus
f different circuits.
Appears to need a separ
utput: Gets too com

a Headache!

10 with switches is a nightmare. itches are used in multiple

re than a double-throw

are reused, hard to keep track to need a separate circuit for each too complex too fast.

SLIDE 90

Bits, Inside

Inputs: Switches

takeOne1 takeTwo1 takeOne2 takeTwo2

Nim Player

nside and Out

Outputs: Lights

You win! I win!

SLIDE 91

Bits, Inside

A = False B = True

Inputs: Switches Inside: Logi

AND AND AND AND NOT NOT

nside and Out

light2On = True light1On = False

Outputs: Lights de: Logic

OR OR OR OR OT

SLIDE 92

Need a New

Let’s consider an alternate w

“and” and “or” logic.

Makes simple things
Makes complex things
That’s a tradeoff we can

a New Approach

an alternate way of building things more complex. things much simpler! adeoff we can deal with.

lightOn = ?

True

A = True

SLIDE 105

A = False

Switch Sw

lightOn = Tru

tch Switcher

lightOn = ?

True

A = True

SLIDE 106

A = False

Switch Sw

lightOn = Tru Before, we used switches to c now, we will use current (v control switches (which con

tch Switcher

lightOn = False

True

A = True es to control the flow of current; ent (via electromagnetism) to ch control the flow of current)!

SLIDE 107

Relay Circuit: A rcuit: A = F, B = F

SLIDE 108

Relay Circuit: A rcuit: A = F, B = F

SLIDE 109

Relay Circuit: A rcuit: A = F, B = T

SLIDE 110

Relay Circuit: A rcuit: A = F, B = T

SLIDE 111

Relay Circuit: A rcuit: A = F, B = T

SLIDE 112

Relay Circuit: A rcuit: A = T, B = F

SLIDE 113

Relay Circuit: A rcuit: A = T, B = F

SLIDE 114

Relay Circuit: A rcuit: A = T, B = F

SLIDE 115

Relay Circuit: A rcuit: A = T, B = T

SLIDE 116

Relay Circuit: A rcuit: A = T, B = T

SLIDE 117

Relay Circuit: A rcuit: A = T, B = T

SLIDE 118

Relay Circuit: A rcuit: A = T, B = T

What is this?

A. NOT gate
B. AND gate
C. OR gate
D. AND-OR gate

SLIDE 119

Relay Circuit: A rcuit: A = T, B = T

SLIDE 120

And One For ne For “Not”

SLIDE 121

And One For

NOT

ne For “Not”

NOT

SLIDE 122

And One For

We saw several slides

ago that a single relay “inverts” its input signal, turning a True to a False and vice versa.

These output summaries

are known as “truth tables”.

ne For “Not”

alse aries

A B

False True True False NOT GATE

A B

B = not A

A B

SLIDE 123

Abstraction: The

Our new relay-based

“and” and “not” gates take current, not switches, as input.

As a result, they are

easier to chain together.

The original switch-based

scheme did not support this kind of modularity.

n: The Black Box

take based

AND GATE NOT GATE NOT GATE NOT GATE

A B C

SLIDE 124

A Third Black

A B C

False False False True True False True True

hird Black Box

AND GATE NOT GATE NOT GATE NOT GATE

A B C

SLIDE 125

A Third Black

A B C

False False False False True True True False True True True True

hird Black Box

AND GATE NOT GATE NOT GATE NOT GATE

A B C

SLIDE 126

Complete Ni

fiveLeft = True
threeLeft = fiveLeft and takeOne
twoLeft = fiveLeft and takeTwo1
C-Win = (threeLeft and (takeOne
r takeTwo2)) or (twoLeft and

takeOne2)

U-Win = twoLeft and takeTwo2

ete Nim5 Logic

5 left 3 left

takeOne1 takeTwo1

2 left

takeOne2 takeTwo2 takeOne2 takeTwo2

C C C U

One1 One2

SLIDE 127

Simplified Nim5

fiveLeft threeLeft twoLeft takeOne1 ta takeTwo1

AND GATE

True

ed Nim5 Circuit

C-Win U-Win takeOne2 takeTwo2

AND GATE OR GATE OR GATE AND GATE AND GATE

SLIDE 128

How to Make

switches/relays
hydraulic valves
tinkertoys
silicon: semiconductors/trans
soap bubble
DNA
quantum material
ptics
Make a Gate

tors/transistors

SLIDE 129

Movi Movie

SLIDE 130

NOT Gate (v3)

1 1

SLIDE 131

Or Gate (v4)

1 1

Relea

1

Release bottom row first

SLIDE 132

Wire, transmitting bi

1

itting bits (v1)

1

SLIDE 133

Could It Wor

My domino “or” gate requi
The first Pentium proces

transistors, or roughly 800K

So, perhaps 19M domi
World record for domino toppl
Oh, and the Pentium di

60M times a second, w might require a week to s

uld It Work?

gate requires 24 dominoes. processor had 3.3M

ughly 800K gates.

dominoes needed. domino toppling: 4M. entium did its computations

nd, whereas dominoes

eek to set up once.

SLIDE 134

But There Are Lot

iPod: 60Gb. 1Gb = one

billion bytes, each of which is 8 bits.

Format uses 128 Kbps

(kilobits or 1000 bits per second of sound).

So, 62,500 minutes of

sound or 15,000 songs at 4 minutes per song.

Screen: 320x240 pixels,

each of which stores 1 byte each of R,G,B intensity (24 bits). That’s 76,800 pixels and 1.8M bits.

At 30 frames per sec.,

that’s 55.3 million bits per second or 144 min. of (quiet) video.

here Are Lots of Them

SLIDE 135

1 Byte = 8 Bits
1 Kilobyte (KB) = 1,000 Byt
1 Megabyte (MB) = 1,000 Kiloby
1 Gigabyte (GB) = 1,000 M

= 1,000,000 = 1,000,000,

You can also have kilobits,

Number of

000 Bytes 1,000 Kilobytes = 1,000,000 Bytes 000 Megabytes 000,000 Kilobytes 000,000,000 Bytes ilobits, megabits and gigabits

umber of Bits

SLIDE 136

An Exampl

When you download a file,

your download speed in kilobit

For example, I am downloading

Firefox, which is 17.6 MB

This means that the file cont
17.6 megabytes = 17,600

bytes

= 140,800,000 bits

An Example

nload a file, you will most likely see peed in kilobits per second downloading a copy of Mozilla 6 MB for the mac he file contains 17,600 kilobytes = 17,600,000

SLIDE 137

An Example C

If my download speed is 300

second, how long will it tak file?

100 kilobits = 100,000 bits
140,800,000 bits * 1 second
= 469 seconds = 7.8 minut

Example Continued

peed is 300 (kbps) kilobits per ill it take me to download the 000 bits 1 second / 300,000 bits 7.8 minutes

SLIDE 138

Another Exam

Your digital camera is 10 m

happen to know that each see why later in this class)

First, how many bits are in
10 megapixels = 10,000 k

pixels

= 240,000,000 bits
= 30,000,000 bytes = 30,000
= 30 megabytes per pic

her Example

is 10 megapixels and you hat each pixel is 24 bits (we will class) are in each picture? 000 kilopixels = 10,000,000 = 30,000 kilobytes per picture

SLIDE 139

Another Exam

Now, if you have a 4 gigaby

pictures can you take?

4 gigabytes = 4,000 megaby
4,000 megabytes * 30 megaby
= 133 pictures

Example Cont....

4 gigabyte card, how many 000 megabytes 30 megabytes / 1 picture