IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf ·...

133
IST 4 Information and Logic

Transcript of IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf ·...

Page 1: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

IST 4Information and Logic

Page 2: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

MQ1 d il dMQ1 grades were emailedplease let the TAs know if you submitted MQ1

d d d h land did not get the email

HW1 will be returned todayAverage is 44/48 ~= 92Average is 44/48 ~= 92

Page 3: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

mon tue wed thr fri30 M1 1= todayT

6 M1

13 1 2M2x= hw#x out

oh oh

oh oh

= todayT

M

20 227 M2

x= hw#x due

idt

oh oh

h h

T

27 M2

4 311 3 4Mx= MQx out

midtermsoh

oh oh

oh = office hours oh

11 3 418 4 525

Mx= MQx out

Mx= MQx dueoh oh

ohoh

25

1 5oh

oh

oh

oh

Page 4: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

MemoryMQ2• You are invited to write short essay on the topic of theM t Q ti

QDeadline Tuesday 4/28/2015 at 10pm

Magenta Question.• Recommended length is 3 pages (not more)• Submit the essay in PDF format to [email protected] the essay in PDF format to [email protected]

file name lastname-firstname.pdf• No collaboration. No extensionsGrading of MQ:3 points (out of 103)

50% for content quality, 50% for writing quality

Some students will be given an opportunityto give a short presentation for up to 3 additional points

Page 5: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Last time...Building blocks

geometricgeometricnumeric

b

a b m ?

symbolica b

0 0

10

1

1 M y1 0

11

1

0 m

Page 6: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

separationBuilding blocks

The path from geometricpnumeric to

symbolic and beyond?

geometricnumeric

symbolic and beyond?

b

a b m ?a b

0 0

10

1

1 M symbolic1 0

11

1

0 m

y

Page 7: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The geography The geography of numbers representations

Page 8: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

MCMXXX = 1930

Page 9: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Roman Numeral Puzzle: The survival of the unfitThe survival of the unfit...

Babylonia 5,000 yafirst positional number system

Base 60

India, China 2,500 yaRoman EmpireMM = 2000 ya Base 10

Central Asia, Persia, Arabs 1,200 yaRoman Empire

B 10

Europe 800 yapositional number system in Europe

Base 10

system in Europe

Page 10: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Babylonians and Egyptians5000 ~5000 years ago

Page 11: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Merv, 2014 Merv, 2014

Merv, 2014

source: wikipedia

Page 12: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Greek - Alexander~2500 years ago 2500 years ago

source: wikipedia

Page 13: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Roman Empire~2000 years ago 2000 years ago

source: wikipedia

Page 14: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Arabs~1200 years ago

Muhammad ibn Mūsā al-Khwārizmī

~1200 years ago

Page 15: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Roman numerals and the abacus

Page 16: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

A Refresher on the Roman Numeral SystemRoman Numeral System

Roman Numeral Number Large

Roman NumberI 1V 5

NumeralsV 5,000

X 10L 50

X 10,000L 50,000C 100 000C 100

D 500M 1000

C 100,000D 500,000M 1 000 000M 1000 M 1,000,000

LCD Monitor

Page 17: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

It s all About Syntax

VLDVIIIII V

2 1

VLDVIIIII

XXXXX

V

L

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

M

Page 18: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDVIIIII V

It s all About SyntaxWhat is the number?

VLDVIIIII

XXXXX

V

L

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

M

Page 19: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDVIIIII V

It s all About SyntaxWhat is the number?

VLDVIIIII

XXXXX

V

L

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

MDCI 601

Page 20: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDVIIIII V

It s all About Syntax

Touch the middle: Yes or NoVLDVIIIII

XXXXX

V

Lit is a binary mechanism

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

MDCI 601

Page 21: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The AbacusCalculating Machine are Based on Syntax

The first actual calculating mechanism known to us is th b s hi h is th ht t h b n in nt d

Calculating Machine are Based on Syntax

the abacus, which is thought to have been invented by the Babylonians sometime between 1,000 BC and 500 BC

The original concept referred to a flat stone covered with sand or dust with pebbles being placed on lines with sand or dust, with pebbles being placed on lines drawn in the sand

Source: Wikipedia

Page 22: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The AbacusCalculating Machine are Based on Syntax

The original concept referred to a flat stone covered

Calculating Machine are Based on Syntax

The original concept referred to a flat stone covered with sand or dust, with pebbles being placed on lines drawn in the sand ?

?

In Phoenician the word abak means sand

In Hebrew the word abhaq ָאָבק means dust

Calculus is Latin for pebble

Source: Wikipedia

Page 23: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDVIIIII V

It s all About Syntax

VLDVIIIII

XXXXX

V

L

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

MDCI 601

Page 24: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDVIIIII V

It s all About SyntaxWhat is the number?

VLDVIIIII

XXXXX

V

L

CCCCC D

MMMMM V

IXCM

LL C

VV X

LL

DD

C

MCCCCLXXXVIIII 489

Page 25: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 26: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 27: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 28: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 29: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 30: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 31: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 32: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 33: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 34: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax2 1

5 1

VLDV

It s all About Syntax2 1

VLDV

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 35: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDV

It s all About Syntax

What is the decimal VLDVWhat is the decimal representation?

MLXXXX ??

IXCM

CCCCLXXXVIIII 489DCI 601 +

Page 36: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Abacus: It’s all About Syntax

VLDV

It s all About Syntax

What is the decimal VLDVWhat is the decimal representation?

MLXXXX 0901

IXCMWhat’s wrongwith this picture?

CCCCLXXXVIIII 489DCI 601 +

Page 37: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Roman Numerals and Base 10 Systemsy

VLDVMLXXXX VLDVMLXXXXRoman numerals

The representation in the abacusis a positional base 10 representation

0901m um

used for numberRepresentation

is a positional base 10 representation

For calculation:we used the abacus

IXCMwe used the abacus

Page 38: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

F Ph l ( b ) From Physical (abacus) to Symbolsy

Algorizmsg

Page 39: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorizmig

A positional number system Operations are done on syntaxp yis a key enabler for efficient arithmetic operations

Operations are done on syntax

Muhammad ibn Mūsā al-Khwārizmī

الخوارزمي موسى بن محمد 780 850ADي رز و ى و 850AD-780 بن

A Persian mathematician, who wrote on Hindu-Arabic numerals and was among the first to use zero as a place numerals and was among the first to use zero as a place holder in positional base notation. The word algorithm derives from his name. His book Kitab al-jabr w'al-muqabala gives us the word algebra

Source: Wikipedia

Page 40: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Beginning of the “Algebra Book ” by “Algorizmi ”

Everything requires computation...

Page 41: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The Beginning of the “Algebra Book ” by “Algorizmi ”Positional: order is important; the base – multiplication by 10;

from 1 to infinity...

Page 42: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Example from the “Algebra Book ” by “Algorizmi ”computation = single digit syntax manipulation

????

It is rhetorical (words) no symbols

Page 43: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms and Algebra in Europeg g pLeonardo Fibonacci1170-1250AD Leonardo was born in Pisa his father directed Leonardo was born in Pisa, his father directed

a trading post in Bugia, a port east of Algiers in North Africa, as a young boy Leonardo traveled there to help him This is where he learned about there to help him. This is where he learned about the Arabic numeral system

Perceiving that arithmetic with Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled ,throughout the Mediterranean world to study under the leading Arab mathematicians of the time, returning around 1200. t me, return ng around 00. In 1202, at age 32, he published what he had learned in Liber Abaci, or Book of Calculation

Source: Wikipedia

Page 44: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Liber Abaci – First ChapterL F p

Introduction of the syntax; from 1 to infinity...

Page 45: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Liber Abaci – First ChapterL F p

Positional: order is importantPositional: order is important

Page 46: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorizmi Algorizmi andand

“brain surgery” brain surgery

Page 47: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

0 1 2 3 4 5 6 7 8 9

0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 102 2 3 4 5 6 7 8 9 10 112 2 3 4 5 6 7 8 9 10 113 3 4 5 6 7 8 9 10 11 124 4 5 6 7 8 9 10 11 12 135 5 6 7 8 9 10 11 12 13 145 5 6 7 8 9 10 11 12 13 146 6 7 8 9 10 11 12 13 14 157 7 8 9 10 11 12 13 14 15 168 8 9 10 11 12 13 14 15 16 178 8 9 10 11 12 13 14 15 16 179 9 10 11 12 13 14 15 16 17 18

Page 48: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

In first grade:We use our BRAIN for remembering We use our BRAIN for remembering

Algorizmi’s syntax

Page 49: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Arithmetic boxesArithmetic boxesdecimal decimal

Page 50: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

digit 1 digit 2digit 1 digit 2

2 symbol addercarry carry

sum

Page 51: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

digit 1 digit 28 6

digit 1 digit 2

2 symbol addercarry carry0

sum

Page 52: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

digit 1 digit 28 6

digit 1 digit 2

2 symbol addercarry 1 carry0

44

sum

Page 53: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

d1 d2 d1 d2 d1 d2 d1 d2

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c

1891 + 8709 = ??

Page 54: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 d2 8 d2 9 d2 1 d2

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

0

1891 + 8709 = ??

Page 55: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

0

1891 + 8709 = ??

Page 56: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adder1

0

0

1891 + 8709 = ??

Page 57: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 1 99 0

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adder1

0

02 symbol adder1

0

1

1891 + 8709 = ??

Page 58: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

2 symbol adderc

c

c 2 symbol adder1

6

1 2 symbol adder1

0

1 2 symbol adder1

0

0

1891 + 8709 = ??

Page 59: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

2 symbol adder1

0

1 2 symbol adder1

6

1 2 symbol adder1

0

1 2 symbol adder1

0

0

1891 + 8709 = ??

Page 60: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

2 symbol adder1

0

1 2 symbol adder1

6

1 2 symbol adder1

0

1 2 symbol adder1

0

0

1891 + 8709 = 10,600

How big are the tables h 2 b l dd in the 2 symbol adder?

Page 61: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 8 8 7 9 0 1 9

Two cases: carry = 0 or carry =1

2 symbol adder1

0

1 2 symbol adder1

6

1 2 symbol adder1

0

1 2 symbol adder1

0

0

0 0 1 2 3 4 5 6 7 8 90 0 1 2 3 4 5 6 7 8 9

1 9 0 1 2 3 4 5 6 7 80 0 1 2 3 4 5 6 7 8 90 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9

1 1 2 3 4 5 6 7 8 9 0

2 2 3 4 5 6 7 8 9 0 1

0 0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 13 0 0 0 0 0 0 0 1 1 1 3 3 4 5 6 7 8 9 0 1 2

4 4 5 6 7 8 9 0 1 2 35 5 6 7 8 9 0 1 2 3 4

3 0 0 0 0 0 0 0 1 1 14 0 0 0 0 0 0 1 1 1 15 0 0 0 0 0 1 1 1 1 16 0 0 0 0 1 1 1 1 1 1 6 6 7 8 9 0 1 2 3 4 5

7 7 8 9 0 1 2 3 4 5 68 8 9 0 1 2 3 4 5 6 7

6 0 0 0 0 1 1 1 1 1 17 0 0 0 1 1 1 1 1 1 18 0 0 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 9 9 0 1 2 3 4 5 6 7 89 0 1 1 1 1 1 1 1 1 1

Page 62: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithm = Algorithm = a procedure for syntax manipulation

Dear Algo and Fibo, we get confused with those glarge tables... can we use a

smaller syntax?m y

Page 63: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

The BinaryThe Binary

Page 64: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

When was the binary When was the binary system “invented”?system invented ?

(11010100111)(11010100111)2

(1 03)(1703)10

1024 512 128 32 4 2 1 1 03 1024+512+128+32+4+2+1 = 1703

Page 65: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Leibniz Binar S stemGottfried Leibniz

1646-1716

Leibniz – Binary System

Page 66: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Gottfried Leibniz1646-1716

Page 67: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Gottfried Leibniz1646-1716

Page 68: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Gottfried Leibniz1646-1716

Use the smallest syntax possible Binary – 0 and 1Binary 0 and 1

Page 69: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Gottfried Leibniz1646-1716

??

8

??

8

Page 70: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Binary AdditionGottfried Leibniz

1646-1716 y

carry

Page 71: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Binary MultiplicationGottfried Leibniz

1646-1716

Binary Multiplication

3 5 5206 2010

Addition of shifted versions

Page 72: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Leibniz: No Need for Flash Cards!No Need for Flash Cards!

Page 73: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

I t d th Bi S t ?Gottfried Leibniz

1646-1716

Invented the Binary System?

Page 74: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Leibniz Binar S stemGottfried Leibniz

1646-1716

Leibniz – Binary SystemWen Wang (who flourished in about 1150 BC) g ( f )is traditionally thought to have been author of the present hexagrams

63

Page 75: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Leibniz Binar S stemGottfried Leibniz

1646-1716

Leibniz – Binary System

Page 76: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Arithmetic BoxesArithmetic Boxesbinarybinary

Page 77: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 2digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry carry

sum

Page 78: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 20 0

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 0 carry0

0sum

Page 79: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 21 0

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 0 carry0

1sum

Page 80: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 21 1

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 1 carry0

0sum

Page 81: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 21 0

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 1 carry1

0sum

Page 82: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 20 1

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 1 carry1

0sum

Page 83: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Adding Bits

digit 1 digit 21 1

digit 1 digit 2

3 bits to 2 bits

2 symbol addercarry 1 carry1

1sum

Page 84: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

0

0 1 2 3 4 5 6 7 8 90 0 1 2 3 4 5 6 7 8 9

0

0 0 1 2 3 4 5 6 7 8 91 1 2 3 4 5 6 7 8 92 2 3 4 5 6 7 8 93 3 4 5 6 7 8 9

2 symbol adderc

d1 d2

c3 3 4 5 6 7 8 94 4 5 6 7 8 95 5 6 7 8 96 6 7 8 9

y

s

6 6 7 8 97 7 8 98 8 99 9

Page 85: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation0 1

0 0 11 1 2

0 0 1

0 1 21 2 3

1

0 1

sum

1 1 2 1 2 3

2 symbol adderc

d1 d2

c

0 1

0 0 11 1 0

0 1

0 1 01 0 1

sum

y

s

1 1 0 1 0 1

0 1

0 1

0

0 1

1

carry0 0 01 0 1

0 0 11 1 1

Page 86: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

0 1

0 1

0

0 1

1

2 symbol adder1

1 1

0

0 0 11 1 0

0 1 01 0 1

y

0 0 1

0 1

0 0 01 0 1

0 1

0 0 11 1 11 0 1 1 1 1

Page 87: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Algorithms – Syntax Manipulation

0 1

0 1

0

0 1

1

2 symbol adder1

1 0

1

0 0 11 1 0

0 1 01 0 1

y

0 0 1

0 1

0 0 01 0 1

0 1

0 0 11 1 11 0 1 1 1 1

Page 88: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

0

0 11101 + 1001 = ??

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

0 1

0

0 1

1

0 0 01 0 1

0 0 11 1 1

Page 89: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adder1

0

0

0 11101 + 1001 = ??

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

0 1

0

0 1

1

0 0 01 0 1

0 0 11 1 1

Page 90: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adderc

c

c 2 symbol adderc

c

c 2 symbol adder0

1

1 2 symbol adder1

0

0

0 11101 + 1001 = ??

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

0 1

0

0 1

1

0 0 01 0 1

0 0 11 1 1

Page 91: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adderc

c

c 2 symbol adder0

1

0 2 symbol adder0

1

1 2 symbol adder1

0

0

0 11101 + 1001 = ??

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

0 1

0

0 1

1

0 0 01 0 1

0 0 11 1 1

Page 92: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adder1

0

0 2 symbol adder0

1

0 2 symbol adder0

1

1 2 symbol adder1

0

0

0 11101 + 1001 = ??

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

0 1

0

0 1

1

0 0 01 0 1

0 0 11 1 1

Page 93: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adder1

0

0 2 symbol adder0

1

0 2 symbol adder0

1

1 2 symbol adder1

0

0

0 1

0 1

0 0 11 1 0

0 1

0 1 01 0 11 1 0 1 0 1

0 1

1101 + 1001 = 10110

0 1

0

0 1

113 + 9 = 22

0 0 01 0 1

0 0 11 1 1

Page 94: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adder1

0

0 2 symbol adder0

1

0 2 symbol adder0

1

1 2 symbol adder1

0

0

0 1

M i b d t k ith ti !!0 1

0 0 11 1 0

0 1

0 1 01 0 1

Magic boxes do not know arithmetic!!However...

1 1 0 1 0 1

0 1

1101 + 1001 = 10110

0 1

0

0 1

113 + 9 = 22

0 0 01 0 1

0 0 11 1 1

Page 95: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Magic Syntax Boxes

There is a finite universal set of building blocks

C st t ‘everything’Can construct everythinga b

a b m

0 0 110

1 011

m11 0

Page 96: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Magic boxes can compute the sum

0 1d1 d2

0 1

compute the sum

0 1

0 0 11 1 0

0 1

0 1 01 0 1

2 symbol adderc

s

c

a bd1 d2 s d1 d2 sd1 d2 s

0 010

01

d1 d2

0 010

s

1010

1 011

110

101 0

11

00111 0

m11 1

Page 97: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Magic boxes can compute the carry

0 1d1 d2

0 1

compute the carry

0 1

0 0 01 0 1

0 10 0 11 1 1

2 symbol adderc

s

c

a bccd1 d2 d1 d2 c

0 010

01

0 010

c

00

d1 d2 d1 d2

101 0

11

111

101 0

11

00111 1

m111

Page 98: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

1 1 1 0 0 0 1 1

2 symbol adder1

0

0 2 symbol adder0

1

0 2 symbol adder0

1

1 2 symbol adder1

0

0

0 1Magic boxes do not know arithmetic,however they can add large numbers!

0 1

0 0 11 1 0

0 1

0 1 01 0 1

however, they can add large numbers!

1 1 0 1 0 1

0 1

1101 + 1001 = 10110

0 1

0

0 1

113 + 9 = 22

0 0 01 0 1

0 0 11 1 1

Page 99: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game timeGame time

Page 100: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN WIN the game

VI VI

Page 101: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 102: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Players take turns

can take as many sticks

y uin removing sticks

yfrom a single group

the player that removesp ythe last stick wins

Page 103: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 104: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 105: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 106: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 107: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 108: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 109: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 110: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 111: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 112: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 113: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 114: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 115: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

Page 116: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game

I CANI CAN

Page 117: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN WIN the game

VI=110

Page 118: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

011011

100

110

001

Page 119: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

011011

100

110

001

Page 120: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

100

110

000

Page 121: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

100

110

000

Page 122: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

100

001

111

Page 123: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

100

001

111

Page 124: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

011

001

000

Page 125: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

011

001

000

Page 126: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

011

001

000

Page 127: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

000

001

011

Page 128: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

010010

000

001

001

Page 129: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

001001

000

001

000

Page 130: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

001001

000

001

000

Page 131: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Timeposition

Who can WIN

WIN

the game

000

I CAN

000

I CAN000

001

001

Page 132: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeAn even number of 1s in every Game Time

Who can WIN

WIN

the game

position

Who can WIN

WIN

the game

000Winning starts with the

I CAN

000g

choice of the right language I CAN

000

g g

000

000

Page 133: IST 4 Information and Logic - Paradiseparadise.caltech.edu/ist4/lectures/lect 0715 p.pdf · 2015-04-21 · IST 4 Information and Logic. MQ1 d MQ1 grades were email diled ... th b

Game TimeGame Time

Who can WIN

WIN

the game