CSC103 How Computers Work

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1 mith College Computer Science CSC103 How Computers Work Fall 2017 Dominique Thiébaut

2 Plan for Day 1 Syllabus Overview Some History

3 Syllabus < Start here Faculty Dominique Thiébaut More Info CSC103 Syllabus Weekly Schedule Piazza < Every Lecture

4 Japanese animé Steamboy Steampunk 2004 Katsuhiro Otomo

5 Some History Anthikythera Abacus Difference Engine

6 Earlier History Anthikythera YouTube video (go to 4 min 12 sec)

7 Earlier History Abacus Used in Europe, China, Russia First appeared BC

8 Earlier History Difference Engine Youtube, Wired video Babbage, 1840 Lady Ada Lovelace ( )

9 Optical Computing Replace electrons by photons Replace transistors by optical transistors Uncertain future

10 Recent History DNA Computing Leonard Adleman, 1994, USC Solves the traveling salesman problem.

11 Estimating the number of possible routes

12 List of Factorials 0! 1 1! 1 2! 2 3! 6 4! 24 5! 120 6! 720 7! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

13 We Stopped Here Last Time

14 Plan for today Pioneers of Computer Science Binary System Counting in Binary Binary Arithmetic Boolean Algebra Electronic Circuits: Logic Gates

15 Important Concepts Code Electricity Binary Code, Binary System Technology (mechanical gears, vacuum tubes, transistors, DNA, ) Math

16 Natural Selection COMPUTING Many Different Solutions & Technologies

17 Natural Selection COMPUTING

18 Natural Selection Shannon von Neumann COMPUTING Boole Turing

19 George Boole George Boole ( ) Logic Values: True & False Operators: AND, OR, NOT Boolean Algebra Credit:

20 Logic Word-Problem The year is 2030, you are sick, in bed, and you send your robot to Stop & Shop, instructing it to pick up some ice cream, with the following request: "Any fruit ice cream or anything with vanilla" Stop & Shop currently carries chocolate ice cream raspberry sorbet Does your logically flawless robot bring anything back? Image credit:

21 Logic Word-Problem The year is 2030, you are sick, in bed, and you send your robot to Stop & Shop, instructing it to pick up some ice cream, with the following request: "Anything with fruit and with vanilla" Stop & Shop currently carries strawberry ice cream lemon sorbet REVISED raspberry vanilla ice cream Does your logically flawless robot bring anything back? Image credit:

22 Rules of Boolean Logic False False True True False True False True > > > >

23 Rules of Boolean Logic Not Not False True > >

24 Math to the rescue! True and False can be "coded" as 1 and 0 We can easily convert decimal numbers into binary numbers We can easily convert binary numbers into decimal numbers We can do arithmetic with binary numbers (Soon to be explored )

25 Second Important Link Claude Shannon s Master s Thesis MIT, 1937 Shows relationship between boolean logic and arithmetic: any integer arithmetic operation can be implemented using logic operations

26 TRUE & FALSE AND, OR, NOT 1, 0 Binary ELECTRICITY ON, OFF

27 Third Important Link John von Neumann, 1945 Writes an unpublished report "First Draft of a Report on the EDVAC" Report becomes defacto standard for how to design computers

28 Third Important Link Early Technologies John von Neumann, 1945 Writes an unpublished report "First Draft of a Report on the EDVAC" Report becomes defacto standard for how to design computers

29 Introduction to Binary Counting in Decimal Counting in Binary Counting in a different base Adding in Decimal Adding in Binary

30 Continue on the whiteboard We just finished counting in decimal on Monday

31 We Stopped Here Last Time

32 "Mechanical" Counting Rule 1: Roll

33 "Mechanical" Counting Rule 2: Increment the digit to the left

34 "Mechanical" Counting?

35 "Mechanical" Counting

36 "Mechanical" Counting

37 "Mechanical" Counting

38 "Mechanical" Counting

39 "Mechanical" Counting

40 "Mechanical" Counting

41 "Mechanical" Counting

42 Counting in Binary Only 2 digits: has no weight (as in decimal) Start 0, 1, and apply Rule 1 and Rule 2, as done previously

43 Exercise Count in a system with 4 digits: O, P, Q, R O has weight zero Assume that O < P < Q < R

44 Arithmetic in Decimal

45

46 Arithmetic in Binary!

47

48 Conversion Binary to Decimal

49 Continue on the whiteboard

50 We Stopped Here Last Time

51 Homework Assignment Released this weekend Due Sunday 09/24 midnight

52 Review We can count in binary We can add in binary We can convert a binary number to its decimal equivalent Converting a decimal number to binary? Yes we can!

53 Review We ll skip this part We can count in binary We can add in binary We can convert a binary number to its decimal equivalent Converting a decimal number to binary? Yes we can!

54 Important: Whichever arithmetic operation we can perform in decimal, we can also do in binary.

55 Back to Boolean Logic a b a and b F F F F T F T F F T T T

56 Back to Boolean Logic a b a and b F F F F T F T F F T T T a b a or b F F F F T T T F T T T T

57 Back to Boolean Logic a b a and b F F F F T F T F F T T T a b a or b F F F F T T T F T T T T a F T not a T F

58 Why just 3 operators? AND, OR, and NOT are necessary and sufficient to implement any boolean function.

59 Example a b a? b F F F F T T T F T T T F

60 Example a b a? b F F F Case 1 Case 2 F T T T F T T T F a?b = (Case 1) OR (Case 2)

61 Example a b a? b Case 1 Case 2 F F F F F Case 1 F T T Case T 1 F Case 2 T F T Case F 2 T T T F F F a?b = (Case 1) OR (Case 2)

62 Example NOT a a b a? b Case 1 Case 2 T F F F F F Case 1 T F T T Case T 1 F Case 2 F T F T Case F 2 T F T T F F F a?b = (Case 1) OR (Case 2)

63 Example NOT a a b a? b Case 1 Case 2 T F F F F F Case 1 T F T T Case T 1 F Case 2 F T F T Case F 2 T F T T F F F a?b = (NOT a AND b) OR (Case 2)

64 Example AND, OR, and NOT are necessary and sufficient to implement any boolean function. NOT b NOT a a b a? b Case 1 Case 2 T T F F F F F Case 1 F T F T T Case T 1 F Case 2 T F T F T Case F 2 T F F T T F F F a?b = (NOT a AND b) OR (Case 2)

65 Example AND, OR, and NOT are necessary and sufficient to implement any boolean function. NOT b NOT a a b a? b Case 1 Case 2 T T F F F F F Case 1 F T F T T Case T 1 F Case 2 T F T F T Case F 2 T F F T T F F F a?b = (NOT a AND b) OR (a AND NOT b)

66 Example vanilla fruit vanilla xor fruit F F F F T T T F T T T F

67 Example vanilla fruit vanilla xor fruit F F F F T T T F T T T F "Get (vanilla and no fruit) or (no vanilla and fruit)"

68 Basic Electricity photo credit:

69 Basic Electricity + - photo credit:

70 Basic Electricity + - photo credit:

71 Basic Electricity + - ON True 1 photo credit:

72 Basic Electricity + - OFF False 0 photo credit:

73 Simplification + - OFF False 0 photo credit:

74 Simplification ON True 1 OFF False 0 photo credit:

75 Boolean Variables a True 1 photo credit:

76 Boolean Variables a False 0 photo credit:

77 Boolean Variables a photo credit:

78 Special Switches a photo credit:

79 Mystery Circuit a b T 1

80 Logic Gates

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