1320 Principles Of Computer Science I Dr. Thomas Hicks Computer - PowerPoint PPT Presentation

1320 Principles Of Computer Science I Dr. Thomas Hicks Computer Science Department Trinity University 1

2 Decimal Numeration System

Base 10 (Decimal) 3

4 Binary Numeration System

Binary  Convert Base 2  Base 10 5 147

Euler's Process 6 10101111 175 (base 10) = (base 2)

Euler Process (Verbal Description) 7

Practical Usage 8

9 Octal Numeration System

Octal  Base 8  Base 10 10 2073

Euler's Process 11 257

Convert Base 8  Base 2 12 10101111

13 Hexadecimal Numeration System

Hexadecimal  Base 16  Base 10 14 267

Convert Base 10  Base 16 15 10  a 11  b 12  c 13  d 14  e 15  f

Convert Base 16  Base 2 16 10101111

17 Storage Of Positive Integers

Physical Representation Of Byte In Memory 18 7 7 6 5 4 3 2 1 0 0 1 1 1 1 1 1 1  Byte – 8 bits   Bits Are Numbered!  High Bit  Called The Sign Bit  0  Positive Numbers  1  Negative Numbers  Biggest Positive Value (127?)  Sign Bit 0    All Other Digits 1

Storage Of Positive Integers 19 7 6 5 4 3 2 1 0 0 1 1 1 1 1 1 1 1 *2 6 + 1 *2 5 + 1 *2 4 + 1 *2 3 + 1 *2 2 + 1 *2 1 + 1 *2 1 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = 127

20 Strategy 1 For Storing Negative Numbers: Sign Magnitude

21 Sign Magnitude Storage Of Negative Integers 7 6 5 4 3 2 1 0 1 1 1 1 1 1 1 1 1 *2 6 + 1 *2 5 + 1 *2 4 + 1 *2 3 + 1 *2 2 + 1 *2 1 + 1 *2 0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = -127 1 1 1 1 1 1 1

22 Strategy 2 For Storing Negative Numbers: One’s Complement Negative Integers

23 One’s Complement Storage Of Negative Integers 7 6 5 4 3 2 1 0 1 0 0 0 0 0 0 0 -127 1 *2 6 + 1 *2 5 + 1 *2 4 + 1 *2 3 + 1 *2 2 + 1 *2 1 + 1 *2 0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = A  Take The Sign Magnitude 1 1 1 1 1 1 1 B  Invert The Digits 1  0 0  1 0 0 0 0 0 0 0

24 Strategy 3 For Storing Negative Numbers: Two’s Complement Negative Integers

25 Two’s Complement Storage Of Negative Integers Used By Almost All 7 6 5 4 3 2 1 0 Modern Day Computers 1 0 0 0 0 0 0 1 -127 1 *2 6 + 1 *2 5 + 1 *2 4 + 1 *2 3 + 1 *2 2 + 1 *2 1 + 1 *2 0 = 64 + 32 + 16 + 8 + 4 + 2 + 1 = A  Take The Sign Magnitude 1 1 1 1 1 1 1 B  Invert The Digits 1  0 0  1 0 0 0 0 0 0 0 C  Add 1 0 0 0 0 0 0 1

26 Short  Just Like Byte ( Except Bit 15 is Sign Bit )

2 Byte Short Integer Container 27 15 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0  Byte – 16 bits   High Bit  Called The Sign Bit  0  Positive Numbers  1  Negative Numbers  Biggest Positive Value (32,767)  Sign Bit 0    All Other Digits 1

28 Int  Just Like Byte ( Except Bit 31 is Sign Bit )

29 Long  Just Like Byte ( Except Bit 63 is Sign Bit )

30 Scala Conversion Functions

31 toBinaryString  toOctalString  toHexString  T  G

32 Byte Container

33 Binary Representation Of 50 in Byte Container 7 6 5 4 3 2 1 0 0 0 1 1 0 0 1 0 Quotient | Remainder 50 | ---------------------------------- 25 | 0 12 | 1 6 | 0 3 | 0 1 | 1 0 | 1

34 Binary Representation Of -50 in Byte Container Two’s Complement 7 6 5 4 3 2 1 0 1 1 0 0 1 1 1 0 Quotient | Remainder 50 | ---------------------------------- 25 | 0 12 | 1 0 0 1 1 0 0 1 0 6 | 0 3 | 0 1 1 0 0 1 1 0 1 1 | 1 0 | 1 1 1 1 0 0 1 1 1 0

35 Short Container

36 Binary Representation Of 160 in Int Container 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 Quotient | Remainder 160 | ---------------------------------- 80 | 0 40 | 0 20 | 0 10 | 0 5 | 0 2 | 1 1 | 0 0 | 1

37 Binary Representation Of -160 in Int Container Two’s Complement 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0 Quotient | Remainder 160 | ---------------------------------- 80 | 0 40 | 0 20 | 0 10 | 0 5 | 0 2 | 1 1 | 0 0 | 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 0 0 0

38 Addition Of Base 2

39 Addition (Base 2) 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 + --------------------------------- 1

40 Addition (Base 2) 1 1 1 0 1 1 0 + 1 1 0 0 1 1 0 1 --------------------------------- 1 1

41 Addition (Base 2) 1 1 1 1 0 1 1 0 + 1 1 0 0 1 1 0 1 --------------------------------- 0 1 1

42 Addition (Base 2) 1 1 1 1 1 0 1 1 0 + 1 1 0 0 1 1 0 1 --------------------------------- 0 0 1 1

43 Addition (Base 2) 1 1 1 1 1 1 0 1 1 0 + 1 1 0 0 1 1 0 1 --------------------------------- 0 0 0 1 1

44 Addition (Base 2) 1 1 1 1 1 1 1 1 0 1 1 0 + 1 1 0 0 1 1 0 1 --------------------------------- 1 0 0 0 0 1 1

45 Addition (Base 2) 1 1 1 1 1 1 1 1 0 1 1 0 + 1 0 0 1 1 0 1 1 --------------------------------- 1 0 1 0 0 0 0 1 1

46 Addition (Base 2) 1 1 1 0 1 1 0 + 1 0 0 1 1 0 1 1 --------------------------------- 1 0 1 0 0 0 0 1 1

47 Convert To Base 10 118 1 1 1 0 1 1 0 = ______________ (base 10) 64 + 32 + 16 + 4 + 2

48 Convert To Base 10 205 1 1 0 0 1 1 0 1 = ______________ (base 10) + + + 128 64 8 + 4 1

49 Convert To Base 10 323 1 0 1 0 0 0 0 1 1 = __________ (base 10) 256 + 64 + 2 + 1

50 Addition (Base 2) 1 1 1 0 1 1 0 118 + 1 0 0 1 1 0 1 1 205 -------- --------------------------------- 323 1 0 1 0 0 0 0 1 1

51 Subtraction Of Base 2

52 Subtraction (Base 2) 1 1 0 0 1 1 0 1 1 - --------------------- 0

53 Subtraction (Base 2) 1 1 0 0 1 1 0 1 1 - -------------------- 0

54 Subtraction (Base 2) 0 2 1 1 0 0 1 x x 1 0 1 1 - -------------------- 0

55 Subtraction (Base 2) 1 2 0 2 x 1 1 0 0 1 x x x 1 0 1 1 - -------------------- 1 0

56 Subtraction (Base 2) 1 0 2 2 x 1 1 0 0 1 x x x 1 0 1 1 - -------------------- 1 1 0

57 Subtraction (Base 2) 1 2 0 2 2 x x 1 1 0 0 1 x x x x 1 0 1 1 - -------------------- 1 1 1 0

58 Subtraction (Base 2) 1 1 0 0 1 1 0 1 1 - -------------------- 1 1 1 0

59 Convert To Base 10 25 1 1 0 0 1 = ______________ (base 10) 16 + 8 + 1

60 Convert To Base 10 11 1 0 1 1 = ______________ (base 10) 8 2 1 + +

61 Convert To Base 10 1 1 1 0 14 = ______________ (base 10) 8 + 4 + 2

62 Subtraction (Base 2) 25 1 1 0 0 1 11 1 0 1 1 - ----- -------------------- 14 1 1 1 0

63 By Default, All Mathematics Is Done With Int & Double!

64 Decision To Optimize Speed We Will Use Mostly Int  Today’s applications store all single Byte & Short in a 32/64 bit chunk of main memory for calculation efficiency!

65 Decision To Optimize Speed We Will Use Mostly Double

66 Why Should A Computer Scientist Know How Data Is Stored On Disk?

67 Why?  I could say that you need to learn it because it will be used in  Computer Architecture  Operating Systems  Compiler Construction

68 Byte 7 6 5 4 3 2 1 0 0 1 1 1 1 1 1 0 7 6 5 4 3 2 1 0 0 1 1 1 1 1 1 1 7 6 5 4 3 2 1 0 1 0 0 0 0 0 0 0

69 Int

70 Principles Of Programming I CSCI 1320 Dr. Thomas E. Hicks Computer Science Department Trinity University Textbook: An Introduction to Programming with Scala By Dr. Mark Lewis Special Thanks To Dr. Mark Lewis For Providing Some Of Text For Use In This Presentation.