1. 1 Ó1998 Morgan Kaufmann Publishers Chapter 4 計算機算數

2. 2 Ó1998 Morgan Kaufmann Publishers Outline

3. 3 Ó1998 Morgan Kaufmann Publishers Problem: Designing MIPS ALU

4. 4 Ó1998 Morgan Kaufmann Publishers Functional Specification

5. 5 Ó1998 Morgan Kaufmann Publishers A Bit-slice ALU

6. 6 Ó1998 Morgan Kaufmann Publishers A 1-bit ALU

7. 7 Ó1998 Morgan Kaufmann Publishers A 4-bit ALU

8. 8 Ó1998 Morgan Kaufmann Publishers How about Subtraction?

9. 9 Ó1998 Morgan Kaufmann Publishers Revised Diagram

10. 10 Ó1998 Morgan Kaufmann Publishers Overflow

11. 11 Ó1998 Morgan Kaufmann Publishers Overflow Detection

12. 12 Ó1998 Morgan Kaufmann Publishers Overflow Detection Logic

13. 13 Ó1998 Morgan Kaufmann Publishers Zero Detection Logic

14. 14 Ó1998 Morgan Kaufmann Publishers Putting It Altogether (I)

15. 15 Ó1998 Morgan Kaufmann Publishers Putting It Altogether (II)

16. 16 Ó1998 Morgan Kaufmann Publishers

17. 17 Ó1998 Morgan Kaufmann Publishers Problems with Ripple Carry Adder

18. 18 Ó1998 Morgan Kaufmann Publishers Carry Lookahead: Theory (I)

19. 19 Ó1998 Morgan Kaufmann Publishers Carry Lookahead: Theory (II)

20. 20 Ó1998 Morgan Kaufmann Publishers Cascaded Carry Lookahead

21. 21 Ó1998 Morgan Kaufmann Publishers

22. 22 Ó1998 Morgan Kaufmann Publishers Carry-select Adder

23. 23 Ó1998 Morgan Kaufmann Publishers Add XOR to ALU

24. 24 Ó1998 Morgan Kaufmann Publishers Shifters

25. 25 Ó1998 Morgan Kaufmann Publishers Combinational Shifter What comes in the MSBs? how many levels for 32-bit shifter? what if we use 4-1 Muxes ?

26. 26 Ó1998 Morgan Kaufmann Publishers Outline

27. 27 Ó1998 Morgan Kaufmann Publishers Multiplication in MIPS

28. 28 Ó1998 Morgan Kaufmann Publishers Division in MIPS

29. 29 Ó1998 Morgan Kaufmann Publishers MIPS Multiply/Divide Summary

30. 30 Ó1998 Morgan Kaufmann Publishers Unsigned Multiply

31. 31 Ó1998 Morgan Kaufmann Publishers Unisigned Multiplier (Ver. 1)

32. 32 Ó1998 Morgan Kaufmann Publishers

33. 33 Ó1998 Morgan Kaufmann Publishers Observations: Multiply Ver. 1

34. 34 Ó1998 Morgan Kaufmann Publishers Unisigned Multiplier (Ver. 2)

35. 35 Ó1998 Morgan Kaufmann Publishers

36. 36 Ó1998 Morgan Kaufmann Publishers Unisigned Multiplier (Ver. 3)

37. 37 Ó1998 Morgan Kaufmann Publishers

38. 38 Ó1998 Morgan Kaufmann Publishers Observations: Multiply Ver. 3

39. 39 Ó1998 Morgan Kaufmann Publishers Booth’s Algorithm: Motivation

40. 40 Ó1998 Morgan Kaufmann Publishers Booth’s Algorithm: Rationale

41. 41 Ó1998 Morgan Kaufmann Publishers Booth’s Algorithm

42. 42 Ó1998 Morgan Kaufmann Publishers Booths Example (2 x 7)

43. 43 Ó1998 Morgan Kaufmann Publishers Booths Example (2 x -3)

44. 44 Ó1998 Morgan Kaufmann Publishers Combinational Multiplier

45. 45 Ó1998 Morgan Kaufmann Publishers How Does It Work?

46. 46 Ó1998 Morgan Kaufmann Publishers Outline

47. 47 Ó1998 Morgan Kaufmann Publishers Divide: Paper & Pencil

48. 48 Ó1998 Morgan Kaufmann Publishers Divide Hardware (Version 1)

49. 49 Ó1998 Morgan Kaufmann Publishers

50. 50 Ó1998 Morgan Kaufmann Publishers Observations: Divide Version 1

51. 51 Ó1998 Morgan Kaufmann Publishers Divide Hardware (Version 2)

52. 52 Ó1998 Morgan Kaufmann Publishers

53. 53 Ó1998 Morgan Kaufmann Publishers Observations: Divide Version 2

54. 54 Ó1998 Morgan Kaufmann Publishers Divide Hardware (Version 3)

55. 55 Ó1998 Morgan Kaufmann Publishers

56. 56 Ó1998 Morgan Kaufmann Publishers Observations: Divide Version 3

57. 57 Ó1998 Morgan Kaufmann Publishers Outline

58. 58 Ó1998 Morgan Kaufmann Publishers Floating-Point: Motivation

59. 59 Ó1998 Morgan Kaufmann Publishers Scientific Notation: Binary

60. 60 Ó1998 Morgan Kaufmann Publishers FP Representation

61. 61 Ó1998 Morgan Kaufmann Publishers Double Precision Representation

62. 62 Ó1998 Morgan Kaufmann Publishers IEEE 754 Standard (1/4)

63. 63 Ó1998 Morgan Kaufmann Publishers IEEE 754 Standard (2/4)

64. 64 Ó1998 Morgan Kaufmann Publishers IEEE 754 Standard (3/4)

65. 65 Ó1998 Morgan Kaufmann Publishers IEEE 754 Standard (4/4)

66. 66 Ó1998 Morgan Kaufmann Publishers Example: FP to Decimal

67. 67 Ó1998 Morgan Kaufmann Publishers Continuing Example: Binary to ???

68. 68 Ó1998 Morgan Kaufmann Publishers Big Idea: Type Not Associated with Data

69. 69 Ó1998 Morgan Kaufmann Publishers Example: Decimal to FP

70. 70 Ó1998 Morgan Kaufmann Publishers Representation for 0

71. 71 Ó1998 Morgan Kaufmann Publishers Special Numbers

72. 72 Ó1998 Morgan Kaufmann Publishers Representation for +/- Infinity

73. 73 Ó1998 Morgan Kaufmann Publishers Representation for Not a Number

74. 74 Ó1998 Morgan Kaufmann Publishers Special Numbers (cont’d)

75. 75 Ó1998 Morgan Kaufmann Publishers Floating-Point Addition

76. 76 Ó1998 Morgan Kaufmann Publishers

77. 77 Ó1998 Morgan Kaufmann Publishers Floating-Point Multiplication (4) set the sign of product

78. 78 Ó1998 Morgan Kaufmann Publishers MIPS Floating Point

79. 79 Ó1998 Morgan Kaufmann Publishers MIPS Floating Point Instructions Organized as a coprocessor –Separate registers $f0-$f31 –Separate operations –Separate data transfer (to same memory) Basic operations –add.s - single add.d - double –sub.s - single sub.d - double –mul.s - single mul.d - double –div.s - single div.d - double

80. 80 Ó1998 Morgan Kaufmann Publishers MIPS Floating Point Instructions (cont’d) Data transfer –lwc1, swcl (l.s, s.s) - load/store float to fp reg –l.d, s.d - load/store double to fp reg pair Testing / branching –c.lt.s, c.lt.d, c.eq.s, c.eq.d, … compare and set condition bit if true –bclt - branch if condition true –bclf - branch if condition false

81. 81 Ó1998 Morgan Kaufmann Publishers Rounding

82. 82 Ó1998 Morgan Kaufmann Publishers Round to Even

83. 83 Ó1998 Morgan Kaufmann Publishers Floating Point Fallacy

84. 84 Ó1998 Morgan Kaufmann Publishers Summary