1. Chapter 4 計算機算數

2. Outline

3. Problem: Designing MIPS ALU

4. Functional Specification

5. A Bit-slice ALU

6. A 1-bit ALU

7. A 4-bit ALU

8. How about Subtraction?

9. Revised Diagram

10. Overflow

11. Overflow Detection

12. Overflow Detection Logic

13. Zero Detection Logic

14. Putting It Altogether (I)

15. Putting It Altogether (II)

17. Problems with Ripple Carry Adder

18. Carry Lookahead: Theory (I)

19. Carry Lookahead: Theory (II)

20. Cascaded Carry Lookahead

22. Carry-select Adder

23. Add XOR to ALU

24. Shifters

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

26. Outline

27. Multiplication in MIPS

28. Division in MIPS

29. MIPS Multiply/Divide Summary

30. Unsigned Multiply

31. Unisigned Multiplier (Ver. 1)

33. Observations: Multiply Ver. 1

34. Unisigned Multiplier (Ver. 2)

36. Unisigned Multiplier (Ver. 3)

38. Observations: Multiply Ver. 3

39. Booth’s Algorithm: Motivation

40. Booth’s Algorithm: Rationale

41. Booth’s Algorithm

42. Booths Example (2 x 7)

43. Booths Example (2 x -3)

44. Combinational Multiplier

45. How Does It Work?

46. Outline

47. Divide: Paper & Pencil

48. Divide Hardware (Version 1)

50. Observations: Divide Version 1

51. Divide Hardware (Version 2)

53. Observations: Divide Version 2

54. Divide Hardware (Version 3)

56. Observations: Divide Version 3

57. Outline

58. Floating-Point: Motivation

59. Scientific Notation: Binary

60. FP Representation

61. Double Precision Representation

62. IEEE 754 Standard (1/4)

63. IEEE 754 Standard (2/4)

64. IEEE 754 Standard (3/4)

65. IEEE 754 Standard (4/4)

66. Example: FP to Decimal

67. Continuing Example: Binary to ???

68. Big Idea: Type Not Associated with Data

69. Example: Decimal to FP

70. Representation for 0

71. Special Numbers

72. Representation for +/- Infinity

73. Representation for Not a Number

74. Special Numbers (cont’d)

75. Floating-Point Addition

77. Floating-Point Multiplication
(4) set the sign of product

78. MIPS Floating Point

79. Rounding

80. Round to Even

81. Floating Point Fallacy

82. Summary