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

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Presentation on theme: "1 Ó1998 Morgan Kaufmann Publishers Chapter 4 計算機算數."— Presentation transcript:

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 Rounding

80 80 Ó1998 Morgan Kaufmann Publishers Round to Even

81 81 Ó1998 Morgan Kaufmann Publishers Floating Point Fallacy

82 82 Ó1998 Morgan Kaufmann Publishers Summary


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