Chapter 4 1998 Morgan Kaufmann Publishers 1 Outline

Chapter 4 計算機算數 Ó 1998 Morgan Kaufmann Publishers 1

Outline Ó 1998 Morgan Kaufmann Publishers 2

Problem: Designing MIPS ALU Ó 1998 Morgan Kaufmann Publishers 3

Functional Specification Ó 1998 Morgan Kaufmann Publishers 4

A Bit-slice ALU Ó 1998 Morgan Kaufmann Publishers 5

A 1 -bit ALU Ó 1998 Morgan Kaufmann Publishers 6

A 4 -bit ALU Ó 1998 Morgan Kaufmann Publishers 7

How about Subtraction? Ó 1998 Morgan Kaufmann Publishers 8

Revised Diagram Ó 1998 Morgan Kaufmann Publishers 9

Overflow Ó 1998 Morgan Kaufmann Publishers 10

Overflow Detection Ó 1998 Morgan Kaufmann Publishers 11

Overflow Detection Logic Ó 1998 Morgan Kaufmann Publishers 12

Zero Detection Logic Ó 1998 Morgan Kaufmann Publishers 13

Putting It Altogether (I) Ó 1998 Morgan Kaufmann Publishers 14

Putting It Altogether (II) Ó 1998 Morgan Kaufmann Publishers 15

Ó 1998 Morgan Kaufmann Publishers 16

Problems with Ripple Carry Adder Ó 1998 Morgan Kaufmann Publishers 17

Carry Lookahead: Theory (I) Ó 1998 Morgan Kaufmann Publishers 18

Carry Lookahead: Theory (II) Ó 1998 Morgan Kaufmann Publishers 19

Cascaded Carry Lookahead Ó 1998 Morgan Kaufmann Publishers 20

Ó 1998 Morgan Kaufmann Publishers 21

Carry-select Adder Ó 1998 Morgan Kaufmann Publishers 22

Add XOR to ALU Ó 1998 Morgan Kaufmann Publishers 23

Shifters Ó 1998 Morgan Kaufmann Publishers 24

Combinational Shifter What comes in the MSBs? how many levels for 32 -bit shifter? what if we use 4 -1 Muxes ? Ó 1998 Morgan Kaufmann Publishers 25

Outline Ó 1998 Morgan Kaufmann Publishers 26

Multiplication in MIPS Ó 1998 Morgan Kaufmann Publishers 27

Division in MIPS Ó 1998 Morgan Kaufmann Publishers 28

MIPS Multiply/Divide Summary Ó 1998 Morgan Kaufmann Publishers 29

Unsigned Multiply Ó 1998 Morgan Kaufmann Publishers 30

Unisigned Multiplier (Ver. 1) Ó 1998 Morgan Kaufmann Publishers 31

Ó 1998 Morgan Kaufmann Publishers 32

Observations: Multiply Ver. 1 Ó 1998 Morgan Kaufmann Publishers 33

Unisigned Multiplier (Ver. 2) Ó 1998 Morgan Kaufmann Publishers 34

Ó 1998 Morgan Kaufmann Publishers 35

Unisigned Multiplier (Ver. 3) Ó 1998 Morgan Kaufmann Publishers 36

Ó 1998 Morgan Kaufmann Publishers 37

Observations: Multiply Ver. 3 Ó 1998 Morgan Kaufmann Publishers 38

Booth’s Algorithm: Motivation Ó 1998 Morgan Kaufmann Publishers 39

Booth’s Algorithm: Rationale Ó 1998 Morgan Kaufmann Publishers 40

Booth’s Algorithm Ó 1998 Morgan Kaufmann Publishers 41

Booths Example (2 x 7) Ó 1998 Morgan Kaufmann Publishers 42

Booths Example (2 x -3) Ó 1998 Morgan Kaufmann Publishers 43

Combinational Multiplier Ó 1998 Morgan Kaufmann Publishers 44

How Does It Work? Ó 1998 Morgan Kaufmann Publishers 45

Outline Ó 1998 Morgan Kaufmann Publishers 46

Divide: Paper & Pencil Ó 1998 Morgan Kaufmann Publishers 47

Divide Hardware (Version 1) Ó 1998 Morgan Kaufmann Publishers 48

Ó 1998 Morgan Kaufmann Publishers 49

Observations: Divide Version 1 Ó 1998 Morgan Kaufmann Publishers 50

Divide Hardware (Version 2) Ó 1998 Morgan Kaufmann Publishers 51

Ó 1998 Morgan Kaufmann Publishers 52

Observations: Divide Version 2 Ó 1998 Morgan Kaufmann Publishers 53

Divide Hardware (Version 3) Ó 1998 Morgan Kaufmann Publishers 54

Ó 1998 Morgan Kaufmann Publishers 55

Observations: Divide Version 3 Ó 1998 Morgan Kaufmann Publishers 56

Outline Ó 1998 Morgan Kaufmann Publishers 57

Floating-Point: Motivation Ó 1998 Morgan Kaufmann Publishers 58

Scientific Notation: Binary Ó 1998 Morgan Kaufmann Publishers 59

FP Representation Ó 1998 Morgan Kaufmann Publishers 60

Double Precision Representation Ó 1998 Morgan Kaufmann Publishers 61

IEEE 754 Standard (1/4) Ó 1998 Morgan Kaufmann Publishers 62

IEEE 754 Standard (2/4) Ó 1998 Morgan Kaufmann Publishers 63

IEEE 754 Standard (3/4) Ó 1998 Morgan Kaufmann Publishers 64

IEEE 754 Standard (4/4) Ó 1998 Morgan Kaufmann Publishers 65

Example: FP to Decimal Ó 1998 Morgan Kaufmann Publishers 66

Continuing Example: Binary to ? ? ? Ó 1998 Morgan Kaufmann Publishers 67

Big Idea: Type Not Associated with Data Ó 1998 Morgan Kaufmann Publishers 68

Example: Decimal to FP Ó 1998 Morgan Kaufmann Publishers 69

Representation for 0 Ó 1998 Morgan Kaufmann Publishers 70

Special Numbers Ó 1998 Morgan Kaufmann Publishers 71

Representation for +/- Infinity Ó 1998 Morgan Kaufmann Publishers 72

Representation for Not a Number Ó 1998 Morgan Kaufmann Publishers 73

Special Numbers (cont’d) Ó 1998 Morgan Kaufmann Publishers 74

Floating-Point Addition Ó 1998 Morgan Kaufmann Publishers 75

Ó 1998 Morgan Kaufmann Publishers 76

Floating-Point Multiplication (4) set the sign of product Ó 1998 Morgan Kaufmann Publishers 77

MIPS Floating Point Ó 1998 Morgan Kaufmann Publishers 78

Rounding Ó 1998 Morgan Kaufmann Publishers 79

Round to Even Ó 1998 Morgan Kaufmann Publishers 80

Floating Point Fallacy Ó 1998 Morgan Kaufmann Publishers 81

Summary Ó 1998 Morgan Kaufmann Publishers 82