Number Representations and Computer Arithmetics - PPT, Engineering Notes | EduRev

: Number Representations and Computer Arithmetics - PPT, Engineering Notes | EduRev

 Page 1


2014/10/20 cpeg323-08F\Topic3-05F 1 
Topic 3 
Number Representations 
and Computer Arithmetics  
Introduction to Computer 
Systems Engineering 
 
(CPEG 323) 
Page 2


2014/10/20 cpeg323-08F\Topic3-05F 1 
Topic 3 
Number Representations 
and Computer Arithmetics  
Introduction to Computer 
Systems Engineering 
 
(CPEG 323) 
2014/10/20 cpeg323-08F\Topic3-05F 2 
Outline 
 Introduction 
 Number representation and 2’s 
complement 
 ALU design 
 Integer multiplication/division  
 Real Numbers 
Page 3


2014/10/20 cpeg323-08F\Topic3-05F 1 
Topic 3 
Number Representations 
and Computer Arithmetics  
Introduction to Computer 
Systems Engineering 
 
(CPEG 323) 
2014/10/20 cpeg323-08F\Topic3-05F 2 
Outline 
 Introduction 
 Number representation and 2’s 
complement 
 ALU design 
 Integer multiplication/division  
 Real Numbers 
2014/10/20 cpeg323-08F\Topic3-05F 3 
Recap 
Review 
? Steps in executing an instruction? 
Decoded opcode 
32 
result 
32 
a 
32 
b 
ALU 
What's up ahead: 
? Number representation 
? Arithmetic algorithms 
? Logic implementation 
? Instructions 
 
? Fields of an instruction? 
? Performance? 
? Base of the operands?  
ALU 
Page 4


2014/10/20 cpeg323-08F\Topic3-05F 1 
Topic 3 
Number Representations 
and Computer Arithmetics  
Introduction to Computer 
Systems Engineering 
 
(CPEG 323) 
2014/10/20 cpeg323-08F\Topic3-05F 2 
Outline 
 Introduction 
 Number representation and 2’s 
complement 
 ALU design 
 Integer multiplication/division  
 Real Numbers 
2014/10/20 cpeg323-08F\Topic3-05F 3 
Recap 
Review 
? Steps in executing an instruction? 
Decoded opcode 
32 
result 
32 
a 
32 
b 
ALU 
What's up ahead: 
? Number representation 
? Arithmetic algorithms 
? Logic implementation 
? Instructions 
 
? Fields of an instruction? 
? Performance? 
? Base of the operands?  
ALU 
2014/10/20 cpeg323-08F\Topic3-05F 4 
Reading 
Up to now, you should have read 
(or are reading) 
? Patterson and Hennessy, chapters 
1-2 and appendix A 
New material 
? Patterson and Hennessy, chapter 3 
Page 5


2014/10/20 cpeg323-08F\Topic3-05F 1 
Topic 3 
Number Representations 
and Computer Arithmetics  
Introduction to Computer 
Systems Engineering 
 
(CPEG 323) 
2014/10/20 cpeg323-08F\Topic3-05F 2 
Outline 
 Introduction 
 Number representation and 2’s 
complement 
 ALU design 
 Integer multiplication/division  
 Real Numbers 
2014/10/20 cpeg323-08F\Topic3-05F 3 
Recap 
Review 
? Steps in executing an instruction? 
Decoded opcode 
32 
result 
32 
a 
32 
b 
ALU 
What's up ahead: 
? Number representation 
? Arithmetic algorithms 
? Logic implementation 
? Instructions 
 
? Fields of an instruction? 
? Performance? 
? Base of the operands?  
ALU 
2014/10/20 cpeg323-08F\Topic3-05F 4 
Reading 
Up to now, you should have read 
(or are reading) 
? Patterson and Hennessy, chapters 
1-2 and appendix A 
New material 
? Patterson and Hennessy, chapter 3 
2014/10/20 cpeg323-08F\Topic3-05F 5 
Numbers Representation 
It may get complicated: 
? How to represent negative numbers? 
? What is the range of numbers? 
? What if a number is out of the range? 
? How about rational and irrational numbers?  
? How does hardware add/sub/div/mul these 
numbers?  
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