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# 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
? 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
? 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
Up to now, you should have read
? 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
? 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
Up to now, you should have read
? 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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