1. CDA 3100 Summer 2011

2. Special Thanks
Thanks to Dr. Zhenghao Zhang for letting me use his class slides and other materials as a base for this course

3. Class organization My name is Jessie Sanders Class web page
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Class organization
My name is Jessie Sanders
Class web page
htm
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CDA3100

4. 9/17/2018
Class Communication
This class will use class web site to post news, changes, and updates. So please check the class website regularly
Please also make sure that you check your s on the account on your University record
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CDA3100

5. Required Textbook The required textbook for this class is
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Required Textbook
The required textbook for this class is
“Computer Organization and Design”
The hardware/software interface
By David A. Patterson and John L. Hennessy
Fourth Edition
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CDA3100

6. Lecture Notes and Textbook
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Lecture Notes and Textbook
All the materials that you will be tested on will be covered in the lectures
Even though you may need to read the textbook for review and further detail explanations
The lectures will be based on the textbook and handouts distributed in class
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CDA3100

7. What you will learn to answer (among other things)
How does the software instruct the hardware to perform the needed functions
What is going on in the processor
How a simple processor is designed

8. Why This Class Important?
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Why This Class Important?
If you want to create better computers
It introduces necessary concepts, components, and principles for a computer scientist
By understanding the existing systems, you may create better ones
If you want to build software with better performance
If you want to have a good choice of jobs
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CDA3100

9. Career Potential for a Computer Science Graduate
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Career Potential for a Computer Science Graduate
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CDA3100

10. Career Potential for a Computer Science Graduate
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Career Potential for a Computer Science Graduate
Source: NACE Fall 2005 Report (
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CDA3100

11. Computer System Overview
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Computer System Overview
A computer system consists of hardware and software that are combined to provide a tool to solve problems (with best performance)
Hardware includes CPU, memory, disks, screen, keyboard, mouse ...
Software includes
System software
A general environment to create specific applications
Application software
A tool to solve a specific problem
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CDA3100

12. Steps to Run a C Program – First, compiling it into machine code
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13. Steps to Run a C Program Then we need to run the program
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Steps to Run a C Program
Then we need to run the program
The operating system locates where the program is
Then it loads the program into memory
The instructions in the program are then executed one by one
When the program is done, the operating system then releases the memory and other resources allocated to the program
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CDA3100

14. 9/17/2018
Opening the Box
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15. A Pentium 4 Processor Chip
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A Pentium 4 Processor Chip
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CDA3100

16. Numbers Numbers are abstraction of quantities
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Numbers
Numbers are abstraction of quantities
How do we represent these quantities?
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CDA3100

17. Decimal Numbering System
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Decimal Numbering System
For any nonnegative integer , its value is given by
Here d0 is the least significant digit and dn is the most significant digit
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CDA3100

18. Decimal Numbering System
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Decimal Numbering System
We humans naturally use a particular numbering system
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CDA3100

19. General Numbering System – Base X
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General Numbering System – Base X
Besides 10, we can use other bases as well
In base X, the value of
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CDA3100

20. Commonly Used Bases Which one is natural to computers? Base
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Commonly Used Bases
Base
Common Name
Representation
Digits 10
Decimal
5023ten or 5023
0-9 2
Binary
two
0-1 8
Octal
11637eight
0-7 16
Hexadecimal
139Fhex or 0x139F
0-9, A-F
Note that other bases are used as well including 12 and 60
Which one is natural to computers?
Why?
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CDA3100

21. Meaning of a Number Representation
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Meaning of a Number Representation
When we specify a number, we need also to specify the base
For example, 10 presents a different quantity in a different base 
There are 10 kinds of mathematicians. Those who can think binarily and those who can't...
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22. 9/17/2018
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23. Conversion between Representations
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Conversion between Representations
Now we can represent a quantity in different number representations
How can we convert a decimal number to binary?
How can we then convert a binary number to a decimal one?
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CDA3100

24. Conversion Between Bases
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Conversion Between Bases
From binary to decimal example 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
215
214
213
212
211
210 29 28 27 26 25 24 23 22 21 20
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25. Conversion Between Bases
Converting from decimal to binary:
given a number in decimal, repeatedly divide it by 2, and write down the remainder from right to the left, until the quotient is 0
Example: 11.
Quotient
Remainder 5 1 2
Do a small exercise here, perhaps to re-engage the students

26. Signed Numbers How to represent negative numbers? Sign and magnitude
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Signed Numbers
How to represent negative numbers?
Sign and magnitude
We use an additional bit to represent the sign of the number
If the sign bit is 1, it represents a negative number
If the sign bit is 0, it represents a positive number
How about zero then?
There are other shortcomings of this representation
Related to the hardware implementation of adders
An extra step is required in general to set the sign since the proper sign can not be determined in advance
It is not widely used for integer representations
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CDA3100

27. Signed Numbers Two’s complement
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Signed Numbers
Two’s complement
The negative of a two’s complement is given by inverting each bit from 0 to 1 and 1 to 0 and then adding 1 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
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28. 2’s complement
In any computer, if numbers are represented in n bits, the non-negative numbers are from 0000…00 to 0111…11, the negative numbers are from 1000…00 to 1111…11.
Do an example here

29. The positive half from 0 to 2,147,483,647
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0ten
1ten
2ten …
-3ten
-2ten
-1ten
The positive half from 0 to 2,147,483,647
The negative half from -2,147,483,648 to -1
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30. Two’s Complement Representation
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Two’s Complement Representation
Properties
All negative numbers have a 1 in the most significant bit
Hardware only needs to test this bit to see if a number is positive or negative
The leading bit is often called the sign bit
For , the decimal value is
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CDA3100

31. Why use 2’s complement?
For example, consider (– 00011) = – = (13-3=10 in decimal).
01101 – = – –
= ( – 00011) –
= – = –
= 01010
11101 is the 2’s complement of
Means that computer (the adder) does not have to be specifically redesigned for dealing with negative numbers, make life easier for the computer
The reason is, assume you are subtracting a with b , where 2^{n}>a>b>0. Note that a-b=a+2^{n+1}-b-2^{n+1}. But 2^{n+1}-b is the 2’s complement of b. Also note that 2^{n}>a-b>0. So if represented in binary forms, a+2^{n+1}-b will be having a 1 bit in bit n+1 and some thing in bit 0 to bit n-1 equal to a-b. Bit n will be 0. So you take what is in bit 0 to bit n and it must be a-b.