Transcript Week1_1 - FSU Computer Science Department

CDA 3100 Fall 2012
Special Thanks
• Thanks to Dr. Xiuwen Liu for letting me use his
class slides and other materials as a base for
this course
About Me
• My name is Zhenghao Zhang
– Why I am teaching this course: I worked for two
years as an embedded system engineer, writing
codes for embedded controllers.
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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
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
• If you want to be a real computer scientist
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Career Potential for a Computer Science Graduate
http://www.jobweb.com/studentarticles.asp
x?id=904&terms=starting+salary
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Career Potential for a Computer Science Graduate
Source: NACE Fall 2005 Report (http://www.jobweb.com/resources/library/Careers_In/Starting_Salary_51_01.htm)
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Required Background
• Based on years of teaching this course, I find that you
will suffer if you do not have the required C/C++
programming background.
• We will need assembly coding, which is more
advanced than C/C++.
• If you do not have a clear understanding at this
moment of array and loop , it is recommended
that you take this course at a later time, after getting
more experience with C/C++ programming.
Array – What Happens?
#include <stdio.h>
int main (void)
{
int A[5] = {16, 2, 77, 40, 12071};
A[A[1]] += 1;
return 0;
}
Loop – What Happens?
#include <stdio.h>
int main ()
{
int A[5] = {16, 20, 77, 40, 12071};
int result = 0;
int i = 0;
while (result < A[i]) {
result += A[i];
i++;
}
return 0;
}
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
emails on the account on your University
record
• Blackboard will be used for posting the grades
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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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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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Decimal Numbering System
• We humans naturally use a particular numbering system
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Decimal Numbering System
• For any nonnegative integer d n d n 1  d1d 0, its
value is given by
n
i
n
n 1
1
0
d

10

d

10

d

10



d

10

d

10
 i
n
n 1
1
0
i 0
 ( ((( 0  10  d n )  10  d n 1 )  10    d1 )  10  d 0
– Here d0 is the least significant digit and dn is the
most significant digit
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General Numbering System – Base X
• Besides 10, we can use other bases as well
– In base X,
n
d  X
i 0
i
i
 d n  X n  d n 1  X n 1    d1  X 1  d 0  X 0
 ( ((( 0  X  d n )  X  d n 1 )  X    d1 )  X  d 0
– Then, the base X representation of this number is
defined as dndn-1…d2d1d0.
– The same number can have many representations
on many bases. For 23 based 10, it is
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• 23ten
• 10111two
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• 17
, often written as 0x17.
16
Commonly Used Bases
Base
Common Name
Representation
Digits
10
Decimal
5023ten or 5023
0-9
2
Binary
1001110011111two
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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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...
http://www.math.ualberta.ca/~runde/jokes.html
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Question
• How many different numbers that can be
represented by 4 bits?
• Always 16 (24), because there are this number
of different combinations with 4 bits,
regardless of the type of the number these 4
bits are representing.
• Obviously, this also applies to other number of
bits. With n bits, we can represent 2n different
numbers. If the number is unsigned integer, it
is from 0 to 2n-1.
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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Conversion Between Bases
• From binary to decimal example
15
10
9
8
7
6
5
4
3
2
1
0
215 214 213 212 211 210
29
28
27
26
25
24
23
22
21
20
1
1
1
0
0
1
1
1
1
1
0
14
0
13
0
12
1
11
0
0
 212  29  28  27  24  23  22  21  20
 4096  512  256  128  16  8  4  2  1
 5023
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Converting from binary to decimal
• Converting from binary to decimal. This
conversion is also based on the formula:
d = dn-12n-1 + dn-22n-2 +…+ d222 + d121 + d020
while remembering that the digits in the
binary representation are the coefficients.
• For example, given 101011two, in decimal, it is
25 + 23 + 21 + 20 = 43.
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
1
1
0
0
1
Digging a little deeper
• Why can a binary number be obtained by keeping on
dividing by 2, and why should the last remainder be
the first bit?
• Note that
– Any integer can be represented by the summation
of the powers of 2:
d = dn-12n-1 + dn-22n-2 +…+ d222 + d121 + d020
– For example, 19 = 16 + 2 + 1 = 1 * 24 + 0 * 23 + 0 *
22 + 1 * 21 + 1 * 20.
– The binary representation is the binary
coefficients. So 19ten in binary is 10011two.
Digging a little deeper
• In fact, any integer can be represented by the summation of
the powers of some base, where the base is either 10, 2 or 16
in this course. For example, 19 = 1 * 101 + 9 * 100. How do you
get the 1 and 9? You divide 19 by 10 repeatedly until the
quotient is 0, same as binary!
• In fact, the dividing process is just an efficient way to get the
coefficients.
• How do you determine whether the last bit is 0 or 1? You can
do it by checking whether the number is even or odd. Once
this is determined, you go ahead to determine the next bit, by
checking (d - d020)/2 is even or odd, and so on, until you don’t
have to check any more (when the number is 0).
Conversion between Base 16 and
Base 2
• Extremely easy.
– From base 2 to base 16: divide the digits in to
groups of 4, then apply the table.
– From base 16 to base 2: replace every digit by a 4bit string according to the table.
• Because 16 is 2 to the power of 4.
Addition in binary
• 39ten + 57ten = ?
• How to do it in binary?
Addition in Binary
• First, convert the numbers to binary forms.
We are using 8 bits.
– 39ten -> 001001112
– 57ten -> 001110012
• Second, add them.
00100111
00111001
01100000
Addition in binary
• The addition is bit by bit.
• We will run in at most 4 cases, where the
leading bit of the result is the carry:
1.
2.
3.
4.
0+0+0=00
1+0+0=01
1+1+0=10
1+1+1=11
Subtraction in Binary
• 57ten – 39ten = ?
Subtraction in Binary
00111001
00100111
00010010
Subtraction in binary
• Do this digit by digit.
• No problem if
– 0 - 0 = 0,
– 1-0=1
– 1 – 1 = 0.
• When encounter 0 - 1, set the result to be 1 first, then borrow 1 from the
next more significant bit, just as in decimal.
– Borrow means setting the borrowed bit to be 0 and the bits from the bit following the
borrowed bit to the bit before the current bit to be 1.
– Think about, for example, subtracting 349 from 5003 (both based 10). The last digit is
first set to be 4, and you will be basically subtracting 34 from 499 from now on.