CDA 3100 Summer 2013

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

Course Information

About Me Name: Britton Dennis 11/27/2018 About Me Name: Britton Dennis Email: dennis@cs.fsu.edu Office: LOV 105A Office Hours: Thursday 9:30 AM – 12:30 PM Site: http://ww2.cs.fsu.edu/~dennis/cda3100_summer_2013 11/27/2018 CDA3100 CDA3100

11/27/2018 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 emails on the account on your University record 11/27/2018 CDA3100 CDA3100

Lecture Notes and Textbook 11/27/2018 Lecture Notes and Textbook All the materials that you will be tested on will be covered in the lectures All lectures will be posted on the website in both (Microsoft Office 2010 published) .pptx and in the more universally viewable .pdf The textbook isn’t required, but it may be worth purchasing for review and for further detail explanations In particular, the appendix will be useful for MIPS instruction references The lectures will be based on the textbook and any handouts distributed in class 11/27/2018 CDA3100 CDA3100

Required Textbook The required textbook for this class is 11/27/2018 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 11/27/2018 CDA3100 CDA3100

Grades and Weighting In Class Exercises – 5% Homework – 40% Exams 11/27/2018 Grades and Weighting In Class Exercises – 5% 5-7 exercises will be given during class throughout the semester Only top 4 will be graded Homework – 40% 7 problems sets will be given throughout the semester There will be two windows to turn them in. Up to the first is the real deadline Up to the second, you will receive a 10% deduction. After that, the assignment won’t be accepted For accreditation reasons, the department requires you to pass a particular assignment to pass the course Exams Midterm – 20% Final – 35% Cumulative About 10 Multiple Choice and 2-3 Short Response 11/27/2018 CDA3100 CDA3100

Motivations

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? 11/27/2018 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 11/27/2018 CDA3100 CDA3100

Required Background

Required Background You will probably suffer if you do not have the required C/C++ programming background. In this class, we will be doing 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; } A[1] = 2, so A[2] <- 78.

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; result = 113, i=3

Getting Started!

Decimal Numbering System 11/27/2018 Decimal Numbering System We humans naturally use a particular numbering system 11/27/2018 CDA3100 CDA3100

Decimal Numbering System 11/27/2018 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 11/27/2018 CDA3100 CDA3100

General Numbering System – Base X 11/27/2018 General Numbering System – Base X Besides 10, we can use other bases as well In base X, 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 23ten 10111two 17sixteen, often written as 0x17. 11/27/2018 CDA3100 CDA3100

Commonly Used Bases Which one is natural to computers? Why? Base 11/27/2018 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? 11/27/2018 CDA3100 CDA3100

Meaning of a Number Representation 11/27/2018 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 11/27/2018 CDA3100 CDA3100

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Question How many different numbers that can be represented by 4 bits?

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 11/27/2018 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? 11/27/2018 CDA3100 CDA3100

Conversion Between Bases 11/27/2018 Conversion Between Bases From binary to decimal example 1 15 14 13 12 11 10 9 8 7 6 5 4 3 2 215 214 213 212 211 210 29 28 27 26 25 24 23 22 21 20 11/27/2018 CDA3100 CDA3100

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: Repeatedly divide it by 2, until the quotient is 0. Going from top to bottom, write down the remainder from right to the left. Example: 11. Quotient Remainder 5 1 2

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 4-bit 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 encounter at most 4 cases, where the leading bit of the result is the carry: 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.