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ECE 200: WEEK 1

by: Mario Borjas

ECE 200: WEEK 1 ECE 200 - A

Mario Borjas
GPA 3.93
Digital Logic Design
Dr. Timothy Kurzweg

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About this Document

Introduction to the course, Digital vs. Analog, Number Systems
Digital Logic Design
Dr. Timothy Kurzweg
Class Notes
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This 6 page Class Notes was uploaded by Mario Borjas on Monday October 5, 2015. The Class Notes belongs to ECE 200 - A at Drexel University taught by Dr. Timothy Kurzweg in Summer 2015. Since its upload, it has received 28 views. For similar materials see Digital Logic Design in ELECTRICAL AND COMPUTER ENGINEERING at Drexel University.

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Date Created: 10/05/15
ECE 200 Digital Logic Design ECE 200 WEEK I Outline I Introduction to the Course II Digital vs Analog III Number Systems Vocobuloru Intelligent Systems Digital Analog Gate FlipFlopLatch Number Systems RadixBase Decimal Binary oam Hexadecimal Most Significant Bit Least Significant Bit I INTRODUCTION TO THE COURSE Summoru In this course we will learn how intelligent systems work and about digital design Intelligent systems can perform really complex actions such as computation and information processing As of today most of these systems are Digital as opposed to Analog Things to keep in mind Textbook Introduction to Logic Design 3rd Edition Alan B Marcovitz McGraw Hill 2010 Midterm exams week 510 Final Exam Week 12 34 Quizzes Week 3 5 8 and 9 in recitation REmEmBER HOITTELUORK IS DUE HT THE BEGl l G OF EVERY LECTURE First Homework due September 30th All Homework need your name recitation section and must be stapled REmEmBER EVERYTHITTG COUNTS Homework quizzes and minilabs are worth a large percentage of your final grade Borjas 1 ECE 200 Digital Logic Design ll ANALOG VSQ DlGlTAl iFFeremces Analog Digital Continuous Discrete registers very specific values F Example Temperature Detector Iisn39lpmtum l lijl 113 34qu 1 Jill 7 5quot 9 quot39 7 I ll 6 quotH a E L 39lllll39lllllllllll39llllllllll quot lm II J l2 lIii 139 2 mg Analog lul l l fll 39l un Example Binary in Computers only 0 5 and 1 s Digital Mintera binary 15 a a 51 til it l LL gm l l c Digtal razul tage emeFits 0 Using igltol Easy to reproduce results Ease of design Easy to program with Fast and Economical Digith evices 1 Basic Digital Device called Gates 2 Flip Flops Latches which remember previous inputs Example of Gate Example of Latch Borjas 2 ECE 200 Digital Logic Design Interesting lnFormotion to know Electronic digital devices do not contain magical quot0 or quot1 When a certain voltage is received or sent by a gate it is either registered as a 0 or 1 w l a M W137 For example if the gate receives a high voltage between 4 and 5 volts a quot1 will be registered If the gate receives a low voltage between 0 and 1 volt a quot0 will be registered All other voltage values are undefined and therefore ignored I Number Sgstems Much of digital system processing is numeric that s why we will start the course by learning about number systems As we know there are many ways to represent a number for example twentyfour can be represented as 24 XXIV and so on However the most common scheme for representing numbers is the radix representation The radix or base is the number of unique digits including 0 used in a number system For example almost all our lives we have used radix 10 called decimal numbers All the digits used are as follows 0 1 2 3 4 5 6 7 8 9 In computers the basic symbols are 0 and 1 A binary system is therefore used Octal radix 8 and Hexadecimal radix 16 are also common number systems used Octal Digits 01234567 Hexadecimal Digits 0123456789ABCDEF Borjas 3 ECE 200 Digital Logic Design Converting From and number sustem to ecimol The following formula can be used to convert any number from any number system to a decimal number radix 10 nl i where n is the number of digits A is the coefficient i is the index and r is E Ar the radix i0 Here IS how we can easily use the formula to convert numbers to radix 10 Example 1 Converting from radix 2 binary to radix 10 110102 1 1 O 1 0 Step 1 4 3 2 1 0 We establish index values for each digit by lt counting from radix point to the left Step 2 1x24 1x23 0x22 1x21 0x20 We use radix formula radix lndex value coefficient Step 3 2610 Solve arithmetically Example 2 Converting from base 5 to base 10 1315 1 3 5 Step 1 2 1 0 We establish index values for each digit by F counting from radix point to the left Step 2 1x52 3x51 5x5O We use radix formula Step 3 4110 Solve arithmetically Borjas 4 ECE 200 Digital Logic Design Example 3 Converting from Hexadecimal to decimal 1ABl6 1 A B Step 1 2 1 0 We establish index values for each digit by 9 counting from radix point to the left Step 2 1x162 10x161 11x160 We use radix formula Step 3 42710 Solve arithmetically Converting From ecimol to anti Bose Two steps are followed to convert from base 10 to any other base 1 Divide Number and All Successive quotients by base that we are converting to until quotient is zero 2 Accumulate the remainders and write them in order The last remainder we get is the Most Significant Bit first digit of our new number The first remainder we got is the Least Significant Bit last digit of our new number Example 1 Converting from Decimal to Octal 32710 Step 1 3278 40 with remainder 7 408 5 with remainder O 58 O with remainder 5 Step2 Remainders 5 O 7 M58 LSB Answer 5078 Borjas 5 ECE 200 Digital Logic Design Example 1 Converting from Decimal to Binary 32710 Step 1 Step 2 3272 163 with remainder 1 1632 81 with remainder 1 812 40 with remainder 1 402 20 with remainder 0 202 10 with remainder 0 102 5 with remainder 0 52 0 with remainder 1 22 5 with remainder 0 12 0 with remainder 1 Remainders 1 0 1 0 0 0 1 1 1 M53 LSB Answer 1010001112 ii lmterestlmg lnFormqtiom to know You can use an alternative method position to convert binary into decimal faster It involves using powers of 2 The rule is to subtract the highest power of 2 possible from your number Example 1 Converting 32710to Binary 1 We can subtract 28 from 327 which is equal to 71 2 We can subtract 26 from 71 which is equal to 7 3 We can subtract 22 from 7 which is equal to 3 4 We can subtract 21 from 3 which is equal to 1 5 We can subtract 20 from 1 which is equal to 0 Powers 29 28 27 26 25 24 23 22 21 20 Of 2 512 256 168 64 32 16 8 4 2 1 Binary 1 0 1 0 0 0 1 1 1 Borjas 6


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