ECE 274 Digital Logic

Size: px
Start display at page:

Download "ECE 274 Digital Logic"

Transcription

1 ECE - Digitl Logic (Textbook - Required) ECE Digitl Logic Instructor: Romn Lysecky, Office Hours: TBA, ECE F Lecture: MWF :-: PM, ILC Course Website: Author: ISBN: Website: ECE - Digitl Logic (Textbook - Optionl) ECE - Digitl Logic (Lbs) Verilog for Author:, Romn Lysecky ISBN: Note: A good Verilog HDL book is required for this course. TAs: Lnce Sldnh, Derek Nielson, Lb Sections: Section : T 8:AM-:AM, ECE, TA: TBD Section : T :PM-:PM, ECE, TA: TBD Section : W :PM-:PM, ECE, TA: TBD Section : R :AM-:PM, ECE, TA: TBD Section 8: F :PM-:PM, ECE, TA: TBD ECE - Digitl Logic (Syllbus - Grding) Course Brekdown: Finl % Midterms () % Quizzes () % Lb Assignments % Homework % Design Chllenges % Grding: % A 8 % B 8% C % D Below % E All grdes re ssigned on n individul bsis. Punctulity: Don t be lte! ECE - Digitl Logic (Course Policies) Cell Phones: Plese turn your cell phone off before coming to clss! Acdemic Dishonesty: Any cdemic dishonesty will no be tolerted, plese consult the UA Code of Acdemic Integrity. ALL course work should be completed entirely on your own You re llowed to discuss generl concepts nd ides But you should not discuss specific homework or lb ssignments

2 ECE - Digitl Logic (Course Policies) Reding: Be prepred, red over mteril BEFORE clss. Regrdes: All requests for regrdes MUST be submitted in writing within one week of the distribution of grded mteril. Chpter : Introduction Slides to ccompny the textbook, First Edition, by, John Wiley nd Sons Publishers,. Copyright Instructors of courses requiring Vhid's textbook (published by John Wiley nd Sons) hve permission to modify nd use these slides for customry course-relted ctivities, subject to keeping this copyright notice in plce nd unmodified. These slides my be posted s unnimted pdf versions on publicly-ccessible course websites.. PowerPoint source (or pdf with nimtions) my not be posted to publicly-ccessible websites, but my be posted for students on internl protected sites or distributed directly to students by other electronic mens. Instructors my mke printouts of the slides vilble to students for resonble photocopying chrge, without incurring roylties. Any other use requires explicit permission. Instructors 8 my obtin PowerPoint source or obtin specil use permissions from Wiley see for informtion. Why Study?. ECE - Digitl Logic (Silicon Wfer nd Die Photos) Look under the hood of computers Solid understnding --> confidence, insight, even better progrmmer when wre of hrdwre resource issues Electronic devices becoming digitl Enbled by shrinking nd more cpble chips Enbles: Better devices: Better sound recorders, cmers, crs, cell phones, medicl devices,... New devices: Video gmes, PDAs,... Known s embedded systems Thousnds of new devices every yer Designers needed: Potentil creer direction Portble music plyers Stellites Cell phones DVD plyers Video recorders Musicl instruments Cmers TVs??? Individul IC (die) FPGA Copyright Yers shown bove indicte when digitl version begn to dominte (Not the first yer tht digitl version ppered) Note: Slides with nimtion re denoted with smll red "" ner the nimted items Pentium Processor ECE - Digitl Logic (Moore s Lw) Gordon Moore: co-founder of Intel. Predicted tht number of trnsistors per chip would grow exponentilly (double every 8 months). Anlog signl Inifinite possible vlues Ex: voltge on wire creted by microphone Sound wves Wht Does Digitl Men? Digitl signl Finite possible vlues Ex: button pressed on keypd. move the membrne, which moves the mgnet, digitl signl microphone which cretes current in the nerby wire vlue Copyright nlog signl Possible vlues:.,.,.,... infinite possibilities vlue Possible vlues:,,,, or. Tht s it.

3 Digitl Signls with Only Two Vlues: Binry Binry digitl signl -- only two possible vlues Typiclly represented s nd One binry digit is bit We ll only consider binry digitl signls Binry is populr becuse Trnsistors, the bsic digitl electric component, operte using two voltges (more in Chpt. ) Storing/trnsmitting one of two vlues is esier thn three or more (e.g., loud beep or quiet beep, reflection or no reflection) Copyright vlue Anlog signl (e.g., udio) my lose qulity Voltge levels not sved/copied/trnsmitted perfectly Digitized version enbles ner-perfect sve/cpy/trn. Smple voltge t prticulr rte, sve smple using bit encoding Voltge levels still not kept perfectly But we cn distinguish s from s Let bit encoding be: V: V: V: Copyright Exmple of Digitiztion Benefit Digitized signl not perfect re-cretion, but higher smpling Volts Volts Volts rte nd more bits per encoding brings closer. originl signl d digitized signl d lengthy trnsmission (e.g, cell phone) lengthy trnsmission (e.g, cell phone) sme received signl How fix -- higher, lower,? Cn fix -- esily distinguish s nd s, restore Digitized Audio: Compression Benefit Digitized udio cn be compressed e.g., MPs A CD cn hold bout songs uncompressed, but bout compressed Compression lso done on digitized pictures (jpeg), movies (mpeg), nd more Digitiztion hs mny other benefits too Copyright Exmple compression scheme: --> --> X --> X How Do We Encode Dt s Binry for Our Digitl System? nlog phenomen electric signl AD digitl dt digitl dt sensors nd other inputs Digitl System DA electric signl ctutors nd other outputs digitl dt digitl dt Copyright Some inputs inherently binry Button: not pressed (), pressed () Some inputs inherently digitl Just need encoding in binry e.g., multi-button input: encode red=, blue=,... Some inputs nlog Need nlog-to-digitl conversion As done in erlier slide -- smple nd encode with bits red red red button blue blue blue ir green green green temperture sensor blck blck blck degrees How to Encode Text: ASCII, Unicode How to Encode Numbers: Binry Numbers ASCII: - (or 8-) bit encoding of ech letter, number, or symbol Unicode: Incresingly populr -bit bit encoding Encodes chrcters from vrious world lnguges Symbol R S T L N E. <tb> Encoding Symbol r s t l n e! <spce> Encoding Question: Wht does this ASCII bit sequence represent? R E S T Ech position represents quntity; symbol in position mens how mny of tht quntity Bse ten (deciml) Ten symbols:,,,..., 8, nd More thn -- next position So ech position power of Nothing specil bout bse -- used becuse we hve fingers Bse two (binry) Two symbols: nd More thn -- next position So ech position power of Q: How much? + = + = Copyright Note: smll red () in slide indictes nimtion Copyright 8

4 How to Encode Numbers: Binry Numbers Working with binry numbers In bse ten, helps to know powers of one, ten, hundred, thousnd, ten thousnd,... In bse two, helps to know powers of one, two, four, eight, sixteen, thirty two, sixty four, one hundred twenty eight (Note: unlike bse ten, we don t hve common nmes, like thousnd, for ech position in bse ten -- so we use the bse ten nme) Q: count up by powers of two Copyright How to Encode Numbers: Binry Numbers Bse (binry) Arithmetic Eights ( ) column Fours ( ) column Twos ( ) column Ones ( ) column = x + x + x + x Convert the following vlue from binry (zero s nd one s) to deciml vlue =????? Choose your nswer: A), B) C) 8 Converting from Deciml to Binry Numbers: Subtrction Method (Esy for Humns) Converting from Deciml to Binry Numbers: Subtrction Method (Esy for Humns) Gol Get the binry weights to dd up to the deciml quntity Work from left to right (Right to left my fill in s tht shouldn t hve been there try it). Desired deciml number: 8 = 8 = 8 =8 8 ok, keep going Subtrction method To mke the job esier (especilly for big numbers), we cn just subtrct selected binry weight from the (remining) quntity Then, we hve new remining quntity, nd we strt gin (from the present binry position) Stop when remining quntity is Remining quntity: 8 is 8 is 8 8 = 8 =8+= 8 DONE -= 8 DONE Copyright nswer 8 Copyright nswer 8 Converting from Deciml to Binry Numbers: Subtrction Method Exmple Converting from Deciml to Binry Numbers: Division Method (Good for Computers) Q: Convert the number from deciml to binry A: Remining quntity Binry Number 8 Copyright is more thn, cn t use 8 8 Done! in deciml is in binry. Divide deciml number by nd insert reminder into new binry number. Continue dividing quotient by until the quotient is. Exmple: Convert deciml number to binry Deciml Number Binry Number divide by - insert reminder Continue dividing since quotient () is greter thn divide by - insert reminder Continue dividing since quotient () is greter thn Copyright

5 M r op r o c Converting from Deciml to Binry Numbers: Division Method (Good for Computers) Exmple: Convert deciml number to binry (continued) Deciml Number Binry Number divide by - insert reminder Continue dividing since quotient () is greter thn divide by 8 - insert reminder Since quotient is, we cn conclude tht is in binry Encoding: Number Systems Bse (binry) Arithmetic Convert the following deciml vlue to binry (zero s nd one s) vlue =??????? Choose your nswer: A) B) C) Copyright Bse Sixteen: Another Bse Somes Used by Digitl Designers Encoding: Number Systems: System Conversion hex binry hex binry Nice becuse ech position represents four bse two positions Used s compct mens to write binry numbers Known s hexdeciml, or just hex hex binry hex binry Convert the following hexdeciml vlue to binry (zero s nd one s) vlue 8 8 CAB =???????????? A B C D E F Q: Write in hex F A B C D E F Choose your nswer: A) B) C) Copyright 8 Implementing Digitl Systems: Progrmming Microprocessors Vs. Designing Digitl Circuits Desired motion-t-night detector Copyright I I I I I I I I P P P P P P P P Progrmmed microprocessor Custom designed digitl Microprocessors common choice to implement digitl system Esy to progrm Chep (s low s $) Avilble now void min() { while () { P = I &&!I; b // F = nd!b, } F } : :: ::. : When Microprocessors Aren t Good Enough With microprocessors so esy, chep, nd vilble, why design digitl? Microprocessor my be too slow Or too big, power hungry, or costly Smple digitl cmer tsk execution s (in seconds) on microprocessor versus digitl : Tsk Microprocessor Custom Digitl Circuit Red. Compress 8. Store.8 Copyright Imge Sensor Microprocessor () (Red, Compress, Memory nd Store) (b) (c) Imge Sensor Memory Imge Sensor Memory Red Red Q: How long for ech implementtion option? Compress Store Compress Microprocessor (Store) +8+ = sec =. sec.+.+ =. sec Good compromise

6 Chpter Summry Digitl systems surround us Inside computers Inside huge vriety of other electronic devices (embedded systems) Digitl systems use s nd s Encoding nlog signls to digitl cn provide mny benefits e.g., udio -- higher-qulity storge/trnsmission, compression, etc. Encoding integers s s nd s: Binry numbers Microprocessors (themselves digitl) cn implement mny digitl systems esily nd inexpensively But often not good enough -- need custom digitl s Where do we go from here? ECE Course Gols: Combintionl Logic Design Sequentil Logic Design Design of Common Dt Components Register-Trnsfer Level (RTL) Design Modern pproch to Optimiztion of Digitl Circuits using HDL (Verilog) Copyright (Humor?) There re types of people in the world: Those who get binry nd those who don t.

ECE 274 Digital Logic Fall 2009 Digital Design

ECE 274 Digital Logic Fall 2009 Digital Design igitl Logic ll igitl esign MW -:PM, IL Romn Lysecky, rlysecky@ece.rizon.edu http://www.ece.rizon.edu/~ece hpter : Introduction Slides to ccompny the textbook igitl esign, irst dition, by rnk Vhid, John

More information

Digital Design. Chapter 1: Introduction

Digital Design. Chapter 1: Introduction Digitl Design Chpter : Introduction Slides to ccompny the textbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com Copyright 2

More information

ECE Digital Logic (Labs) ECE 274 Digital Logic. ECE Digital Logic (Textbook) ECE Digital Logic (Optional Textbook)

ECE Digital Logic (Labs) ECE 274 Digital Logic. ECE Digital Logic (Textbook) ECE Digital Logic (Optional Textbook) ECE 74 Digitl Logic ECE 74 - Digitl Logic (Ls) Instructor: Romn Lysecky, rlysecky@ece.rizon.edu Office Hours: MW :-: PM, ECE Lecture: MW :-: PM, ILC 4 Course Wesite: http://www.ece.rizon.edu/~ece74/ TAs:

More information

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design

ECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,

More information

Digital Design. Sequential Logic Design -- Controllers. Copyright 2007 Frank Vahid

Digital Design. Sequential Logic Design -- Controllers. Copyright 2007 Frank Vahid Digitl Design Sequentil Logic Design -- Controllers Slides to ccompny the tetook Digitl Design, First Edition, y, John Wiley nd Sons Pulishers, 27. http://www.ddvhid.com Copyright 27 Instructors of courses

More information

CHAPTER 2 LITERATURE STUDY

CHAPTER 2 LITERATURE STUDY CHAPTER LITERATURE STUDY. Introduction Multipliction involves two bsic opertions: the genertion of the prtil products nd their ccumultion. Therefore, there re two possible wys to speed up the multipliction:

More information

Topic 20: Huffman Coding

Topic 20: Huffman Coding Topic 0: Huffmn Coding The uthor should gze t Noh, nd... lern, s they did in the Ark, to crowd gret del of mtter into very smll compss. Sydney Smith, dinburgh Review Agend ncoding Compression Huffmn Coding

More information

EE Controls Lab #2: Implementing State-Transition Logic on a PLC

EE Controls Lab #2: Implementing State-Transition Logic on a PLC Objective: EE 44 - Controls Lb #2: Implementing Stte-rnsition Logic on PLC ssuming tht speed is not of essence, PLC's cn be used to implement stte trnsition logic. he dvntge of using PLC over using hrdwre

More information

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates

CS 135: Computer Architecture I. Boolean Algebra. Basic Logic Gates Bsic Logic Gtes : Computer Architecture I Boolen Algebr Instructor: Prof. Bhgi Nrhri Dept. of Computer Science Course URL: www.ses.gwu.edu/~bhgiweb/cs35/ Digitl Logic Circuits We sw how we cn build the

More information

Dataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1)

Dataflow Language Model. DataFlow Models. Applications of Dataflow. Dataflow Languages. Kahn process networks. A Kahn Process (1) The slides contin revisited mterils from: Peter Mrwedel, TU Dortmund Lothr Thiele, ETH Zurich Frnk Vhid, University of liforni, Riverside Dtflow Lnguge Model Drsticlly different wy of looking t computtion:

More information

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR

MEASURE THE CHARACTERISTIC CURVES RELEVANT TO AN NPN TRANSISTOR Electricity Electronics Bipolr Trnsistors MEASURE THE HARATERISTI URVES RELEVANT TO AN NPN TRANSISTOR Mesure the input chrcteristic, i.e. the bse current IB s function of the bse emitter voltge UBE. Mesure

More information

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin

METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or

More information

Sequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12

Sequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12 9//2 Sequentil (2) ENGG5 st Semester, 22 Dr. Hden So Deprtment of Electricl nd Electronic Engineering http://www.eee.hku.hk/~engg5 Snchronous vs Asnchronous Sequentil Circuit This Course snchronous Sequentil

More information

Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Ideal Operational Amplifiers Experiment 3: Non-Idel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

More information

First Round Solutions Grades 4, 5, and 6

First Round Solutions Grades 4, 5, and 6 First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,

More information

Experiment 3: Non-Ideal Operational Amplifiers

Experiment 3: Non-Ideal Operational Amplifiers Experiment 3: Non-Idel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output

More information

Application Note. Differential Amplifier

Application Note. Differential Amplifier Appliction Note AN367 Differentil Amplifier Author: Dve n Ess Associted Project: Yes Associted Prt Fmily: CY8C9x66, CY8C7x43, CY8C4x3A PSoC Designer ersion: 4. SP3 Abstrct For mny sensing pplictions, desirble

More information

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):

Kirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR): SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween

More information

Math Circles Finite Automata Question Sheet 3 (Solutions)

Math Circles Finite Automata Question Sheet 3 (Solutions) Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how

More information

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES

MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNEL-SHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine E-mil: rt_science@hotmil.com 1 INTRODUCTION During the considertion

More information

Synchronous Machine Parameter Measurement

Synchronous Machine Parameter Measurement Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

More information

ECE 274 Digital Logic. Digital Design. RTL Design RTL Design Method. RTL Design Memory Components

ECE 274 Digital Logic. Digital Design. RTL Design RTL Design Method. RTL Design Memory Components ECE 27 Digitl Logic Memories n Hierrchy Digitl Design 5.6 5. Digitl Design Chpter 5: Slies to ccompny the textbook Digitl Design, First Eition, by Frnk Vhi, John Wiley n Sons Publishers, 27. http://www.vhi.com

More information

The Discussion of this exercise covers the following points:

The Discussion of this exercise covers the following points: Exercise 4 Bttery Chrging Methods EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the different chrging methods nd chrge-control techniques commonly used when chrging Ni-MI

More information

Synchronous Machine Parameter Measurement

Synchronous Machine Parameter Measurement Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions

More information

Student Book SERIES. Patterns and Algebra. Name

Student Book SERIES. Patterns and Algebra. Name E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing

More information

Abacaba-Dabacaba! by Michael Naylor Western Washington University

Abacaba-Dabacaba! by Michael Naylor Western Washington University Abcb-Dbcb! by Michel Nylor Western Wshington University The Abcb structure shows up in n mzing vriety of plces. This rticle explores 10 surprising ides which ll shre this pttern, pth tht will tke us through

More information

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.

Lecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts. Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is

More information

ABB STOTZ-KONTAKT. ABB i-bus EIB Current Module SM/S Intelligent Installation Systems. User Manual SM/S In = 16 A AC Un = 230 V AC

ABB STOTZ-KONTAKT. ABB i-bus EIB Current Module SM/S Intelligent Installation Systems. User Manual SM/S In = 16 A AC Un = 230 V AC User Mnul ntelligent nstlltion Systems A B 1 2 3 4 5 6 7 8 30 ma 30 ma n = AC Un = 230 V AC 30 ma 9 10 11 12 C ABB STOTZ-KONTAKT Appliction Softwre Current Vlue Threshold/1 Contents Pge 1 Device Chrcteristics...

More information

Section 16.3 Double Integrals over General Regions

Section 16.3 Double Integrals over General Regions Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is

More information

Unit 1: Chapter 4 Roots & Powers

Unit 1: Chapter 4 Roots & Powers Unit 1: Chpter 4 Roots & Powers Big Ides Any number tht cn be written s the frction mm, nn 0, where m nd n re integers, is nn rtionl. Eponents cn be used to represent roots nd reciprocls of rtionl numbers.

More information

Algorithms for Memory Hierarchies Lecture 14

Algorithms for Memory Hierarchies Lecture 14 Algorithms for emory Hierrchies Lecture 4 Lecturer: Nodri Sitchinv Scribe: ichel Hmnn Prllelism nd Cche Obliviousness The combintion of prllelism nd cche obliviousness is n ongoing topic of reserch, in

More information

Make Your Math Super Powered

Make Your Math Super Powered Mke Your Mth Super Powered: Use Gmes, Chllenges, nd Puzzles Where s the fun? Lern Mth Workshop model by prticipting in one nd explore fun nocost/low-cost gmes nd puzzles tht you cn esily bring into your

More information

Module 9. DC Machines. Version 2 EE IIT, Kharagpur

Module 9. DC Machines. Version 2 EE IIT, Kharagpur Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson-40) 4 40.1 Gols

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-236 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our

More information

& Y Connected resistors, Light emitting diode.

& Y Connected resistors, Light emitting diode. & Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd

More information

Example. Check that the Jacobian of the transformation to spherical coordinates is

Example. Check that the Jacobian of the transformation to spherical coordinates is lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.

More information

Lab 8. Speed Control of a D.C. motor. The Motor Drive

Lab 8. Speed Control of a D.C. motor. The Motor Drive Lb 8. Speed Control of D.C. motor The Motor Drive Motor Speed Control Project 1. Generte PWM wveform 2. Amplify the wveform to drive the motor 3. Mesure motor speed 4. Mesure motor prmeters 5. Control

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-297 Technicl notes on using Anlog Devices DSPs, processors nd development tools Visit our Web resources http://www.nlog.com/ee-notes nd http://www.nlog.com/processors or e-mil

More information

Understanding Basic Analog Ideal Op Amps

Understanding Basic Analog Ideal Op Amps Appliction Report SLAA068A - April 2000 Understnding Bsic Anlog Idel Op Amps Ron Mncini Mixed Signl Products ABSTRACT This ppliction report develops the equtions for the idel opertionl mplifier (op mp).

More information

Ultra Low Cost ACCELEROMETER

Ultra Low Cost ACCELEROMETER Chip Scle Pckged Digitl Therml Orienttion Sensing Accelerometer MXC6226XC Document Version D Pge 1 of 13 Fetures Generl Description Fully Integrted Therml Accelerometer X/Y Axis, 8 bit, Accelertion A/D

More information

Ultra Low Cost ACCELEROMETER

Ultra Low Cost ACCELEROMETER Chip Scle Pckged Fully Integrted Therml Accelerometer MXC622xXC Rev,A 8/19/2011 Pge 1 of 13 Fetures Generl Description Fully Integrted Therml Accelerometer X/Y Axis, 8 bit, Accelertion A/D Output (± 2g)

More information

University of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009

University of North Carolina-Charlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009 Problem 1: Using DC Mchine University o North Crolin-Chrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:

More information

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION

Exercise 1-1. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION Exercise 1-1 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You

More information

MOS Transistors. Silicon Lattice

MOS Transistors. Silicon Lattice rin n Width W chnnel p-type (doped) sustrte MO Trnsistors n Gte Length L O 2 (insultor) ource Conductor (poly) rin rin Gte nmo trnsistor Gte ource pmo trnsistor licon sustrte doped with impurities dding

More information

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN fall 2008

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN fall 2008 CS224 DIGITAL LOGIC & STATE MACHINE DESIGN fll 28 STAND ALONE XILINX PROJECT 2-TO- MULTIPLEXER. Gols : Lern how to develop stnd lone 2-to- multiplexer () Xilinx project during which the following re introduced

More information

Regular languages can be expressed as regular expressions.

Regular languages can be expressed as regular expressions. Regulr lnguges cn e expressed s regulr expressions. A generl nondeterministic finite utomton (GNFA) is kind of NFA such tht: There is unique strt stte nd is unique ccept stte. Every pir of nodes re connected

More information

Misty. Sudnow Dot Songs

Misty. Sudnow Dot Songs Sudnow Dot Songs isty T The Dot Song is nottionl system tht depicts voiced chords in wy where the non-music reder cn find these firly redily. But the Dot Song is not intended be red, not s sight reder

More information

TIME: 1 hour 30 minutes

TIME: 1 hour 30 minutes UNIVERSITY OF AKRON DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 4400: 34 INTRODUCTION TO COMMUNICATION SYSTEMS - Spring 07 SAMPLE FINAL EXAM TIME: hour 30 minutes INSTRUCTIONS: () Write your nme

More information

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations

9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations 54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show

More information

Synchronous Generator Line Synchronization

Synchronous Generator Line Synchronization Synchronous Genertor Line Synchroniztion 1 Synchronous Genertor Line Synchroniztion Introduction One issue in power genertion is synchronous genertor strting. Typiclly, synchronous genertor is connected

More information

Student Book SERIES. Fractions. Name

Student Book SERIES. Fractions. Name D Student Book Nme Series D Contents Topic Introducing frctions (pp. ) modelling frctions frctions of collection compring nd ordering frctions frction ingo pply Dte completed / / / / / / / / Topic Types

More information

Homework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week

Homework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week Announcements Homework #1 due Mondy t 6pm White drop ox in Student Lounge on the second floor of Cory Tuesdy ls cncelled next week Attend your other l slot Books on reserve in Bechtel Hmley, 2 nd nd 3

More information

Solutions to exercise 1 in ETS052 Computer Communication

Solutions to exercise 1 in ETS052 Computer Communication Solutions to exercise in TS52 Computer Communiction 23 Septemer, 23 If it occupies millisecond = 3 seconds, then second is occupied y 3 = 3 its = kps. kps If it occupies 2 microseconds = 2 6 seconds, then

More information

Arduino for Model Railroaders

Arduino for Model Railroaders Steve Mssikker Arduino for Model Rilroders Ornge Book Protocol 2 Full Description November 28 Tble of contents Dontors Documenttion Kit V.4-8 Pge 2 I wnt to tke the time to sincerely thnk you for your

More information

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005

CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2005 EXPERIMENT 1 FUNDAMENTALS 1. GOALS : Lern how to develop cr lrm digitl circuit during which the following re introduced : CS2204 l fundmentls, nd

More information

Outline. A.I. Applications. Searching for the solution. Chess game. Deep Blue vs. Kasparov 20/03/2017

Outline. A.I. Applications. Searching for the solution. Chess game. Deep Blue vs. Kasparov 20/03/2017 Outline Giorgio Buttzzo E-mil: g.buttzzo@sssup.it Scuol Superiore Snt Ann retis.sssup.it/~giorgio/slides/neurl/inn.html Motivtions Neurl processing Lerning prdigms Associtive memories Pttern recognitions

More information

How to Build Wealth Like Warren Buffett.

How to Build Wealth Like Warren Buffett. Your FREE gift for ordering How to Build Welth Like Wrren Buffett The video ABC-TV clled lively, informtive, nd lot of fun. You cn t help but get swept up by the enthusism of this rewrding film. Don t

More information

Polar Coordinates. July 30, 2014

Polar Coordinates. July 30, 2014 Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xy-plne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes

More information

Engineer-to-Engineer Note

Engineer-to-Engineer Note Engineer-to-Engineer Note EE-247 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t dsp.support@nlog.com nd t dsptools.support@nlog.com Or visit our

More information

(CATALYST GROUP) B"sic Electric"l Engineering

(CATALYST GROUP) Bsic Electricl Engineering (CATALYST GROUP) B"sic Electric"l Engineering 1. Kirchhoff s current l"w st"tes th"t (") net current flow "t the junction is positive (b) Hebr"ic sum of the currents meeting "t the junction is zero (c)

More information

Geometric quantities for polar curves

Geometric quantities for polar curves Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions

More information

Series. Teacher. Numbers

Series. Teacher. Numbers Series B Techer Copyright 2009 3P Lerning. All rights reserved. First edition printed 2009 in Austrli. A ctlogue record for this book is vilble from 3P Lerning Ltd. ISBN 978-1-921860-17-1 Ownership of

More information

Engineering: Elec 3509 Electronics II Instructor: Prof. Calvin Plett,

Engineering: Elec 3509 Electronics II Instructor: Prof. Calvin Plett, Engineering: Elec 3509 Electronics II Instructor: Prof. Clvin Plett, emil cp@doe.crleton.c Objective: To study the principles, design nd nlysis of nlog electronic circuits. Description: In this course,

More information

JUMO Wtrans B Programmable Head Transmitter with Radio Transmission

JUMO Wtrans B Programmable Head Transmitter with Radio Transmission Dt Sheet 707060 Seite 1/10 JUMO Wtrns B Progrmmble Hed Trnsmitter with Rdio Trnsmission Brief description The Wtrns B hed trnsmitter with wireless dt trnsmission is used in connection with Wtrns receiver

More information

ECE 274 Digital Logic Spring Digital Design. Combinational Logic Design Process and Common Combinational Components Digital Design

ECE 274 Digital Logic Spring Digital Design. Combinational Logic Design Process and Common Combinational Components Digital Design ECE 27 Digitl Logi Spring 29 Comintionl Logi Design Proess n Common Comintionl Components Digitl Design 2.7 2. Digitl Design Chpter 2: Comintionl Logi Design Slies to ompn the tetook Digitl Design, irst

More information

A Novel Back EMF Zero Crossing Detection of Brushless DC Motor Based on PWM

A Novel Back EMF Zero Crossing Detection of Brushless DC Motor Based on PWM A ovel Bck EMF Zero Crossing Detection of Brushless DC Motor Bsed on PWM Zhu Bo-peng Wei Hi-feng School of Electricl nd Informtion, Jingsu niversity of Science nd Technology, Zhenjing 1003 Chin) Abstrct:

More information

Electronic Circuits I - Tutorial 03 Diode Applications I

Electronic Circuits I - Tutorial 03 Diode Applications I Electronic Circuits I - Tutoril 03 Diode Applictions I -1 / 9 - T & F # Question 1 A diode cn conduct current in two directions with equl ese. F 2 When reverse-bised, diode idelly ppers s short. F 3 A

More information

Spiral Tilings with C-curves

Spiral Tilings with C-curves Spirl Tilings with -curves Using ombintorics to Augment Trdition hris K. Plmer 19 North Albny Avenue hicgo, Illinois, 0 chris@shdowfolds.com www.shdowfolds.com Abstrct Spirl tilings used by rtisns through

More information

Extremely small "footprint" and the highest circuit density available AK550. Front Wire Entry

Extremely small footprint and the highest circuit density available AK550. Front Wire Entry FIXED PRINTED CIRCUIT Tubulr Screw Clmp For use when stndrd size printed circuit terminl blocks re too lrge for vilble spce or where very smll circuit bord is utilized. Our new subminiture design offers

More information

Domination and Independence on Square Chessboard

Domination and Independence on Square Chessboard Engineering nd Technology Journl Vol. 5, Prt, No. 1, 017 A.A. Omrn Deprtment of Mthemtics, College of Eduction for Pure Science, University of bylon, bylon, Irq pure.hmed.omrn@uobby lon.edu.iq Domintion

More information

Addition Mission: Facts Practice

Addition Mission: Facts Practice Addition Mission: Fcts Prctice ++ Tble of Contents Addition Mission: Fcts Prctice Mth Counting Apple Mth Hippity Hop Crunchy Celery Addition Superstr Cherry Mth At the Librry Mth Sld -0 Sunny Summer Mth

More information

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad Hll Ticket No Question Pper Code: AEC009 INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigl, Hyderd - 500 043 MODEL QUESTION PAPER Four Yer B.Tech V Semester End Exmintions, Novemer - 2018 Regultions:

More information

NP10 DIGITAL MULTIMETER Functions and features of the multimeter:

NP10 DIGITAL MULTIMETER Functions and features of the multimeter: NP10 DIGITL MULTIMETER. unctions nd fetures of the multimeter: 1000 V CT III tri requencies from 10.00...10 M. Diode mesurement nd continuity testing. HOLD mesurement. Reltive mesurement. Duty cycle (%)

More information

DP400 / DM350. Inverter. Total Solutions from the Single Source Provider DP400 PULSED MAG - PULSED MIG CO2 - MAG - MIG - FCAW

DP400 / DM350. Inverter. Total Solutions from the Single Source Provider DP400 PULSED MAG - PULSED MIG CO2 - MAG - MIG - FCAW DP400 / DM350 Digitl Controlled DC Inverter Arc Welding Mchines CAT. NO. A446 Simple Opertion Perfect Welds from Arc Strt to End Inverter Totl Solutions from Single Source Provider DP400 PULSED MAG - PULSED

More information

Mini Mario & Friends: amiibo Challenge

Mini Mario & Friends: amiibo Challenge Mrio & Friends: Chllenge 1 Importnt Informtion Bsic Informtion 2 Introduct ion 3 About Gme 4 Gettin g Strted 5 Sving nd Deleting Dt How to Ply 6 Level Mp 7 Plying Levels 8 Mi ni Toy Abilities 9 Objects/

More information

Array chip resistors size ARC241/ARC242 ARV241/ARV242

Array chip resistors size ARC241/ARC242 ARV241/ARV242 Arry chip resistors FEATURES 4 0603 sized resistors in one 1206-sized pckge Reduced reel exchnge time Low ssembly costs Reduced PCB re Reduced size of finl equipment Higher component nd equipment relibility.

More information

Crime Scene Documentation. Crime Scene Documentation. Taking the C.S. What should my notes include. Note Taking 9/26/2013

Crime Scene Documentation. Crime Scene Documentation. Taking the C.S. What should my notes include. Note Taking 9/26/2013 Crime Scene Documenttion Crime Scene Documenttion Most importnt step in C.S. processing Purpose: permnently record the condition of C.S. & physicl evidence Time consuming Documenter must be orgnized nd

More information

FOMA M702iG Manual for Data Communication

FOMA M702iG Manual for Data Communication FOMA M702iG Mnul for Dt Communiction Dt Communictions... 1 Before Using... 2 Prepring for Dt Communiction... 3 Instlling the Communiction Configurtion Files (Drivers)... 4 Connecting the FOMA Hndset nd

More information

MATH 118 PROBLEM SET 6

MATH 118 PROBLEM SET 6 MATH 118 PROBLEM SET 6 WASEEM LUTFI, GABRIEL MATSON, AND AMY PIRCHER Section 1 #16: Show tht if is qudrtic residue modulo m, nd b 1 (mod m, then b is lso qudrtic residue Then rove tht the roduct of the

More information

Pro Series White Toner and Neon Range

Pro Series White Toner and Neon Range Pro Series White Toner nd Neon Rnge Discover New Dimension in Colour printing for grment decortion, signge nd design Pro7411WT White Toner (CMYW) A4 printer Pro8432WT White Toner (CMYW) A3 printer Pro6410

More information

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your From Off-The-Shelf to Market-Ready New ge Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your end-use. visit newageenclosures.com/services or call 855-4N-ENCL

More information

Job Sheet 2. Variable Speed Drive Operation OBJECTIVE PROCEDURE. To install and operate a Variable Speed Drive.

Job Sheet 2. Variable Speed Drive Operation OBJECTIVE PROCEDURE. To install and operate a Variable Speed Drive. Job Sheet 2 Vrible Speed Drive Opertion OBJECTIVE To instll nd operte Vrible Speed Drive. PROCEDURE Before proceeding with this job, complete the sfety check list in Appendix B. 1. On the Vrible Speed

More information

Direct Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.

Direct Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28. P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices

More information

TRUMBULL PUBLIC SCHOOLS

TRUMBULL PUBLIC SCHOOLS PS TRUMBULL PUBLC SCHOOLS CURRCULUM DEPARTMENT 6254 Min St., Trumbull, CT 06611 (203) 452-4336 FAX (203) 452-4342 Lind S. Pslov, Ed.D. Director of Curriculum, nstruction, & Assessments e-mil: pslovl@trumbullps.org

More information

Power rating at 80 C watts R0005 ohms R0006 to R01. R001 to R01 Power. to R015. (mω) 1 0.2, 0.25, 0.3, 0.

Power rating at 80 C watts R0005 ohms R0006 to R01. R001 to R01 Power. to R015. (mω) 1 0.2, 0.25, 0.3, 0. Resistors Metl Strip Current Sense Resistors Surfce Mount Resistors Metl Element Current Metl Element Sense Resistor UR Series UR Current Series Sense Resistor Resistnce R000 (m ) to R0 (m ) Metl UR Robust

More information

Challenge! 1 Warm-up. 2 Conversation. Language box. a Discuss the pictures with a partner.

Challenge! 1 Warm-up. 2 Conversation. Language box. a Discuss the pictures with a partner. Focus Grmmr Vocbulry Strtegy tlking bout wishes nd possibilities second conditionl I wish + simple pst verbs nd definitions moving to new country showing surprise 1 Wrm-up Discuss the pictures with prtner.

More information

Have u Herd? Herd is the Word. join. toolkit. COOL WAYS to TALK ABOUT BOOKS WITH YOUR

Have u Herd? Herd is the Word. join. toolkit. COOL WAYS to TALK ABOUT BOOKS WITH YOUR Hve u Herd? Herd is the Word join Th to K nks Wel ir from Libr lingto comin ry L n b g brilli up with for The nt nme the Word o Herd f! toolkit COOL WAYS to TALK ABOUT BOOKS WITH YOUR your friends for

More information

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your

From Off-The-Shelf to Market-Ready New Age Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your From Off-The-Shelf to Market-Ready New ge Enclosures is your Single Source Solution. Let us quote modifiying our Stock Enclosures to meet your end-use. visit newageenclosures.com/services or call 855-4N-ENCL

More information

Digital Migration Radio PD60X. DMR Standard Radio, Feature-Rich, Innovative Design, Compact Size, Integrates with Hytera Applications

Digital Migration Radio PD60X. DMR Standard Radio, Feature-Rich, Innovative Design, Compact Size, Integrates with Hytera Applications Digitl Migrtion Rdio PD60X DMR Stndrd Rdio, Feture-Rich, Innovtive Design, Compct Size, Integrtes with Applictions Fetures Smll, Sleek, Light Full Bnd The size is 119 X 54 X 27mm, PC & Metl frme, weight

More information

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 300Q Model the concept of ddition for sums to 10. (QT N 36) Model the concept of sutrction using numers less thn or equl to 10. (QT N 37) Write ddition

More information

April 9, 2000 DIS chapter 10 CHAPTER 3 : INTEGRATED PROCESSOR-LEVEL ARCHITECTURES FOR REAL-TIME DIGITAL SIGNAL PROCESSING

April 9, 2000 DIS chapter 10 CHAPTER 3 : INTEGRATED PROCESSOR-LEVEL ARCHITECTURES FOR REAL-TIME DIGITAL SIGNAL PROCESSING April 9, 2000 DIS chpter 0 CHAPTE 3 : INTEGATED POCESSO-LEVEL ACHITECTUES FO EAL-TIME DIGITAL SIGNAL POCESSING April 9, 2000 DIS chpter 3.. INTODUCTION The purpose of this chpter is twofold. Firstly, bsic

More information

Series AE W PFC INDUSTRIAL POWER SUPPLY

Series AE W PFC INDUSTRIAL POWER SUPPLY FEATURES Progrmmle output voltge (0%~05%) Progrmmle output current (0%~05%) Universl AC input / Full rnge Constnt current limiting Optionl glol control vi RS3 Selectle +5V / 0.5A or +9V / 0.3A uxiliry

More information

MAYWOOD. Hospitality & ConferenCe tables FURNITURE CORP. GSA Approved! Contract #GS-28F-0050W. Established 1918

MAYWOOD. Hospitality & ConferenCe tables FURNITURE CORP.   GSA Approved! Contract #GS-28F-0050W. Established 1918 MAYWOOD FURNITURE CORP. Mnufctured in the U.S.A. Estblished 1918 Hospitlity & ConferenCe tbles www.mywood.com GSA Approved! Contrct #GS-28F-0050W bout us Circ 1930 Mywood Furniture Corportion ws estblished

More information

L I THE COMMONWEALTH INFORMATION

L I THE COMMONWEALTH INFORMATION L I THE COMMONWEALTH INFORMATION DATABASE A Cse Study - Multimedi on Shoestring Scott Ewings Reserch & Design Commonwelth Informtion Dtbse Commonwelth lnstitute London The Commonwelth Institute The Commonwelth

More information

ITEC2620 Introduction to Data Structures

ITEC2620 Introduction to Data Structures /5/20 ITEC220 Introdution to Dt Strutures Leture 0 Gme Trees Two-Plyer Gmes Rules for gme define the sttespe Nodes re gme sttes Links re possile moves Build serh tree y rute fore Exmple I Exmple II A Our

More information

Seven Sisters. Visit for video tutorials

Seven Sisters. Visit   for video tutorials Seven Sisters This imge is from www.quiltstudy.org. Plese visit this website for more informtion on Seven Sisters quilt ptterns. Visit www.blocloc.com for video tutorils 1 The Seven Sisters design cn be

More information

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or

1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole

More information

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17.

Section 17.2: Line Integrals. 1 Objectives. 2 Assignments. 3 Maple Commands. 1. Compute line integrals in IR 2 and IR Read Section 17. Section 7.: Line Integrls Objectives. ompute line integrls in IR nd IR 3. Assignments. Red Section 7.. Problems:,5,9,,3,7,,4 3. hllenge: 6,3,37 4. Red Section 7.3 3 Mple ommnds Mple cn ctully evlute line

More information

Spotted at APA. Top Points this week. Spring f ro. Year 7. Year 8. Year 9. Year 10. Year 11. Student Newsletter ~

Spotted at APA. Top Points this week. Spring f ro. Year 7. Year 8. Year 9. Year 10. Year 11. Student Newsletter ~ Spring 2017 Top Points this week Yer 7 ly l x Mo Ale Yer 8 ict is Le w ed Be n Yer 9 sh er Ele Du ej on e Yer 10 Yer 11 ri em Me Another very busy week in the cdemy hs just gone by s we hd our APA World

More information

Joanna Towler, Roading Engineer, Professional Services, NZTA National Office Dave Bates, Operations Manager, NZTA National Office

Joanna Towler, Roading Engineer, Professional Services, NZTA National Office Dave Bates, Operations Manager, NZTA National Office . TECHNICA MEMOANDM To Cc repred By Endorsed By NZTA Network Mngement Consultnts nd Contrctors NZTA egionl Opertions Mngers nd Are Mngers Dve Btes, Opertions Mnger, NZTA Ntionl Office Jonn Towler, oding

More information