COMP303 Computer Architecture Lecture 11. An Overview of Pipelining
|
|
- Abigayle Susan Willis
- 5 years ago
- Views:
Transcription
1 COMP303 Compute Achitectue Lectue 11 An Oveview of Pipelining
2 Pipelining Pipelining povides a method fo executing multiple instuctions at the same time. Laundy Example: Ann, Bian, Cathy, Dave each have one load of clothes to wash, dy, and fold Washe takes 30 minutes A B C D Dye takes 40 minutes Folde takes 20 minutes
3 Sequential Laundy 6 PM Midnight Time T a s k O d e A B C D Sequential laundy takes 6 hous fo 4 loads If they leaned pipelining, how long would laundy take?
4 Pipelined Laundy: Stat wok ASAP 6 PM Midnight Time T a s k O d e A B C D Pipelined laundy takes 3.5 hous fo 4 loads
5 Pipelining Lessons T a s k O d e 6 PM Time A B C D Pipelining doesn t help latency of single task, it helps thoughput of entie wokload Pipeline ate limited by slowest pipeline stage Multiple tasks opeating simultaneously using diffeent esouces Potential speedup = Numbe pipe stages Unbalanced lengths of pipe stages educes speedup Time to fill pipeline and time to dain it educes speedup Stall fo Dependences
6 Total Time fo Eight Instuctions Inst. class Inst. fetch Registe ead opeation Data access Registe wite Total time Load wod 2 ns 1 ns 2 ns 2 ns 1 ns 8 ns Stoe wod 2 ns 1 ns 2 ns 2 ns 7 ns R-type 2 ns 1 ns 2 ns 1 ns 6 ns Banch 2 ns 1 ns 2 ns 5 ns R-type instuctions: add, sub, and, o, slt
7 Single Cycle vs. Pipelined Execution Pogam execution ode lw $1,10($0) lw $2,20($0) lw $3,30($0) Inst. fetch Reg Data access Reg 8 ns Inst. fetch Reg Data access Reg 8 ns Inst. fetch 8 ns Pogam execution ode Inst. lw $1,10($0) fetch lw $2,20($0) lw $3,30($0) 2 ns Reg Inst. fetch 2 ns Reg Inst. fetch Data access Reg Reg Data access Reg Data access Reg Total: 24 ns 2 ns 2 ns 2 ns 2 ns 2 ns Total: 14 ns
8 Pipelining Speedup If the stages ae pefectly balanced: Time between instuctions pipelined = Time between instuctions nonpipelined Numbe of pipeline stages Potential speedup = Numbe of pipeline stages In pevious example, 3 instuctions takes 14 ns. If we would add 1000 instuctions then each instuction will add 2 ns to the total execution time: Total execution time pipelined = = 2014 ns Total execution time nonpipelined = 1003 * 8 = 8024 ns 8024 / 2014 = 3.98 ~ 8 / 2 =
9 The Five Stages of the Load Instuction Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Load Ifetch Reg/Dec Exec Mem W Ifetch: Instuction Fetch Fetch the instuction fom the Instuction Memoy Reg/Dec: Registes Fetch and Instuction Decode Exec: Calculate the memoy addess Mem: Read the data fom the Data Memoy W: Wite the data back to the egiste file
10 Pipelined Execution Time IFetch Dcd Exec Mem WB IFetch Dcd Exec Mem WB IFetch Dcd Exec Mem WB IFetch Dcd Exec Mem WB IFetch Dcd Exec Mem WB Pogam Flow IFetch Dcd Exec Mem WB On a pocesso multiple instuctions ae in vaious stages at the same time. Assume each instuction takes five cycles
11 Single Cycle, Multiple Cycle, vs. Pipeline Clk Cycle 1 Cycle 2 Single Cycle Implementation: Load Stoe Waste Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6 Cycle 7 Cycle 8 Cycle 9 Cycle 10 Clk Multiple Cycle Implementation: Load Ifetch Reg Exec Mem W Stoe Ifetch Reg Exec Mem R-type Ifetch Pipeline Implementation: Load Ifetch Reg Exec Mem W Stoe Ifetch Reg Exec Mem W R-type Ifetch Reg Exec Mem W
12 Gaphically Repesenting Pipelines Time (clock cycles) I n s t. Inst 0 Inst 1 Can help with answeing questions like: How many cycles does it take to execute this code? What is the doing duing cycle 4? Ae two instuctions tying to use the same esouce at the same time?
13 Why Pipeline? Because the esouces ae thee! Time (clock cycles) I n s t. O d e Inst 0 Inst 1 Inst 2 Inst 3 Inst 4
14 Why Pipeline? Suppose 100 instuctions ae executed The single cycle machine has a cycle time of 45 ns The multicycle and pipeline machines have cycle times of 10 ns The multicycle machine has a CPI of 3.6 Single Cycle Machine 45 ns/cycle x 1 CPI x 100 inst = 4500 ns Multicycle Machine 10 ns/cycle x 3.6 CPI x 100 inst = 3600 ns Ideal pipelined machine 10 ns/cycle x (1 CPI x 100 inst + 4 cycle dain) = 1040 ns Ideal pipelined vs. single cycle speedup 4500 ns / 1040 ns = 4.33 What has not yet been consideed?
15 Can pipelining get us into touble? Yes: Pipeline Hazads stuctual hazads: attempt to use the same esouce (hadwae unit) two diffeent ways at the same time E.g., two instuctions ty to ead the same memoy at the same time data hazads: attempt to use item befoe it is eady instuction depends on esult of pio instuction still in the pipeline add 1, 2, 3 sub 4, 2, 1 contol hazads: attempt to make a decision befoe condition is evaluated banch instuctions beq 1, 2, loop add 3, 4, 5 Can always esolve hazads by waiting pipeline contol must detect the hazad take action (o delay action) to esolve hazads
16 Single Memoy is a Stuctual Hazad Time (clock cycles) I n s t. O d e Load Inst 1 Inst 2 Inst 3 Inst 4 Mem Reg Mem Reg Detection is easy in this case! (ight half highlight means ead, left half wite)
17 What s the Solution? Solution 1: Use sepaate instuction and data memoies Solution 2: Allow memoy to ead and wite moe than one wod pe cycle Solution 3: Stall
18 Solution 3: Stall Time (clock cycles) I n s t. O d e Load Inst 1 Inst 2 nop Inst 3 Inst 4 bubble bubble bubble bubble bubble Mem Reg Mem Reg
19 Contol Hazad Solutions Stall: wait until decision is clea It is possible to move up decision to 2nd stage by adding exta hadwae to check egistes as being ead I n s t. O d e Add Beq Load Time (clock cycles) Mem Reg Mem Reg Impact: 2 clock cycles pe banch instuction => slow
20 Contol Hazad Solutions Pedict: guess one diection then back up if wong Pedict not taken I n s t. O d e Add Beq Load Time (clock cycles) Mem Reg Mem Reg Impact: 1 clock cycle pe banch instuction if ight, 2 if wong (ight - 50% of time) Moe dynamic scheme: histoy of 1 banch (- 90%)
21 Contol Hazad Solutions Redefine banch behavio (takes place afte next instuction) delayed banch I n s t. O d e Add Beq Misc Load Time (clock cycles) Mem Impact: 1 clock cycles pe banch instuction if can find instuction to put in slot (- 50% of time) Reg Mem Reg Mem Reg Mem Reg
22 Data Hazad on 1 Poblem: 1 cannot be ead by othe instuctions befoe it is witten by the add. add 1, 2, 3 sub 4, 1, 3 and 6, 1, 7 o 8, 1, 9 xo 10, 1, 11
23 Data Hazad on 1: Dependencies backwads in time ae hazads I n s t. O d e Time (clock cycles) IF ID/RF EX MEM WB add 1,2,3 sub 4,1,3 and 6,1,7 o 8,1,9 xo 10,1,11 Im Reg Dm Reg
24 Data Hazad Solution: Fowad esult fom one stage to anothe I n s t. O d e Time (clock cycles) IF ID/RF EX MEM WB add 1,2,3 sub 4,1,3 and 6,1,7 o 8,1,9 xo 10,1,11 Im Reg Dm Reg o instuction is OK if define ead/wite popely
25 Fowading (o Bypassing): What about Loads Dependencies backwads in time ae hazads Time (clock cycles) IF ID/RF EX MEM WB lw 1,0(2) sub 4,1,3 Can t solve with fowading: Must delay/stall instuction dependent on loads
CMP N 301 Computer Architecture. Appendix C
CMP N 301 Computer Architecture Appendix C Outline Introduction Pipelining Hazards Pipelining Implementation Exception Handling Advanced Issues (Dynamic Scheduling, Out of order Issue, Superscalar, etc)
More informationInstruction Execution
MIPS Piplining Cpt280 D Cuti Nlon Intuction Excution C intuction: x = a + b; Ambly intuction: a a,b,x Stp 1: Stp 2: Stp 3: Stp : Stp 5: Stp 6: Ftch th intuction Dtmin it i an a intuction Ftch th ata a
More informationEXAMPLES 4/12/2018. The MIPS Pipeline. Hazard Summary. Show the pipeline diagram. Show the pipeline diagram. Pipeline Datapath and Control
The MIPS Pipeline CSCI206 - Computer Organization & Programming Pipeline Datapath and Control zybook: 11.6 Developed and maintained by the Bucknell University Computer Science Department - 2017 Hazard
More informationSimple Instruction-Pipelining. Pipelined Harvard Datapath
6.823, L8--1 Simple ruction-pipelining Laboratory for Computer Science M.I.T. http://www.csg.lcs.mit.edu/6.823 Pipelined Harvard path 6.823, L8--2. I fetch decode & eg-fetch execute memory Clock period
More informationITI Introduction to Computing II
ITI 1121. Intoduction to Computing II Macel Tucotte School of Electical Engineeing and Compute Science Abstact data type: Stack Stack-based algoithms Vesion of Febuay 2, 2013 Abstact These lectue notes
More informationMATHEMATICS GRADE 12 SESSION 38 (LEARNER NOTES)
EXAM PREPARATION PAPER (A) Leane Note: In this session you will be given the oppotunity to wok on a past examination pape (Feb/Ma 010 DoE Pape ). The pape consists of 1 questions. Question 1, and will
More informationPushdown Automata (PDAs)
CHAPTER 2 Context-Fee Languages Contents Context-Fee Gammas definitions, examples, designing, ambiguity, Chomsky nomal fom Pushdown Automata definitions, examples, euivalence with context-fee gammas Non-Context-Fee
More informationSimple Instruction-Pipelining. Pipelined Harvard Datapath
6.823, L8--1 Simple ruction-pipelining Updated March 6, 2000 Laboratory for Computer Science M.I.T. http://www.csg.lcs.mit.edu/6.823 Pipelined Harvard path 6.823, L8--2. fetch decode & eg-fetch execute
More informationA Deep Convolutional Neural Network Based on Nested Residue Number System
A Deep Convolutional Neual Netwok Based on Nested Residue Numbe System Hioki Nakahaa Ehime Univesity, Japan Tsutomu Sasao Meiji Univesity, Japan Abstact A pe-tained deep convolutional neual netwok (DCNN)
More informationAlgebra. Substitution in algebra. 3 Find the value of the following expressions if u = 4, k = 7 and t = 9.
lgeba Substitution in algeba Remembe... In an algebaic expession, lettes ae used as substitutes fo numbes. Example Find the value of the following expessions if s =. a) s + + = = s + + = = Example Find
More informationComputer Architecture ELEC2401 & ELEC3441
Last Time Pipeline Hazard Computer Architecture ELEC2401 & ELEC3441 Lecture 8 Pipelining (3) Dr. Hayden Kwok-Hay So Department of Electrical and Electronic Engineering Structural Hazard Hazard Control
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electical and Compute Engineeing, Conell Univesity ECE 303: Electomagnetic Fields and Waves Fall 007 Homewok 8 Due on Oct. 19, 007 by 5:00 PM Reading Assignments: i) Review the lectue notes.
More informationINTRODUCTION. 2. Vectors in Physics 1
INTRODUCTION Vectos ae used in physics to extend the study of motion fom one dimension to two dimensions Vectos ae indispensable when a physical quantity has a diection associated with it As an example,
More informationMULTILAYER PERCEPTRONS
Last updated: Nov 26, 2012 MULTILAYER PERCEPTRONS Outline 2 Combining Linea Classifies Leaning Paametes Outline 3 Combining Linea Classifies Leaning Paametes Implementing Logical Relations 4 AND and OR
More informationPipelining. Traditional Execution. CS 365 Lecture 12 Prof. Yih Huang. add ld beq CS CS 365 2
Pipelining CS 365 Lecture 12 Prof. Yih Huang CS 365 1 Traditional Execution 1 2 3 4 1 2 3 4 5 1 2 3 add ld beq CS 365 2 1 Pipelined Execution 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
More informationImplementing the Controller. Harvard-Style Datapath for DLX
6.823, L6--1 Implementing the Controller Laboratory for Computer Science M.I.T. http://www.csg.lcs.mit.edu/6.823 6.823, L6--2 Harvard-Style Datapath for DLX Src1 ( j / ~j ) Src2 ( R / RInd) RegWrite MemWrite
More informationECE 3401 Lecture 23. Pipeline Design. State Table for 2-Cycle Instructions. Control Unit. ISA: Instruction Specifications (for reference)
ECE 3401 Lecture 23 Pipeline Design Control State Register Combinational Control Logic New/ Modified Control Word ISA: Instruction Specifications (for reference) P C P C + 1 I N F I R M [ P C ] E X 0 PC
More informationChapter Eight Notes N P U1C8S4-6
Chapte Eight Notes N P UC8S-6 Name Peiod Section 8.: Tigonometic Identities An identit is, b definition, an equation that is alwas tue thoughout its domain. B tue thoughout its domain, that is to sa that
More informationLecture 8 - Gauss s Law
Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.
More informationCurrent Balance Warm Up
PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field
More informationPhysics 121 Hour Exam #5 Solution
Physics 2 Hou xam # Solution This exam consists of a five poblems on five pages. Point values ae given with each poblem. They add up to 99 points; you will get fee point to make a total of. In any given
More informationPhysics 161 Fall 2011 Extra Credit 2 Investigating Black Holes - Solutions The Following is Worth 50 Points!!!
Physics 161 Fall 011 Exta Cedit Investigating Black Holes - olutions The Following is Woth 50 Points!!! This exta cedit assignment will investigate vaious popeties of black holes that we didn t have time
More informationPAPER 39 STOCHASTIC NETWORKS
MATHEMATICAL TRIPOS Pat III Tuesday, 2 June, 2015 1:30 pm to 4:30 pm PAPER 39 STOCHASTIC NETWORKS Attempt no moe than FOUR questions. Thee ae FIVE questions in total. The questions cay equal weight. STATIONERY
More informationMarkscheme May 2017 Calculus Higher level Paper 3
M7/5/MATHL/HP3/ENG/TZ0/SE/M Makscheme May 07 Calculus Highe level Pape 3 pages M7/5/MATHL/HP3/ENG/TZ0/SE/M This makscheme is the popety of the Intenational Baccalaueate and must not be epoduced o distibuted
More information0606 ADDITIONAL MATHEMATICS
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Intenational Geneal Cetificate of Seconday Education MARK SCHEME fo the Octobe/Novembe 011 question pape fo the guidance of teaches 0606 ADDITIONAL MATHEMATICS
More information1D2G - Numerical solution of the neutron diffusion equation
DG - Numeical solution of the neuton diffusion equation Y. Danon Daft: /6/09 Oveview A simple numeical solution of the neuton diffusion equation in one dimension and two enegy goups was implemented. Both
More informationHOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?
6th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS? Cecília Sitkuné Göömbei College of Nyíegyháza Hungay Abstact: The
More informationMotion in One Dimension
Motion in One Dimension Intoduction: In this lab, you will investigate the motion of a olling cat as it tavels in a staight line. Although this setup may seem ovesimplified, you will soon see that a detailed
More informationMultifrontal sparse QR factorization on the GPU
Multifontal spase QR factoization on the GPU Tim Davis, Sanjay Ranka, Shaanyan Chetlu, Nui Yealan Univesity of Floida Feb 2012 GPU-based Multifontal QR factoization why spase QR? multifontal spase QR in
More informationPhys 1215, First Test. September 20, minutes Name:
Phys 115, Fist Test. Septembe 0, 011 50 minutes Name: Show all wok fo maximum cedit. Each poblem is woth 10 points. k =.0 x 10 N m / C ε 0 = 8.85 x 10-1 C / N m e = 1.60 x 10-1 C ρ = 1.68 x 10-8 Ω m fo
More informationEN40: Dynamics and Vibrations. Midterm Examination Thursday March
EN40: Dynamics and Vibations Midtem Examination Thusday Mach 9 2017 School of Engineeing Bown Univesity NAME: Geneal Instuctions No collaboation of any kind is pemitted on this examination. You may bing
More information30 The Electric Field Due to a Continuous Distribution of Charge on a Line
hapte 0 The Electic Field Due to a ontinuous Distibution of hage on a Line 0 The Electic Field Due to a ontinuous Distibution of hage on a Line Evey integal ust include a diffeential (such as d, dt, dq,
More informationCS 52 Computer rchitecture and Engineering Lecture 4 - Pipelining Krste sanovic Electrical Engineering and Computer Sciences University of California at Berkeley http://www.eecs.berkeley.edu/~krste! http://inst.eecs.berkeley.edu/~cs52!
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationPhysics 111 Lecture 5 (Walker: 3.3-6) Vectors & Vector Math Motion Vectors Sept. 11, 2009
Physics 111 Lectue 5 (Walke: 3.3-6) Vectos & Vecto Math Motion Vectos Sept. 11, 2009 Quiz Monday - Chap. 2 1 Resolving a vecto into x-component & y- component: Pola Coodinates Catesian Coodinates x y =
More informationProject Two RISC Processor Implementation ECE 485
Project Two RISC Processor Implementation ECE 485 Chenqi Bao Peter Chinetti November 6, 2013 Instructor: Professor Borkar 1 Statement of Problem This project requires the design and test of a RISC processor
More informationHASHING METHODS. Hanan Samet
hs0 HASHING METHODS Hanan Samet Compute Science Depatment and Cente fo Automation Reseach and Institute fo Advanced Compute Studies Univesity of Mayland College Pak, Mayland 20742 e-mail: hjs@umiacs.umd.edu
More informationSuggested Solutions to Homework #4 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homewok #4 Econ 5b (Pat I), Sping 2004. Conside a neoclassical gowth model with valued leisue. The (epesentative) consume values steams of consumption and leisue accoding to P t=0
More informationSection 26 The Laws of Rotational Motion
Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to
More informationExploration of the three-person duel
Exploation of the thee-peson duel Andy Paish 15 August 2006 1 The duel Pictue a duel: two shootes facing one anothe, taking tuns fiing at one anothe, each with a fixed pobability of hitting his opponent.
More informationCSCI-564 Advanced Computer Architecture
CSCI-564 Advanced Computer Architecture Lecture 8: Handling Exceptions and Interrupts / Superscalar Bo Wu Colorado School of Mines Branch Delay Slots (expose control hazard to software) Change the ISA
More informationChapter 3: Theory of Modular Arithmetic 38
Chapte 3: Theoy of Modula Aithmetic 38 Section D Chinese Remainde Theoem By the end of this section you will be able to pove the Chinese Remainde Theoem apply this theoem to solve simultaneous linea conguences
More informationVoltage ( = Electric Potential )
V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More information0606 ADDITIONAL MATHEMATICS 0606/01 Paper 1, maximum raw mark 80
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Intenational Geneal Cetificate of Seconday Education MARK SCHEME fo the Octobe/Novembe 009 question pape fo the guidance of teaches 0606 ADDITIONAL MATHEMATICS
More informationThe Substring Search Problem
The Substing Seach Poblem One algoithm which is used in a vaiety of applications is the family of substing seach algoithms. These algoithms allow a use to detemine if, given two chaacte stings, one is
More informationTo Feel a Force Chapter 7 Static equilibrium - torque and friction
To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on
More informationICS 233 Computer Architecture & Assembly Language
ICS 233 Computer Architecture & Assembly Language Assignment 6 Solution 1. Identify all of the RAW data dependencies in the following code. Which dependencies are data hazards that will be resolved by
More informationWelcome to Physics 272
Welcome to Physics 272 Lectue 1 Electic Chage and Coulombs Law Bob Mose mose@phys.hawaii.edu http://www.phys.hawaii.edu/~mose/physics272.html GO TO THIS SITE FOR ALL COURSE INFORMATION Phys-272 Bob Mose
More information763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012
763620SS STATISTICAL PHYSICS Solutions 2 Autumn 2012 1. Continuous Random Walk Conside a continuous one-dimensional andom walk. Let w(s i ds i be the pobability that the length of the i th displacement
More informationMotithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100
Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee
More informationName. Date. Period. Engage Examine the pictures on the left. 1. What is going on in these pictures?
AP Physics 1 Lesson 9.a Unifom Cicula Motion Outcomes 1. Define unifom cicula motion. 2. Detemine the tangential velocity of an object moving with unifom cicula motion. 3. Detemine the centipetal acceleation
More informationME 3600 Control Systems Frequency Domain Analysis
ME 3600 Contol Systems Fequency Domain Analysis The fequency esponse of a system is defined as the steady-state esponse of the system to a sinusoidal (hamonic) input. Fo linea systems, the esulting steady-state
More informationSimple Instruction-Pipelining (cont.) Pipelining Jumps
6.823, L9--1 Simple ruction-pipelining (cont.) + Interrupts Updated March 6, 2000 Laboratory for Computer Science M.I.T. http://www.csg.lcs.mit.edu/6.823 Src1 ( j / ~j ) Src2 ( / Ind) Pipelining Jumps
More informationWhen two numbers are written as the product of their prime factors, they are in factored form.
10 1 Study Guide Pages 420 425 Factos Because 3 4 12, we say that 3 and 4 ae factos of 12. In othe wods, factos ae the numbes you multiply to get a poduct. Since 2 6 12, 2 and 6 ae also factos of 12. The
More informationHistory of Astronomy - Part II. Tycho Brahe - An Observer. Johannes Kepler - A Theorist
Histoy of Astonomy - Pat II Afte the Copenican Revolution, astonomes stived fo moe obsevations to help bette explain the univese aound them Duing this time (600-750) many majo advances in science and astonomy
More informationQuantum Fourier Transform
Chapte 5 Quantum Fouie Tansfom Many poblems in physics and mathematics ae solved by tansfoming a poblem into some othe poblem with a known solution. Some notable examples ae Laplace tansfom, Legende tansfom,
More informationReading Assignment. Problem Description for Homework #9. Read Chapters 29 and 30.
Reading Assignment Read Chaptes 29 and 30. Poblem Desciption fo Homewok #9 In this homewok, you will solve the inhomogeneous Laplace s equation to calculate the electic scala potential that exists between
More informationSpring 2001 Physics 2048 Test 3 solutions
Sping 001 Physics 048 Test 3 solutions Poblem 1. (Shot Answe: 15 points) a. 1 b. 3 c. 4* d. 9 e. 8 f. 9 *emembe that since KE = ½ mv, KE must be positive Poblem (Estimation Poblem: 15 points) Use momentum-impulse
More informationCBE Transport Phenomena I Final Exam. December 19, 2013
CBE 30355 Tanspot Phenomena I Final Exam Decembe 9, 203 Closed Books and Notes Poblem. (20 points) Scaling analysis of bounday laye flows. A popula method fo measuing instantaneous wall shea stesses in
More informationr cos, and y r sin with the origin of coordinate system located at
Lectue 3-3 Kinematics of Rotation Duing ou peious lectues we hae consideed diffeent examples of motion in one and seeal dimensions. But in each case the moing object was consideed as a paticle-like object,
More informationExam 1. Exam 1 is on Tuesday, February 14, from 5:00-6:00 PM.
Exam 1 Exam 1 is on Tuesday, Febuay 14, fom 5:00-6:00 PM. Testing Cente povides accommodations fo students with special needs I must set up appointments one week befoe exam Deadline fo submitting accommodation
More information4/18/2005. Statistical Learning Theory
Statistical Leaning Theoy Statistical Leaning Theoy A model of supevised leaning consists of: a Envionment - Supplying a vecto x with a fixed but unknown pdf F x (x b Teache. It povides a desied esponse
More informationAuchmuty High School Mathematics Department Advanced Higher Notes Teacher Version
The Binomial Theoem Factoials Auchmuty High School Mathematics Depatment The calculations,, 6 etc. often appea in mathematics. They ae called factoials and have been given the notation n!. e.g. 6! 6!!!!!
More informationEasy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is
Chapte 8 Homewok Solutions Easy P8. Assume the velocity of the blood is constant ove the 0.60 s. Then the patient s body and pallet will have a constant velocity of 6 0 5 m 3.75 0 4 m/ s 0.60 s in the
More information9.1 POLAR COORDINATES
9. Pola Coodinates Contempoay Calculus 9. POLAR COORDINATES The ectangula coodinate system is immensely useful, but it is not the only way to assign an addess to a point in the plane and sometimes it is
More informationV G. In this class, we will look at a possible hypothesis for way the time dependence is t
ECE65R : Reliability Physics of anoelectonic Devices Lectue : CI Time Exponents Date : Dec. 4, 6 Classnote : Saakshi Gangwal Review : Lutfe A Siddiqui. Review We have spent seveal weeks discussing discussing
More informationParticle Systems. University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell
Paticle Systems Univesity of Texas at Austin CS384G - Compute Gaphics Fall 2010 Don Fussell Reading Requied: Witkin, Paticle System Dynamics, SIGGRAPH 97 couse notes on Physically Based Modeling. Witkin
More informationPS113 Chapter 5 Dynamics of Uniform Circular Motion
PS113 Chapte 5 Dynamics of Unifom Cicula Motion 1 Unifom cicula motion Unifom cicula motion is the motion of an object taveling at a constant (unifom) speed on a cicula path. The peiod T is the time equied
More informationGraphs of Sine and Cosine Functions
Gaphs of Sine and Cosine Functions In pevious sections, we defined the tigonometic o cicula functions in tems of the movement of a point aound the cicumfeence of a unit cicle, o the angle fomed by the
More informationEM Boundary Value Problems
EM Bounday Value Poblems 10/ 9 11/ By Ilekta chistidi & Lee, Seung-Hyun A. Geneal Desciption : Maxwell Equations & Loentz Foce We want to find the equations of motion of chaged paticles. The way to do
More information16.1 Permanent magnets
Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and
More informationL07-L09 recap: Fundamental lesson(s)!
L7-L9 recap: Fundamental lesson(s)! Over the next 3 lectures (using the IPS ISA as context) I ll explain:! How functions are treated and processed in assembly! How system calls are enabled in assembly!
More informationPY208 Matter & Interactions Final Exam S2005
PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula
More informationProblem 1: Multiple Choice Questions
Mathematics 102 Review Questions Poblem 1: Multiple Choice Questions 1: Conside the function y = f(x) = 3e 2x 5e 4x (a) The function has a local maximum at x = (1/2)ln(10/3) (b) The function has a local
More informationSolutions to Problem Set 8
Massachusetts Institute of Technology 6.042J/18.062J, Fall 05: Mathematics fo Compute Science Novembe 21 Pof. Albet R. Meye and Pof. Ronitt Rubinfeld evised Novembe 27, 2005, 858 minutes Solutions to Poblem
More informationLecture: Pipelining Basics
Lecture: Pipelining Basics Topics: Performance equations wrap-up, Basic pipelining implementation Video 1: What is pipelining? Video 2: Clocks and latches Video 3: An example 5-stage pipeline Video 4:
More informationComputer Engineering Department. CC 311- Computer Architecture. Chapter 4. The Processor: Datapath and Control. Single Cycle
Computer Engineering Department CC 311- Computer Architecture Chapter 4 The Processor: Datapath and Control Single Cycle Introduction The 5 classic components of a computer Processor Input Control Memory
More informationCPU DESIGN The Single-Cycle Implementation
CSE 202 Computer Organization CPU DESIGN The Single-Cycle Implementation Shakil M. Khan (adapted from Prof. H. Roumani) Dept of CS & Eng, York University Sequential vs. Combinational Circuits Digital circuits
More informationRelated Rates - the Basics
Related Rates - the Basics In this section we exploe the way we can use deivatives to find the velocity at which things ae changing ove time. Up to now we have been finding the deivative to compae the
More informationQuestion 1: The dipole
Septembe, 08 Conell Univesity, Depatment of Physics PHYS 337, Advance E&M, HW #, due: 9/5/08, :5 AM Question : The dipole Conside a system as discussed in class and shown in Fig.. in Heald & Maion.. Wite
More informationCircular Orbits. and g =
using analyse planetay and satellite motion modelled as unifom cicula motion in a univesal gavitation field, a = v = 4π and g = T GM1 GM and F = 1M SATELLITES IN OBIT A satellite is any object that is
More information9.1 The multiplicative group of a finite field. Theorem 9.1. The multiplicative group F of a finite field is cyclic.
Chapte 9 Pimitive Roots 9.1 The multiplicative goup of a finite fld Theoem 9.1. The multiplicative goup F of a finite fld is cyclic. Remak: In paticula, if p is a pime then (Z/p) is cyclic. In fact, this
More information3. (2) What is the difference between fixed and hybrid instructions?
1. (2 pts) What is a "balanced" pipeline? 2. (2 pts) What are the two main ways to define performance? 3. (2) What is the difference between fixed and hybrid instructions? 4. (2 pts) Clock rates have grown
More informationFARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09
FARADAY'S LAW No. of lectues allocated Actual No. of lectues dates : 3 9/5/09-14 /5/09 31.1 Faaday's Law of Induction In the pevious chapte we leaned that electic cuent poduces agnetic field. Afte this
More informationPhysics 1114: Unit 5 Hand-out Homework (Answers)
Physics 1114: Unit 5 Hand-out Homewok (Answes) Poblem set 1 1. The flywheel on an expeimental bus is otating at 420 RPM (evolutions pe minute). To find (a) the angula velocity in ad/s (adians/second),
More informationNuclear and Particle Physics - Lecture 20 The shell model
1 Intoduction Nuclea and Paticle Physics - Lectue 0 The shell model It is appaent that the semi-empiical mass fomula does a good job of descibing tends but not the non-smooth behaviou of the binding enegy.
More information10/04/18. P [P(x)] 1 negl(n).
Mastemath, Sping 208 Into to Lattice lgs & Cypto Lectue 0 0/04/8 Lectues: D. Dadush, L. Ducas Scibe: K. de Boe Intoduction In this lectue, we will teat two main pats. Duing the fist pat we continue the
More informationΔt The textbook chooses to say that the average velocity is
1-D Motion Basic I Definitions: One dimensional motion (staight line) is a special case of motion whee all but one vecto component is zeo We will aange ou coodinate axis so that the x-axis lies along the
More informationC/CS/Phys C191 Shor s order (period) finding algorithm and factoring 11/12/14 Fall 2014 Lecture 22
C/CS/Phys C9 Sho s ode (peiod) finding algoithm and factoing /2/4 Fall 204 Lectue 22 With a fast algoithm fo the uantum Fouie Tansfom in hand, it is clea that many useful applications should be possible.
More information. Using our polar coordinate conversions, we could write a
504 Chapte 8 Section 8.4.5 Dot Poduct Now that we can add, sutact, and scale vectos, you might e wondeing whethe we can multiply vectos. It tuns out thee ae two diffeent ways to multiply vectos, one which
More information- 5 - TEST 1R. This is the repeat version of TEST 1, which was held during Session.
- 5 - TEST 1R This is the epeat vesion of TEST 1, which was held duing Session. This epeat test should be attempted by those students who missed Test 1, o who wish to impove thei mak in Test 1. IF YOU
More informationCOMP Parallel Computing SMM (3) OpenMP Case Study: The Barnes-Hut N-body Algorithm
COMP 633 - Paallel Computing Lectue 8 Septembe 14, 2017 SMM (3) OpenMP Case Study: The Banes-Hut N-body Algoithm Topics Case study: the Banes-Hut algoithm Study an impotant algoithm in scientific computing»
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More informationDonnishJournals
DonnishJounals 041-1189 Donnish Jounal of Educational Reseach and Reviews. Vol 1(1) pp. 01-017 Novembe, 014. http:///dje Copyight 014 Donnish Jounals Oiginal Reseach Pape Vecto Analysis Using MAXIMA Savaş
More informationMath 301: The Erdős-Stone-Simonovitz Theorem and Extremal Numbers for Bipartite Graphs
Math 30: The Edős-Stone-Simonovitz Theoem and Extemal Numbes fo Bipatite Gaphs May Radcliffe The Edős-Stone-Simonovitz Theoem Recall, in class we poved Tuán s Gaph Theoem, namely Theoem Tuán s Theoem Let
More informationAP Physics Electric Potential Energy
AP Physics lectic Potential negy Review of some vital peviously coveed mateial. The impotance of the ealie concepts will be made clea as we poceed. Wok takes place when a foce acts ove a distance. W F
More informationTitle. Author(s)Y. IMAI; T. TSUJII; S. MOROOKA; K. NOMURA. Issue Date Doc URL. Type. Note. File Information
Title CALCULATION FORULAS OF DESIGN BENDING OENTS ON TH APPLICATION OF THE SAFETY-ARGIN FRO RC STANDARD TO Autho(s)Y. IAI; T. TSUJII; S. OROOKA; K. NOURA Issue Date 013-09-1 Doc URL http://hdl.handle.net/115/538
More informationReview of the H-O model. Problem 1. Assume that the production functions in the standard H-O model are the following:
Revie of the H-O model Poblem 1 Assume that the poduction functions in the standad H-O model ae the folloing: f 1 L 1 1 ) L 1/ 1 1/ 1 f L ) L 1/3 /3 In addition e assume that the consume pefeences ae given
More informationArea of Circles. Fold a paper plate in half four times to. divide it into 16 equal-sized sections. Label the radius r as shown.
-4 Aea of Cicles MAIN IDEA Find the aeas of cicles. Fold a pape plate in half fou times to New Vocabulay Label the adius as shown. Let C secto Math Online glencoe.com Exta Examples Pesonal Tuto Self-Check
More informationLab #0. Tutorial Exercises on Work and Fields
Lab #0 Tutoial Execises on Wok and Fields This is not a typical lab, and no pe-lab o lab epot is equied. The following execises will emind you about the concept of wok (fom 1130 o anothe intoductoy mechanics
More information