s1 s2 d B (F/D.IR.RS1 == D/X.IR.RD) (F/D.IR.RS2 == D/X.IR.RD) (F/D.IR.RS1 == X/M.IR.RD) (F/D.IR.RS2 == X/M.IR.RD) = 1 = 1

Size: px
Start display at page:

Download "s1 s2 d B (F/D.IR.RS1 == D/X.IR.RD) (F/D.IR.RS2 == D/X.IR.RD) (F/D.IR.RS1 == X/M.IR.RD) (F/D.IR.RS2 == X/M.IR.RD) = 1 = 1"

Transcription

1 Hrwre Interlock Exmple: cycle Hrwre Interlock Exmple: cycle ile s s / / / t em / ile s s / / / t em / nop nop hzr hzr $,$,$ $,$,$ (/..R == /..R) (/..R == /..R) (/..R == /..R) (/..R == /..R) = (/..R == /..R) (/..R == /..R) (/..R == /..R) (/..R == /..R) = 00 niel J. orin from Roth 00 niel J. orin from Roth Hrwre Interlock Exmple: cycle ipeline Control Terminology ile s s / / / nop hzr t em / Hrwre interlock mneuver is clle stll or bubble echnism is clle stll logic rt of more generl pipeline control mechnism Controls vncement of insns through pipeline istinguishe from pipeline tpth control Controls tpth t ech stge ipeline control controls vncement of tpth control $,$,$ (/..R == /..R) (/..R == /..R) (/..R == /..R) (/..R == /..R) = 0 00 niel J. orin from Roth 00 niel J. orin from Roth

2 ipeline igrm with t Hzrs t hzr stll inicte with * tll propgtes to younger insns Hrwre Interlock erformnce me el rnch: 0%, lo: 0%, store: 0%, other: 0% $,$,$ sw $,($) * * Hrwre interlocks: sme s softwre interlocks 0% of insns require cycle stll (i.e., insertion of nop) % of insns require cycle stll (i.e., insertion of nops) This is not K (why?) $,$,$ sw $,($) * * CI = + 0.0* + 0.0* =. o, either CI stys t n #insns increses 0% (softwre) r, #insns stys t (reltive) n CI increses 0% (hrwre) me ifference nywy, we cn o better 00 niel J. orin from Roth 00 niel J. orin from Roth bserve ypssing ile s s / / / $,$,$ This sitution seems broken hs lrey re $ from regfile $,$,$ hsn t yet written $ to regfile ut funmentlly, everything is still K hsn t ctully use $ yet $,$,$ hs lrey compute $ t em / ile s s / / / t em $,$,$ / ypssing Reing vlue from n intermeite (μrchitecturl) source Not witing until it is vilble from primry source (Regile) Here, we re bypssing the register file lso clle forwring 00 niel J. orin from Roth 00 niel J. orin from Roth 0

3 ypssing LUin ypssing ile s s / / / t em / ile s s / / / t em / $,$,$ $,$,$ $,$,$ ht bout this combintion? nother bypss pth n U input irst one ws n bypss This one is bypss Cn lso bypss to LU input 00 niel J. orin from Roth 00 niel J. orin from Roth ypssing? ypss Logic ile t s s em / / / / ile s s / / / t em / sw $,0($) lw $,0($) oes bypssing mke sense? Not to the ress input (why not?) ut to the store t input, yes bypss Ech U hs its own, here it is for U LUin (/..R == /..R) mux select = 0 (/..R == /..R) mux select = Else mux select = 00 niel J. orin from Roth 00 niel J. orin from Roth

4 ypss n tll Logic Two seprte things tll logic controls pipeline registers ypss logic controls muxes ut complementry or given t hzr: if cn t bypss, must stll lie # shows full bypssing: ll bypsses possible Is stll logic still necessry? Yes, Lo utput to LU Input ile t s s em / / / / nop stll $,$,$ $,$,$ lw $,0($) lw $,0($) tll = (/.. == L) && ((/..R == /..R) ((/..R == /..R) && (/..!= TRE)) 00 niel J. orin from Roth 00 niel J. orin from Roth ipeline igrm ith ypssing $,$,$ i $,$, ometimes you will see it like this enotes tht stll logic implemente t stge, rther thn Equivlent, oesn t mtter when you stll s long s you o $,$,$ i $,$, * * ipelining n ulti-cycle pertions ile s s / / / ht if you wnte to multi-cycle opertion? E.g., -cycle multiply /: seprte output ltch connects to stge Controlle by pipeline control n multiplier ctrl / t em 00 niel J. orin from Roth 00 niel J. orin from Roth

5 ipeline ultiplier ht bout tll Logic? ile s s / / / t em ile s s / / / t em /0 0/ / / ultiplier itself is often pipeline: wht oes this men? rouct/multiplicn register/lus/ltches replicte Cn strt ifferent multiply opertions in consecutive cycles /0 0/ / / tll = (ltlllogic) (/..R == /0..R) (/..R == /0..R) (/..R == 0/..R) (/..R == 0/..R) (/..R == /..R) (/..R == /..R) 00 niel J. orin from Roth 00 niel J. orin from Roth 0 ctully, It s omewht Nstier Honestly, It s Even Nstier Thn Tht ile s s / / / t em ile s s / / / t em /0 0/ / / ht oes this o? Hint: think bout structurl hzrs tll = (ltlllogic) (/..R!= null && 0/..R!= null) /0 0/ / / n wht bout this? tll = (ltlllogic) (/..R == /0..R) (/..R == 0/..R) 00 niel J. orin from Roth 00 niel J. orin from Roth

6 ipeline igrm with ultiplier ore ultiplier Nsties mul $,$,$ i $,$, 0 * * * This is the sitution tht slie # logic tries to voi is-orere writes to the sme register Compiler thinks gets $ from i, ctully gets it from mul This is the sitution tht slie #0 logic tries to voi Two instructions trying to write Regile in sme cycle mul $,$,$ i $,$, $,$,$0 0 mul $,$,$ i $,$, $0,$,$ ulti-cycle opertions complicte pipeline logic They re not impossible, but they require more complexity 0 00 niel J. orin from Roth 00 niel J. orin from Roth

Pipeline Example: Cycle 1. Pipeline Example: Cycle 2. Pipeline Example: Cycle 4. Pipeline Example: Cycle 3. 3 instructions. 3 instructions.

Pipeline Example: Cycle 1. Pipeline Example: Cycle 2. Pipeline Example: Cycle 4. Pipeline Example: Cycle 3. 3 instructions. 3 instructions. ipeline Exmple: Cycle 1 ipeline Exmple: Cycle X X/ /W X X/ /W $3,$,$1 lw $,0($5) $3,$,$1 3 instructions 8 9 ipeline Exmple: Cycle 3 ipeline Exmple: Cycle X X/ /W X X/ /W sw $6,($7) lw $,0($5) $3,$,$1 sw

More information

This Unit: (Scalar In-Order) Pipelining. CIS 501 Computer Architecture. Readings. Pre-Class Exercises

This Unit: (Scalar In-Order) Pipelining. CIS 501 Computer Architecture. Readings. Pre-Class Exercises This Unit: (clr In-rer) Pipelining CI 501 Computer rchitecture Unit : Pipelining pp pp pp ystem softwre CPU I/ Principles of pipelining Effects of overhe n hzrs Pipeline igrms hzrs tlling n bypssing Control

More information

Datapath Background. This Unit: (Scalar In-Order) Pipelining. CIS 501 Computer Architecture. Readings

Datapath Background. This Unit: (Scalar In-Order) Pipelining. CIS 501 Computer Architecture. Readings This Unit: (clr In-rer) Pipelining CI 501 Computer rchitecture Unit 6: Pipelining pp pp pp ystem softwre CPU I/ Principles of pipelining Effects of overhe n hzrs Pipeline igrms hzrs tlling n bypssing Control

More information

This Unit: Processor Design. What Is Control? Example: Control for sw. Example: Control for add

This Unit: Processor Design. What Is Control? Example: Control for sw. Example: Control for add This Unit: rocessor Design Appliction O ompiler U ory Firmwre I/O Digitl ircuits Gtes & Trnsistors pth components n timing s n register files ories (RAMs) locking strtegies Mpping n IA to tpth ontrol Exceptions

More information

ECE / CS 250 Introduction to Computer Architecture

ECE / CS 250 Introduction to Computer Architecture ECE / CS 250 Introduction to Computer rchitecture Pipelining enjamin C. Lee Duke University Slides from Daniel Sorin (Duke) and are derived from work by mir Roth (Penn) and lvy Lebeck (Duke) 1 This Unit:

More information

ECE/CS 250 Computer Architecture. Fall 2017

ECE/CS 250 Computer Architecture. Fall 2017 ECE/CS 250 Computer rchitecture Fall 2017 Pipelining Tyler letsch Duke University Includes material adapted from Dan Sorin (Duke) and mir Roth (Penn). This Unit: Pipelining pplication S Compiler Firmware

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Overview. Making the Fast Case Common and the Uncommon Case Simple in Unbounded Transactional Memory. Running Example. Background

Overview. Making the Fast Case Common and the Uncommon Case Simple in Unbounded Transactional Memory. Running Example. Background Overview king the Fst Cse Common n the Uncommon Cse imple in Unoune Trnsctionl Colin Blunell (University of Pennsylvni) Joe Devietti (University of Pennsylvni) E Christopher Lewis (Vwre, Inc.) ilo. K.

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

EECS150 - Digital Design Lecture 23 - High-level Design and Optimization 3, Parallelism and Pipelining

EECS150 - Digital Design Lecture 23 - High-level Design and Optimization 3, Parallelism and Pipelining EECS150 - Digitl Design Lecture 23 - High-level Design nd Optimiztion 3, Prllelism nd Pipelining Nov 12, 2002 John Wwrzynek Fll 2002 EECS150 - Lec23-HL3 Pge 1 Prllelism Prllelism is the ct of doing more

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology

More information

SIMPLIFYING ALGEBRA PASSPORT.

SIMPLIFYING ALGEBRA PASSPORT. SIMPLIFYING ALGEBRA PASSPORT www.mthletics.com.u This booklet is ll bout turning complex problems into something simple. You will be ble to do something like this! ( 9- # + 4 ' ) ' ( 9- + 7-) ' ' Give

More information

Small Business Networking

Small Business Networking Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology

More information

12-B FRACTIONS AND DECIMALS

12-B FRACTIONS AND DECIMALS -B Frctions nd Decimls. () If ll four integers were negtive, their product would be positive, nd so could not equl one of them. If ll four integers were positive, their product would be much greter thn

More information

In the last lecture, we discussed how valid tokens may be specified by regular expressions.

In the last lecture, we discussed how valid tokens may be specified by regular expressions. LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.

More information

EECS 281: Homework #4 Due: Thursday, October 7, 2004

EECS 281: Homework #4 Due: Thursday, October 7, 2004 EECS 28: Homework #4 Due: Thursdy, October 7, 24 Nme: Emil:. Convert the 24-bit number x44243 to mime bse64: QUJD First, set is to brek 8-bit blocks into 6-bit blocks, nd then convert: x44243 b b 6 2 9

More information

Unit #9 : Definite Integral Properties, Fundamental Theorem of Calculus

Unit #9 : Definite Integral Properties, Fundamental Theorem of Calculus Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl

More information

Computer Arithmetic Logical, Integer Addition & Subtraction Chapter

Computer Arithmetic Logical, Integer Addition & Subtraction Chapter Computer Arithmetic Logicl, Integer Addition & Sutrction Chpter 3.-3.3 3.3 EEC7 FQ 25 MIPS Integer Representtion -it signed integers,, e.g., for numeric opertions 2 s s complement: one representtion for

More information

CS201 Discussion 10 DRAWTREE + TRIES

CS201 Discussion 10 DRAWTREE + TRIES CS201 Discussion 10 DRAWTREE + TRIES DrwTree First instinct: recursion As very generic structure, we could tckle this problem s follows: drw(): Find the root drw(root) drw(root): Write the line for the

More information

10.5 Graphing Quadratic Functions

10.5 Graphing Quadratic Functions 0.5 Grphing Qudrtic Functions Now tht we cn solve qudrtic equtions, we wnt to lern how to grph the function ssocited with the qudrtic eqution. We cll this the qudrtic function. Grphs of Qudrtic Functions

More information

EXPONENTIAL & POWER GRAPHS

EXPONENTIAL & POWER GRAPHS Eponentil & Power Grphs EXPONENTIAL & POWER GRAPHS www.mthletics.com.u Eponentil EXPONENTIAL & Power & Grphs POWER GRAPHS These re grphs which result from equtions tht re not liner or qudrtic. The eponentil

More information

Tries. Yufei Tao KAIST. April 9, Y. Tao, April 9, 2013 Tries

Tries. Yufei Tao KAIST. April 9, Y. Tao, April 9, 2013 Tries Tries Yufei To KAIST April 9, 2013 Y. To, April 9, 2013 Tries In this lecture, we will discuss the following exct mtching prolem on strings. Prolem Let S e set of strings, ech of which hs unique integer

More information

Stack. A list whose end points are pointed by top and bottom

Stack. A list whose end points are pointed by top and bottom 4. Stck Stck A list whose end points re pointed by top nd bottom Insertion nd deletion tke plce t the top (cf: Wht is the difference between Stck nd Arry?) Bottom is constnt, but top grows nd shrinks!

More information

Simplifying Algebra. Simplifying Algebra. Curriculum Ready.

Simplifying Algebra. Simplifying Algebra. Curriculum Ready. Simplifying Alger Curriculum Redy www.mthletics.com This ooklet is ll out turning complex prolems into something simple. You will e le to do something like this! ( 9- # + 4 ' ) ' ( 9- + 7-) ' ' Give this

More information

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork

MA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork MA1008 Clculus nd Liner Algebr for Engineers Course Notes for Section B Stephen Wills Deprtment of Mthemtics University College Cork s.wills@ucc.ie http://euclid.ucc.ie/pges/stff/wills/teching/m1008/ma1008.html

More information

Section 3.1: Sequences and Series

Section 3.1: Sequences and Series Section.: Sequences d Series Sequences Let s strt out with the definition of sequence: sequence: ordered list of numbers, often with definite pttern Recll tht in set, order doesn t mtter so this is one

More information

Definition of Regular Expression

Definition of Regular Expression Definition of Regulr Expression After the definition of the string nd lnguges, we re redy to descrie regulr expressions, the nottion we shll use to define the clss of lnguges known s regulr sets. Recll

More information

Subtracting Fractions

Subtracting Fractions Lerning Enhncement Tem Model Answers: Adding nd Subtrcting Frctions Adding nd Subtrcting Frctions study guide. When the frctions both hve the sme denomintor (bottom) you cn do them using just simple dding

More information

Here is an example where angles with a common arm and vertex overlap. Name all the obtuse angles adjacent to

Here is an example where angles with a common arm and vertex overlap. Name all the obtuse angles adjacent to djcent tht do not overlp shre n rm from the sme vertex point re clled djcent ngles. me the djcent cute ngles in this digrm rm is shred y + + me vertex point for + + + is djcent to + djcent simply mens

More information

Chapter Spline Method of Interpolation More Examples Electrical Engineering

Chapter Spline Method of Interpolation More Examples Electrical Engineering Chpter. Spline Method of Interpoltion More Exmples Electricl Engineering Exmple Thermistors re used to mesure the temperture of bodies. Thermistors re bsed on mterils chnge in resistnce with temperture.

More information

What do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers

What do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers Wht do ll those bits men now? bits (...) Number Systems nd Arithmetic or Computers go to elementry school instruction R-formt I-formt... integer dt number text chrs... floting point signed unsigned single

More information

CS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig

CS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig CS311H: Discrete Mthemtics Grph Theory IV Instructor: Işıl Dillig Instructor: Işıl Dillig, CS311H: Discrete Mthemtics Grph Theory IV 1/25 A Non-plnr Grph Regions of Plnr Grph The plnr representtion of

More information

Dr. D.M. Akbar Hussain

Dr. D.M. Akbar Hussain Dr. D.M. Akr Hussin Lexicl Anlysis. Bsic Ide: Red the source code nd generte tokens, it is similr wht humns will do to red in; just tking on the input nd reking it down in pieces. Ech token is sequence

More information

Matrices and Systems of Equations

Matrices and Systems of Equations Mtrices Mtrices nd Sstems of Equtions A mtri is rectngulr rr of rel numbers. CHAT Pre-Clculus Section 8. m m m............ n n n mn We will use the double subscript nottion for ech element of the mtri.

More information

Assignment 4. Due 09/18/17

Assignment 4. Due 09/18/17 Assignment 4. ue 09/18/17 1. ). Write regulr expressions tht define the strings recognized by the following finite utomt: b d b b b c c b) Write FA tht recognizes the tokens defined by the following regulr

More information

Finite Automata. Lecture 4 Sections Robb T. Koether. Hampden-Sydney College. Wed, Jan 21, 2015

Finite Automata. Lecture 4 Sections Robb T. Koether. Hampden-Sydney College. Wed, Jan 21, 2015 Finite Automt Lecture 4 Sections 3.6-3.7 Ro T. Koether Hmpden-Sydney College Wed, Jn 21, 2015 Ro T. Koether (Hmpden-Sydney College) Finite Automt Wed, Jn 21, 2015 1 / 23 1 Nondeterministic Finite Automt

More information

Engineer To Engineer Note

Engineer To Engineer Note Engineer To Engineer Note EE-186 Technicl Notes on using Anlog Devices' DSP components nd development tools Contct our technicl support by phone: (800) ANALOG-D or e-mil: dsp.support@nlog.com Or visit

More information

Section 10.4 Hyperbolas

Section 10.4 Hyperbolas 66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol

More information

Unit 5 Vocabulary. A function is a special relationship where each input has a single output.

Unit 5 Vocabulary. A function is a special relationship where each input has a single output. MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with

More information

INTRODUCTION TO SIMPLICIAL COMPLEXES

INTRODUCTION TO SIMPLICIAL COMPLEXES INTRODUCTION TO SIMPLICIAL COMPLEXES CASEY KELLEHER AND ALESSANDRA PANTANO 0.1. Introduction. In this ctivity set we re going to introduce notion from Algebric Topology clled simplicil homology. The min

More information

COMP 423 lecture 11 Jan. 28, 2008

COMP 423 lecture 11 Jan. 28, 2008 COMP 423 lecture 11 Jn. 28, 2008 Up to now, we hve looked t how some symols in n lphet occur more frequently thn others nd how we cn sve its y using code such tht the codewords for more frequently occuring

More information

Class Overview. Database Design. Database Design Process. Database Design. Introduction to Data Management CSE 414

Class Overview. Database Design. Database Design Process. Database Design. Introduction to Data Management CSE 414 Introution to Dt Mngement CSE 44 Unit 6: Coneptul Design E/R Digrms Integrity Constrints BCNF Introution to Dt Mngement CSE 44 E/R Digrms ( letures) CSE 44 Autumn 08 Clss Overview Dtse Design Unit : Intro

More information

ECEN 468 Advanced Logic Design Lecture 36: RTL Optimization

ECEN 468 Advanced Logic Design Lecture 36: RTL Optimization ECEN 468 Advnced Logic Design Lecture 36: RTL Optimiztion ECEN 468 Lecture 36 RTL Design Optimiztions nd Trdeoffs 6.5 While creting dtpth during RTL design, there re severl optimiztions nd trdeoffs, involving

More information

2 Computing all Intersections of a Set of Segments Line Segment Intersection

2 Computing all Intersections of a Set of Segments Line Segment Intersection 15-451/651: Design & Anlysis of Algorithms Novemer 14, 2016 Lecture #21 Sweep-Line nd Segment Intersection lst chnged: Novemer 8, 2017 1 Preliminries The sweep-line prdigm is very powerful lgorithmic design

More information

Section 2.3 Functions. Definition: Let A and B be sets. A function (mapping, map) f from A to B, denoted f :A B, is a subset of A B such that

Section 2.3 Functions. Definition: Let A and B be sets. A function (mapping, map) f from A to B, denoted f :A B, is a subset of A B such that Setion 2.3 Funtions Definition: Let n e sets. funtion (mpping, mp) f from to, enote f :, is suset of suh tht x[x y[y < x, y > f ]] n [< x, y 1 > f < x, y 2 > f ] y 1 = y 2 Note: f ssoites with eh x in

More information

MIPS I/O and Interrupt

MIPS I/O and Interrupt MIPS I/O nd Interrupt Review Floting point instructions re crried out on seprte chip clled coprocessor 1 You hve to move dt to/from coprocessor 1 to do most common opertions such s printing, clling functions,

More information

Solutions to Math 41 Final Exam December 12, 2011

Solutions to Math 41 Final Exam December 12, 2011 Solutions to Mth Finl Em December,. ( points) Find ech of the following its, with justifiction. If there is n infinite it, then eplin whether it is or. ( ) / ln() () (5 points) First we compute the it:

More information

Fig.25: the Role of LEX

Fig.25: the Role of LEX The Lnguge for Specifying Lexicl Anlyzer We shll now study how to uild lexicl nlyzer from specifiction of tokens in the form of list of regulr expressions The discussion centers round the design of n existing

More information

Angle Properties in Polygons. Part 1 Interior Angles

Angle Properties in Polygons. Part 1 Interior Angles 2.4 Angle Properties in Polygons YOU WILL NEED dynmic geometry softwre OR protrctor nd ruler EXPLORE A pentgon hs three right ngles nd four sides of equl length, s shown. Wht is the sum of the mesures

More information

3.5.1 Single slit diffraction

3.5.1 Single slit diffraction 3..1 Single slit diffrction ves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. e will consider this lter. Tke

More information

10.2 Graph Terminology and Special Types of Graphs

10.2 Graph Terminology and Special Types of Graphs 10.2 Grph Terminology n Speil Types of Grphs Definition 1. Two verties u n v in n unirete grph G re lle jent (or neighors) in G iff u n v re enpoints of n ege e of G. Suh n ege e is lle inient with the

More information

What do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers

What do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers Wht do ll those bits men now? bits (...) Number Systems nd Arithmetic or Computers go to elementry school instruction R-formt I-formt... integer dt number text chrs... floting point signed unsigned single

More information

MTH 146 Conics Supplement

MTH 146 Conics Supplement 105- Review of Conics MTH 146 Conics Supplement In this section we review conics If ou ne more detils thn re present in the notes, r through section 105 of the ook Definition: A prol is the set of points

More information

Chapter 2. 3/28/2004 H133 Spring

Chapter 2. 3/28/2004 H133 Spring Chpter 2 Newton believe tht light ws me up of smll prticles. This point ws ebte by scientists for mny yers n it ws not until the 1800 s when series of experiments emonstrte wve nture of light. (But be

More information

1 The Definite Integral

1 The Definite Integral The Definite Integrl Definition. Let f be function defined on the intervl [, b] where

More information

Suffix Tries. Slides adapted from the course by Ben Langmead

Suffix Tries. Slides adapted from the course by Ben Langmead Suffix Tries Slides dpted from the course y Ben Lngmed en.lngmed@gmil.com Indexing with suffixes Until now, our indexes hve een sed on extrcting sustrings from T A very different pproch is to extrct suffixes

More information

Introduction to hardware design using VHDL

Introduction to hardware design using VHDL Introuction to hrwre esign using VHDL Tim Güneysu n Nele Mentens ECC school Novemer 11, 2017, Nijmegen Outline Implementtion pltforms Introuction to VHDL Hrwre tutoril 1 Implementtion pltforms Microprocessor

More information

Systems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits

Systems I. Logic Design I. Topics Digital logic Logic gates Simple combinational logic circuits Systems I Logic Design I Topics Digitl logic Logic gtes Simple comintionl logic circuits Simple C sttement.. C = + ; Wht pieces of hrdwre do you think you might need? Storge - for vlues,, C Computtion

More information

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve.

If f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve. Line Integrls The ide of line integrl is very similr to tht of single integrls. If the function f(x) is bove the x-xis on the intervl [, b], then the integrl of f(x) over [, b] is the re under f over the

More information

Dynamic Programming. Andreas Klappenecker. [partially based on slides by Prof. Welch] Monday, September 24, 2012

Dynamic Programming. Andreas Klappenecker. [partially based on slides by Prof. Welch] Monday, September 24, 2012 Dynmic Progrmming Andres Klppenecker [prtilly bsed on slides by Prof. Welch] 1 Dynmic Progrmming Optiml substructure An optiml solution to the problem contins within it optiml solutions to subproblems.

More information

ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών

ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών ΕΠΛ323 - Θωρία και Πρακτική Μταγλωττιστών Lecture 3 Lexicl Anlysis Elis Athnsopoulos elisthn@cs.ucy.c.cy Recognition of Tokens if expressions nd reltionl opertors if è if then è then else è else relop

More information

Math 464 Fall 2012 Notes on Marginal and Conditional Densities October 18, 2012

Math 464 Fall 2012 Notes on Marginal and Conditional Densities October 18, 2012 Mth 464 Fll 2012 Notes on Mrginl nd Conditionl Densities klin@mth.rizon.edu October 18, 2012 Mrginl densities. Suppose you hve 3 continuous rndom vribles X, Y, nd Z, with joint density f(x,y,z. The mrginl

More information

Today. Search Problems. Uninformed Search Methods. Depth-First Search Breadth-First Search Uniform-Cost Search

Today. Search Problems. Uninformed Search Methods. Depth-First Search Breadth-First Search Uniform-Cost Search Uninformed Serch [These slides were creted by Dn Klein nd Pieter Abbeel for CS188 Intro to AI t UC Berkeley. All CS188 mterils re vilble t http://i.berkeley.edu.] Tody Serch Problems Uninformed Serch Methods

More information

Lists in Lisp and Scheme

Lists in Lisp and Scheme Lists in Lisp nd Scheme Lists in Lisp nd Scheme Lists re Lisp s fundmentl dt structures, ut there re others Arrys, chrcters, strings, etc. Common Lisp hs moved on from eing merely LISt Processor However,

More information

3.5.1 Single slit diffraction

3.5.1 Single slit diffraction 3.5.1 Single slit diffrction Wves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. We will consider this lter.

More information

6.2 Volumes of Revolution: The Disk Method

6.2 Volumes of Revolution: The Disk Method mth ppliction: volumes by disks: volume prt ii 6 6 Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem 6) nd the ccumultion process is to determine so-clled volumes

More information

Midterm 2 Sample solution

Midterm 2 Sample solution Nme: Instructions Midterm 2 Smple solution CMSC 430 Introduction to Compilers Fll 2012 November 28, 2012 This exm contins 9 pges, including this one. Mke sure you hve ll the pges. Write your nme on the

More information

Questions About Numbers. Number Systems and Arithmetic. Introduction to Binary Numbers. Negative Numbers?

Questions About Numbers. Number Systems and Arithmetic. Introduction to Binary Numbers. Negative Numbers? Questions About Numbers Number Systems nd Arithmetic or Computers go to elementry school How do you represent negtive numbers? frctions? relly lrge numbers? relly smll numbers? How do you do rithmetic?

More information

x )Scales are the reciprocal of each other. e

x )Scales are the reciprocal of each other. e 9. Reciprocls A Complete Slide Rule Mnul - eville W Young Chpter 9 Further Applictions of the LL scles The LL (e x ) scles nd the corresponding LL 0 (e -x or Exmple : 0.244 4.. Set the hir line over 4.

More information

Premaster Course Algorithms 1 Chapter 6: Shortest Paths. Christian Scheideler SS 2018

Premaster Course Algorithms 1 Chapter 6: Shortest Paths. Christian Scheideler SS 2018 Premster Course Algorithms Chpter 6: Shortest Pths Christin Scheieler SS 8 Bsic Grph Algorithms Overview: Shortest pths in DAGs Dijkstr s lgorithm Bellmn-For lgorithm Johnson s metho SS 8 Chpter 6 Shortest

More information

a(e, x) = x. Diagrammatically, this is encoded as the following commutative diagrams / X

a(e, x) = x. Diagrammatically, this is encoded as the following commutative diagrams / X 4. Mon, Sept. 30 Lst time, we defined the quotient topology coming from continuous surjection q : X! Y. Recll tht q is quotient mp (nd Y hs the quotient topology) if V Y is open precisely when q (V ) X

More information

CSCI 3130: Formal Languages and Automata Theory Lecture 12 The Chinese University of Hong Kong, Fall 2011

CSCI 3130: Formal Languages and Automata Theory Lecture 12 The Chinese University of Hong Kong, Fall 2011 CSCI 3130: Forml Lnguges nd utomt Theory Lecture 12 The Chinese University of Hong Kong, Fll 2011 ndrej Bogdnov In progrmming lnguges, uilding prse trees is significnt tsk ecuse prse trees tell us the

More information

CMU Fall VLSI CAD

CMU Fall VLSI CAD CMU Fll 01 18-760 VLSI CAD [120 pts] Homework 2. Out Thu Sep 13, Due Thu Sep 27 01. 1. BDD ordering [10 pts] We sw tht vrible order is highly significnt for something s simple s multiplexor. How bout something

More information

Algorithm Design (5) Text Search

Algorithm Design (5) Text Search Algorithm Design (5) Text Serch Tkshi Chikym School of Engineering The University of Tokyo Text Serch Find sustring tht mtches the given key string in text dt of lrge mount Key string: chr x[m] Text Dt:

More information

CSEP 573 Artificial Intelligence Winter 2016

CSEP 573 Artificial Intelligence Winter 2016 CSEP 573 Artificil Intelligence Winter 2016 Luke Zettlemoyer Problem Spces nd Serch slides from Dn Klein, Sturt Russell, Andrew Moore, Dn Weld, Pieter Abbeel, Ali Frhdi Outline Agents tht Pln Ahed Serch

More information

CS 130 : Computer Systems - II. Shankar Balachandran Dept. of Computer Science & Engineering IIT Madras

CS 130 : Computer Systems - II. Shankar Balachandran Dept. of Computer Science & Engineering IIT Madras CS 3 : Computer Systems - II Shnkr Blchndrn (shnkr@cse.iitm.c.in) Dept. of Computer Science & Engineering IIT Mdrs Recp Differentite Between s nd s Truth Tbles b AND b OR NOT September 4, 27 Introduction

More information

CS 221: Artificial Intelligence Fall 2011

CS 221: Artificial Intelligence Fall 2011 CS 221: Artificil Intelligence Fll 2011 Lecture 2: Serch (Slides from Dn Klein, with help from Sturt Russell, Andrew Moore, Teg Grenger, Peter Norvig) Problem types! Fully observble, deterministic! single-belief-stte

More information

Data sharing in OpenMP

Data sharing in OpenMP Dt shring in OpenMP Polo Burgio polo.burgio@unimore.it Outline Expressing prllelism Understnding prllel threds Memory Dt mngement Dt cluses Synchroniztion Brriers, locks, criticl sections Work prtitioning

More information

Functor (1A) Young Won Lim 8/2/17

Functor (1A) Young Won Lim 8/2/17 Copyright (c) 2016-2017 Young W. Lim. Permission is grnted to copy, distribute nd/or modify this document under the terms of the GNU Free Documenttion License, Version 1.2 or ny lter version published

More information

MATH 2530: WORKSHEET 7. x 2 y dz dy dx =

MATH 2530: WORKSHEET 7. x 2 y dz dy dx = MATH 253: WORKSHT 7 () Wrm-up: () Review: polr coordintes, integrls involving polr coordintes, triple Riemnn sums, triple integrls, the pplictions of triple integrls (especilly to volume), nd cylindricl

More information

Example: 2:1 Multiplexer

Example: 2:1 Multiplexer Exmple: 2:1 Multiplexer Exmple #1 reg ; lwys @( or or s) egin if (s == 1') egin = ; else egin = ; 1 s B. Bs 114 Exmple: 2:1 Multiplexer Exmple #2 Normlly lwys include egin nd sttements even though they

More information

1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)

1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) Numbers nd Opertions, Algebr, nd Functions 45. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) In sequence of terms involving eponentil growth, which the testing service lso clls geometric

More information

Pythagoras theorem and trigonometry (2)

Pythagoras theorem and trigonometry (2) HPTR 10 Pythgors theorem nd trigonometry (2) 31 HPTR Liner equtions In hpter 19, Pythgors theorem nd trigonometry were used to find the lengths of sides nd the sizes of ngles in right-ngled tringles. These

More information

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012

Grade 7/8 Math Circles Geometric Arithmetic October 31, 2012 Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt

More information

Stained Glass Design. Teaching Goals:

Stained Glass Design. Teaching Goals: Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to

More information

McAfee Network Security Platform

McAfee Network Security Platform 10/100/1000 Copper Active Fil-Open Bypss Kit Guide Revision E McAfee Network Security Pltform This document descries the contents nd how to instll the McAfee 10/100/1000 Copper Active Fil-Open Bypss Kit

More information

Enginner To Engineer Note

Enginner To Engineer Note Technicl Notes on using Anlog Devices DSP components nd development tools from the DSP Division Phone: (800) ANALOG-D, FAX: (781) 461-3010, EMAIL: dsp_pplictions@nlog.com, FTP: ftp.nlog.com Using n ADSP-2181

More information

Uninformed Search. Hal Daumé III. Computer Science University of Maryland CS 421: Introduction to Artificial Intelligence 31 Jan 2012

Uninformed Search. Hal Daumé III. Computer Science University of Maryland CS 421: Introduction to Artificial Intelligence 31 Jan 2012 1 Hl Dumé III (me@hl3.nme) Uninformed Serch Hl Dumé III Comuter Science University of Mrylnd me@hl3.nme CS 421: Introduction to Artificil Intelligence 31 Jn 2012 Mny slides courtesy of Dn Klein, Sturt

More information

ECE 468/573 Midterm 1 September 28, 2012

ECE 468/573 Midterm 1 September 28, 2012 ECE 468/573 Midterm 1 September 28, 2012 Nme:! Purdue emil:! Plese sign the following: I ffirm tht the nswers given on this test re mine nd mine lone. I did not receive help from ny person or mteril (other

More information

Functor (1A) Young Won Lim 10/5/17

Functor (1A) Young Won Lim 10/5/17 Copyright (c) 2016-2017 Young W. Lim. Permission is grnted to copy, distribute nd/or modify this document under the terms of the GNU Free Documenttion License, Version 1.2 or ny lter version published

More information

Hyperbolas. Definition of Hyperbola

Hyperbolas. Definition of Hyperbola CHAT Pre-Clculus Hyperols The third type of conic is clled hyperol. For n ellipse, the sum of the distnces from the foci nd point on the ellipse is fixed numer. For hyperol, the difference of the distnces

More information

Agilent Mass Hunter Software

Agilent Mass Hunter Software Agilent Mss Hunter Softwre Quick Strt Guide Use this guide to get strted with the Mss Hunter softwre. Wht is Mss Hunter Softwre? Mss Hunter is n integrl prt of Agilent TOF softwre (version A.02.00). Mss

More information

V = set of vertices (vertex / node) E = set of edges (v, w) (v, w in V)

V = set of vertices (vertex / node) E = set of edges (v, w) (v, w in V) Definitions G = (V, E) V = set of verties (vertex / noe) E = set of eges (v, w) (v, w in V) (v, w) orere => irete grph (igrph) (v, w) non-orere => unirete grph igrph: w is jent to v if there is n ege from

More information

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it.

6.3 Volumes. Just as area is always positive, so is volume and our attitudes towards finding it. 6.3 Volumes Just s re is lwys positive, so is volume nd our ttitudes towrds finding it. Let s review how to find the volume of regulr geometric prism, tht is, 3-dimensionl oject with two regulr fces seprted

More information

RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING

RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING When finding the LCD of problem involving the ddition or subtrction of frctions, it my be necessry to fctor some denomintors to discover some restricted

More information