Chapter 5: Processor Design Advanced Topics. Microprogramming: Basic Idea

Size: px
Start display at page:

Download "Chapter 5: Processor Design Advanced Topics. Microprogramming: Basic Idea"

Transcription

1 5-1 Chapter 5 Processor Desig Advaced Topics Chapter 5: Processor Desig Advaced Topics Topics 5.3 Microprogrammig Cotrol store ad microbrachig Horizotal ad vertical microprogrammig 5- Chapter 5 Processor Desig Advaced Topics Microprogrammig: Basic Idea Recall cotrol sequece for 1-bus SRC Step Cocrete RTN Cotrol Sequece T0 MA PC: C PC + 4; PC out, MA i, INC4, C i, Read T1 MD M[MA]: PC C; C out, PC i, Wait T IR MD; MD out, IR i T3 A R[rb]; Grb, R out, A i T4 C A + R[rc]; Grc, R out, ADD, C i T5 R[ra] C; C out, Gra, R i, Ed Cotrol uit job is to geerate the sequece of cotrol sigals How about buildig a computer to do this? Page 1

2 5-3 Chapter 5 Processor Desig Advaced Topics The Microcode Egie A computer to geerate cotrol sigals is much simpler tha a ordiary computer At the simplest, it just reads the cotrol sigals i order from a read-oly memory The memory is called the cotrol store A cotrol store word, or microistructio, cotais a bit patter tellig which cotrol sigals are true i a specific step The major issue is determiig the order i which microistructios are read 5-4 Chapter 5 Processor Desig Advaced Topics Fig 5.16 Block Diagram of Microcoded Cotrol Uit Ck CCs Other Sequecer k IR Opcode PLA (computes start addr) Icremet 4 1Mux µpc Cotrol store Exteral source Microistructio has brach cotrol, brach, ad cotrol sigal fields Microprogram couter ca be set from several sources to do the required sequecig m µbrach cotrol µir Cotrol sigals PC out,etc. Brach Page

3 5-5 Chapter 5 Processor Desig Advaced Topics Parts of the Microprogrammed Cotrol Uit Sice the cotrol sigals are just read from memory, the mai fuctio is sequecig This is reflected i the several ways the µpc ca be loaded Output of icremeter µpc + 1 PLA output start for a macroistructio Brach from µistructio Exteral source say for exceptio or reset Micro coditioal braches ca deped o coditio codes, data path state, exteral sigals, etc. 5-6 Chapter 5 Processor Desig Advaced Topics Cotets of a Microistructio Microistructio format Brach cotrol Cotrol sigals Brach PC out MA i PC i C out A i Ed Mai compoet is list of 1/0 cotrol sigal values There is a brach i the cotrol store There are brach cotrol bits to determie whe to use the brach ad whe to use µpc + 1 Page 3

4 . 5-7 Chapter 5 Processor Desig Advaced Topics Fig 5.17 The Cotrol Store 0 µcode for istructio fetch a1 Micro a a3 µcode for add µcode for br µcode for shr Commo istructio fetch sequece Separate sequeces for each (macro) istructio Wide words -1 m bits wide k µbrach cotrol bits c cotrol sigals brach addr. bits 5-8 Chapter 5 Processor Desig Advaced Topics Tbl 5. Cotrol Sigals for the add Istructio Addresses are the istructio fetch Addresses 00 0 do the add Chage of µcotrol from 103 to 00 uses a kid of µbrach Page 4

5 5-9 Chapter 5 Processor Desig Advaced Topics Uses for µbrachig i the Microprogrammed Cotrol Uit (1) Brach to start of µcode for a specific ist. () Coditioal cotrol sigals, e.g. CON PC i (3) Loopig o coditios, e.g Goto6 Coditios will cotrol µbraches istead of beig ANDed with cotrol sigals Microbraches are frequet ad cotrol store es are short, so it is reasoable to have a µbrach field i every µ istructio 5-10 Chapter 5 Processor Desig Advaced Topics Illustratio of µbrachig Cotrol Logic We illustrate a µbrachig cotrol scheme by a machie havig coditio code bits N ad Z Brach cotrol has parts: (1) selectig the iput applied to the µpc ad () specifyig whether this iput or µpc + 1 is used We allow 4 possible iputs to µpc The icremeted value µpc + 1 The PLA lookup table for the start of a macroistructio A exterally supplied The brach field i the µistructio word Page 5

6 . BrNotZ BrNotN BrN 5-11 Chapter 5 Processor Desig Advaced Topics Fig 5.18 Brachig Cotrols i the Microcoded Cotrol Uit ZN Sequecer Mux cotrol BrU BrNotZ BrZ BrNotN BrN Icr PLA 4 1 Mux µpc Cotrol store Exteral Cotrol sigals Mux Ctl Brach Select Icremet µpc PLA Exteral Brach 5 brach coditios NotN N NotZ Z Ucoditioal To 1 of 4 places Next µistructio PLA Exteral Brach 5-1 Chapter 5 Processor Desig Advaced Topics Some Possible µbraches Usig the Illustrated Logic (Refer to Tbl 5.3) Cot rol Sigals Brach Address Brachig act io XXX XXX XXX Noe ext ist ruct io Brach to output of PLA Br if Z t o Ext er. Addr. Br if N t o 300 (else ext ) Br if N t o 06 (else ext ) Br to 04 If the cotrol sigals are all zero, the µistructio oly does a test Otherwise test is combied with data path activity Page 6

7 5-13 Chapter 5 Processor Desig Advaced Topics Horizotal versus Vertical Microcode Schemes I horizotal microcode, each cotrol sigal is represeted by a bit i the µistructio I vertical microcode, a set of true cotrol sigals is represeted by a shorter code The ame horizotal implies fewer cotrol store words of more bits per word Vertical µcode oly allows RTs i a step for which there is a vertical µistructio code Thus vertical µcode may take more cotrol store words of fewer bits 5-14 Chapter 5 Processor Desig Advaced Topics Fig 5.0 Completely Horizotal ad Vertical Microcodig µpc µpc Horizotal cotrol store Vertical cotrol store C i Ic4 MA i PC out todecoder Data path PC out MA i Ic4 C i Page 7

8 5-15 Chapter 5 Processor Desig Advaced Topics Savig Cotrol Store Bits with Horizotal Microcode Some cotrol sigals caot possibly be true at the same time Oe ad oly oe ALU fuctio ca be selected Oly oe register out gate ca be true with a sigle bus Memory read ad write caot be true at the same step A set of m such sigals ca be ecoded usig log m bits (log (m + 1) to allow for o sigal true) The raw cotrol sigals ca the be geerated by a k to k decoder, where k m (or k m + 1) This is a compromise betwee horizotal ad vertical ecodig 5-16 Chapter 5 Processor Desig Advaced Topics Fig 5.19 A Somewhat Vertical Ecodig µir ALU ops field F5 Register-out field F decoder 3 8 decoder 16 ALU 7 Reg out cotrol cotrol sigals sigals Scheme would save (16 + 7) - (4 + 3) = 16 bits/word i the case illustrated Page 8

9 Chapter 5 Processor Desig Advaced Topics A Microprogrammed Cotrol Uit for the 1-Bus SRC Usig the 1-bus SRC data path desig gives a specific set of cotrol sigals There are o coditio codes, but data path sigals CON ad = 0 will eed to be tested We will use µbraches BrCON, Br = 0, ad Br 0 We adopt the clockig logic of Fig Logic for exceptio ad reset sigals is added to the microcode sequecer logic Exceptio ad reset are assumed to have bee sychroized to the clock 5-18 Chapter 5 Processor Desig Advaced Topics Tbl 5.4 The add Istructio Addr Ot her Br Cot rol Addr. Sigals Actios XXX MA PC: C PC+ 4 ; XXX MD M[ MA] : PC C; XXX IR MD; µpc PLA; XXX A R[rb] ; XXX C A+R[rc]; R[ra] C: µpc 100; Br(!=0) Ed MA i Microbrachig to the output of the PLA is show at 10 Microbrach to 100 at 0 starts ext fetch Page 9

10 5-19 Chapter 5 Processor Desig Advaced Topics Fig 5.16 Block Diagram of Microcoded Cotrol Uit Ck CCs Other Sequecer k IR Opcode PLA (computes start addr) Icremet 4 1Mux µpc Cotrol store m Exteral source Microistructio has brach cotrol, brach, ad cotrol sigal fields Microprogram couter ca be set from several sources to do the required sequecig µbrach cotrol µir Cotrol sigals PC out,etc. Brach 5-0 Chapter 5 Processor Desig Advaced Topics Fig 5.1 SRC Microcode Sequecer CON =0 Exceptio Reset 400 Sequecer 10 1Mux Icremet 000 PLA Brach Exteral 4 1 Mux µpc BrCON BrN 0 BrN = 0 Ed Mux cotrol BrU Mux Ctl Select Icremet µpc PLA Exteral Brach Page 10

11 5-1 Chapter 5 Processor Desig Advaced Topics Tbl 5.6 Somewhat Vertical Ecodig of the SRC Microistructio F1 F F3 F4 F5 F6 F7 F8 F9 Mux Ct l Brach cotrol 000 BrU 001 BrCON 010 BrCON 011Br =0 100 Br Noe Ed Out sigals 0 Cot. 000 PC out 1 Ed 001 C out 010 MD out 011 R out 100 BA out 101 c1 out 110 c out 111 Noe I sigals Misc. Gat e regs. 000 MA i 000 Read 00 Gra 001 PC 001 i Write 01 Grb IR Wait 10 Grc i 011 Decr 11 Noe 011 A i 100 CON i 100 R i 101 C i 101 MD i 110 Stop 110 Ld 111 Noe 111 Noe Brach ALU 0000 ADD 0001 C=B 10 bits 0010 SHR 0011 Ic NOT bits 3 bits 1 bit 3 bits 3 bits 3 bits bits 4 bits 10 bits 5- Chapter 5 Processor Desig Advaced Topics Other Microprogrammig Issues A hardware push-dow stack for the µpc ca tur repeated µsequeces ito µsubrouties Vertical µcode ca be implemeted usig a horizotal µegie, sometimes called aocode Page 11

12 5-3 Chapter 5 Processor Desig Advaced Topics Microprogrammig Summary Microprogrammig is a desig method with a target of easig the desig task ad allowig for easy desig chage or multiple compatible implemetatios of the same istructio set Page 1

Microprogramming: Basic Idea

Microprogramming: Basic Idea 5-45 Chapter 5 Processor Design Advanced Topics Microprogramming: Basic Idea Recall control sequence for 1-bus SRC Step Concrete RTN Control Sequence T0 MA PC: C PC + 4; PC out, MA in, INC4, C in, Read

More information

Appendix D. Controller Implementation

Appendix D. Controller Implementation COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Appedix D Cotroller Implemetatio Cotroller Implemetatios Combiatioal logic (sigle-cycle); Fiite state machie (multi-cycle, pipelied);

More information

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Part A Datapath Design

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Part A Datapath Design COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter The Processor Part A path Desig Itroductio CPU performace factors Istructio cout Determied by ISA ad compiler. CPI ad

More information

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design College of Computer ad Iformatio Scieces Departmet of Computer Sciece CSC 220: Computer Orgaizatio Uit 11 Basic Computer Orgaizatio ad Desig 1 For the rest of the semester, we ll focus o computer architecture:

More information

EE 459/500 HDL Based Digital Design with Programmable Logic. Lecture 13 Control and Sequencing: Hardwired and Microprogrammed Control

EE 459/500 HDL Based Digital Design with Programmable Logic. Lecture 13 Control and Sequencing: Hardwired and Microprogrammed Control EE 459/500 HDL Based Digital Desig with Programmable Logic Lecture 13 Cotrol ad Sequecig: Hardwired ad Microprogrammed Cotrol Refereces: Chapter s 4,5 from textbook Chapter 7 of M.M. Mao ad C.R. Kime,

More information

End Semester Examination CSE, III Yr. (I Sem), 30002: Computer Organization

End Semester Examination CSE, III Yr. (I Sem), 30002: Computer Organization Ed Semester Examiatio 2013-14 CSE, III Yr. (I Sem), 30002: Computer Orgaizatio Istructios: GROUP -A 1. Write the questio paper group (A, B, C, D), o frot page top of aswer book, as per what is metioed

More information

Elementary Educational Computer

Elementary Educational Computer Chapter 5 Elemetary Educatioal Computer. Geeral structure of the Elemetary Educatioal Computer (EEC) The EEC coforms to the 5 uits structure defied by vo Neuma's model (.) All uits are preseted i a simplified

More information

Chapter 4 The Datapath

Chapter 4 The Datapath The Ageda Chapter 4 The Datapath Based o slides McGraw-Hill Additioal material 24/25/26 Lewis/Marti Additioal material 28 Roth Additioal material 2 Taylor Additioal material 2 Farmer Tae the elemets that

More information

Description of Single Cycle Computer (SCC)

Description of Single Cycle Computer (SCC) Descriptio of Sigle Cycle Computer (SCC) Refereces: Chapter 9 of M. Morris Mao ad Charles Kime, Logic ad Computer Desig Fudametals, Pearso Pretice Hall, 4 th Editio, 28. Overview Part Datapaths Itroductio

More information

Chapter 5 Processor Design Advanced Topics

Chapter 5 Processor Design Advanced Topics Chapter 5 Processor esign dvanced Topics The principles of pipelining pipelined design of RC Pipeline hazards Instruction-level parallelism (ILP) uperscalar processors Very Long Instruction Word (VLIW)

More information

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Single-Cycle Disadvantages & Advantages

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Single-Cycle Disadvantages & Advantages COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 4 The Processor Pipeliig Sigle-Cycle Disadvatages & Advatages Clk Uses the clock cycle iefficietly the clock cycle must

More information

CMSC Computer Architecture Lecture 3: ISA and Introduction to Microarchitecture. Prof. Yanjing Li University of Chicago

CMSC Computer Architecture Lecture 3: ISA and Introduction to Microarchitecture. Prof. Yanjing Li University of Chicago CMSC 22200 Computer Architecture Lecture 3: ISA ad Itroductio to Microarchitecture Prof. Yajig Li Uiversity of Chicago Lecture Outlie ISA uarch (hardware implemetatio of a ISA) Logic desig basics Sigle-cycle

More information

Microprogrammed Control

Microprogrammed Control Calcolatori Elettroici e Sistemi Operativi Microprogrammed Microprogrammed Iputs (state) Status sigals (from datapath) NS = δ(s,i) = ((S),I) O = λ(s) Next state Outputs sigals (to datapath) Microprogrammed

More information

Advanced Computer Architecture

Advanced Computer Architecture Advanced Computer Architecture Lecture No. 22 Reading Material Vincent P. Heuring&Harry F. Jordan Chapter 5 Computer Systems Design and Architecture 5.3 Summary Microprogramming Working of a General Microcoded

More information

Chapter 4 Topics. Comp. Sys. Design & Architecture 2 nd Edition Prentice Hall, Mark Franklin,S06

Chapter 4 Topics. Comp. Sys. Design & Architecture 2 nd Edition Prentice Hall, Mark Franklin,S06 Chapter 4 Topics The Design Process A 1-bus Microarchitecture for SRC Data Path Implementation Logic Design for the 1-bus SRC The Control Unit The 2- and 3-bus Processor Designs The Machine Reset Process

More information

Computer Architecture. Microcomputer Architecture and Interfacing Colorado School of Mines Professor William Hoff

Computer Architecture. Microcomputer Architecture and Interfacing Colorado School of Mines Professor William Hoff Computer rchitecture Microcomputer rchitecture ad Iterfacig Colorado School of Mies Professor William Hoff Computer Hardware Orgaizatio Processor Performs all computatios; coordiates data trasfer Iput

More information

4-1 Chapter 4 - Processor Design. Chapter 4 Topics

4-1 Chapter 4 - Processor Design. Chapter 4 Topics 4-1 Chapter 4 - Processor Design Chapter 4 Topics The Design Process A 1-bus Microarchitecture for SRC Data Path Implementation Logic Design for the 1-bus SRC The Control Unit The 2- and 3-bus Processor

More information

Threads and Concurrency in Java: Part 1

Threads and Concurrency in Java: Part 1 Cocurrecy Threads ad Cocurrecy i Java: Part 1 What every computer egieer eeds to kow about cocurrecy: Cocurrecy is to utraied programmers as matches are to small childre. It is all too easy to get bured.

More information

Threads and Concurrency in Java: Part 1

Threads and Concurrency in Java: Part 1 Threads ad Cocurrecy i Java: Part 1 1 Cocurrecy What every computer egieer eeds to kow about cocurrecy: Cocurrecy is to utraied programmers as matches are to small childre. It is all too easy to get bured.

More information

Module Instantiation. Finite State Machines. Two Types of FSMs. Finite State Machines. Given submodule mux32two: Instantiation of mux32two

Module Instantiation. Finite State Machines. Two Types of FSMs. Finite State Machines. Given submodule mux32two: Instantiation of mux32two Give submodule mux32two: 2-to- MUX module mux32two (iput [3:] i,i, iput sel, output [3:] out); Module Istatiatio Fiite Machies esig methodology for sequetial logic -- idetify distict s -- create trasitio

More information

Chapter 4: Processor Design. Block Diagram of 1-Bus SRC

Chapter 4: Processor Design. Block Diagram of 1-Bus SRC 4-1 Chapter 4 Processor Design Chapter 4: Processor Design Topics 4.1 The Design Process 4.2 1-Bus Microarchitecture for the SRC 4.3 Data Path Implementation 4.4 Logic Design for the 1-Bus SRC 4.5 The

More information

CMSC Computer Architecture Lecture 12: Virtual Memory. Prof. Yanjing Li University of Chicago

CMSC Computer Architecture Lecture 12: Virtual Memory. Prof. Yanjing Li University of Chicago CMSC 22200 Computer Architecture Lecture 12: Virtual Memory Prof. Yajig Li Uiversity of Chicago A System with Physical Memory Oly Examples: most Cray machies early PCs Memory early all embedded systems

More information

Computers and Scientific Thinking

Computers and Scientific Thinking Computers ad Scietific Thikig David Reed, Creighto Uiversity Chapter 15 JavaScript Strigs 1 Strigs as Objects so far, your iteractive Web pages have maipulated strigs i simple ways use text box to iput

More information

CMSC22200 Computer Architecture Lecture 9: Out-of-Order, SIMD, VLIW. Prof. Yanjing Li University of Chicago

CMSC22200 Computer Architecture Lecture 9: Out-of-Order, SIMD, VLIW. Prof. Yanjing Li University of Chicago CMSC22200 Computer Architecture Lecture 9: Out-of-Order, SIMD, VLIW Prof. Yajig Li Uiversity of Chicago Admiistrative Stuff Lab2 due toight Exam I: covers lectures 1-9 Ope book, ope otes, close device

More information

EE260: Digital Design, Spring /16/18. n Example: m 0 (=x 1 x 2 ) is adjacent to m 1 (=x 1 x 2 ) and m 2 (=x 1 x 2 ) but NOT m 3 (=x 1 x 2 )

EE260: Digital Design, Spring /16/18. n Example: m 0 (=x 1 x 2 ) is adjacent to m 1 (=x 1 x 2 ) and m 2 (=x 1 x 2 ) but NOT m 3 (=x 1 x 2 ) EE26: Digital Desig, Sprig 28 3/6/8 EE 26: Itroductio to Digital Desig Combiatioal Datapath Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Combiatioal Logic Blocks Multiplexer Ecoders/Decoders

More information

UNIVERSITY OF MORATUWA

UNIVERSITY OF MORATUWA UNIVERSITY OF MORATUWA FACULTY OF ENGINEERING DEPARTMENT OF COMPUTER SCIENCE & ENGINEERING B.Sc. Egieerig 2014 Itake Semester 2 Examiatio CS2052 COMPUTER ARCHITECTURE Time allowed: 2 Hours Jauary 2016

More information

Digital System Design

Digital System Design July, 22 9:55 vra235_ch Sheet umber Page umber 65 black chapter Digital System Desig a b c d e f g h 8 7 6 5 4 3 2. Bd3 g6+, Ke8 d8 65 July, 22 9:55 vra235_ch Sheet umber 2 Page umber 66 black 66 CHAPTER

More information

MOTIF XF Extension Owner s Manual

MOTIF XF Extension Owner s Manual MOTIF XF Extesio Ower s Maual Table of Cotets About MOTIF XF Extesio...2 What Extesio ca do...2 Auto settig of Audio Driver... 2 Auto settigs of Remote Device... 2 Project templates with Iput/ Output Bus

More information

1. SWITCHING FUNDAMENTALS

1. SWITCHING FUNDAMENTALS . SWITCING FUNDMENTLS Switchig is the provisio of a o-demad coectio betwee two ed poits. Two distict switchig techiques are employed i commuicatio etwors-- circuit switchig ad pacet switchig. Circuit switchig

More information

CMSC Computer Architecture Lecture 2: ISA. Prof. Yanjing Li Department of Computer Science University of Chicago

CMSC Computer Architecture Lecture 2: ISA. Prof. Yanjing Li Department of Computer Science University of Chicago CMSC 22200 Computer Architecture Lecture 2: ISA Prof. Yajig Li Departmet of Computer Sciece Uiversity of Chicago Admiistrative Stuff Lab1 out toight Due Thursday (10/18) Lab1 review sessio Tomorrow, 10/05,

More information

CS252 Spring 2017 Graduate Computer Architecture. Lecture 6: Out-of-Order Processors

CS252 Spring 2017 Graduate Computer Architecture. Lecture 6: Out-of-Order Processors CS252 Sprig 2017 Graduate Computer Architecture Lecture 6: Out-of-Order Processors Lisa Wu, Krste Asaovic http://ist.eecs.berkeley.edu/~cs252/sp17 WU UCB CS252 SP17 2 WU UCB CS252 SP17 Last Time i Lecture

More information

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 5 Fuctios for All Subtasks Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 5.1 void Fuctios 5.2 Call-By-Referece Parameters 5.3 Usig Procedural Abstractio 5.4 Testig ad Debuggig

More information

CIS 121 Data Structures and Algorithms with Java Spring Stacks and Queues Monday, February 12 / Tuesday, February 13

CIS 121 Data Structures and Algorithms with Java Spring Stacks and Queues Monday, February 12 / Tuesday, February 13 CIS Data Structures ad Algorithms with Java Sprig 08 Stacks ad Queues Moday, February / Tuesday, February Learig Goals Durig this lab, you will: Review stacks ad queues. Lear amortized ruig time aalysis

More information

Τεχνολογία Λογισμικού

Τεχνολογία Λογισμικού ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ Σχολή Ηλεκτρολόγων Μηχανικών και Μηχανικών Υπολογιστών Τεχνολογία Λογισμικού, 7ο/9ο εξάμηνο 2018-2019 Τεχνολογία Λογισμικού Ν.Παπασπύρου, Αν.Καθ. ΣΗΜΜΥ, ickie@softlab.tua,gr

More information

Behavioral Modeling in Verilog

Behavioral Modeling in Verilog Behavioral Modelig i Verilog COE 202 Digital Logic Desig Dr. Muhamed Mudawar Kig Fahd Uiversity of Petroleum ad Mierals Presetatio Outlie Itroductio to Dataflow ad Behavioral Modelig Verilog Operators

More information

A collection of open-sourced RISC-V processors

A collection of open-sourced RISC-V processors Riscy Processors A collectio of ope-sourced RISC-V processors Ady Wright, Sizhuo Zhag, Thomas Bourgeat, Murali Vijayaraghava, Jamey Hicks, Arvid Computatio Structures Group, CSAIL, MIT 4 th RISC-V Workshop

More information

Python Programming: An Introduction to Computer Science

Python Programming: An Introduction to Computer Science Pytho Programmig: A Itroductio to Computer Sciece Chapter 1 Computers ad Programs 1 Objectives To uderstad the respective roles of hardware ad software i a computig system. To lear what computer scietists

More information

Using VTR Emulation on Avid Systems

Using VTR Emulation on Avid Systems Usig VTR Emulatio o Avid Systems VTR emulatio allows you to cotrol a sequece loaded i the Record moitor from a edit cotroller for playback i the edit room alog with other sources. I this sceario the edit

More information

Weston Anniversary Fund

Weston Anniversary Fund Westo Olie Applicatio Guide 2018 1 This guide is desiged to help charities applyig to the Westo to use our olie applicatio form. The Westo is ope to applicatios from 5th Jauary 2018 ad closes o 30th Jue

More information

Chapter 3 Classification of FFT Processor Algorithms

Chapter 3 Classification of FFT Processor Algorithms Chapter Classificatio of FFT Processor Algorithms The computatioal complexity of the Discrete Fourier trasform (DFT) is very high. It requires () 2 complex multiplicatios ad () complex additios [5]. As

More information

COMPUTER ORGANIZATION AND DESIGN

COMPUTER ORGANIZATION AND DESIGN COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Review Istructio Set Architecture Istructio Set The repertoire of istructios of a computer Differet computers have differet istructio

More information

Lecture 3. RTL Design Methodology. Transition from Pseudocode & Interface to a Corresponding Block Diagram

Lecture 3. RTL Design Methodology. Transition from Pseudocode & Interface to a Corresponding Block Diagram Lecture 3 RTL Desig Methodology Trasitio from Pseudocode & Iterface to a Correspodig Block Diagram Structure of a Typical Digital Data Iputs Datapath (Executio Uit) Data Outputs System Cotrol Sigals Status

More information

Lecture 2. RTL Design Methodology. Transition from Pseudocode & Interface to a Corresponding Block Diagram

Lecture 2. RTL Design Methodology. Transition from Pseudocode & Interface to a Corresponding Block Diagram Lecture 2 RTL Desig Methodology Trasitio from Pseudocode & Iterface to a Correspodig Block Diagram Structure of a Typical Digital Data Iputs Datapath (Executio Uit) Data Outputs System Cotrol Sigals Status

More information

L6: FSMs and Synchronization

L6: FSMs and Synchronization L6: FSMs ad Sychroizatio Ackowledgemets: Materials i this lecture are courtesy of the followig sources ad are used with permissio. Rex Mi J. Rabaey, A. Chadrakasa, B. Nikolic. igital Itegrated Circuits:

More information

Today s objectives. CSE401: Introduction to Compiler Construction. What is a compiler? Administrative Details. Why study compilers?

Today s objectives. CSE401: Introduction to Compiler Construction. What is a compiler? Administrative Details. Why study compilers? CSE401: Itroductio to Compiler Costructio Larry Ruzzo Sprig 2004 Today s objectives Admiistrative details Defie compilers ad why we study them Defie the high-level structure of compilers Associate specific

More information

Master Informatics Eng. 2017/18. A.J.Proença. Memory Hierarchy. (most slides are borrowed) AJProença, Advanced Architectures, MiEI, UMinho, 2017/18 1

Master Informatics Eng. 2017/18. A.J.Proença. Memory Hierarchy. (most slides are borrowed) AJProença, Advanced Architectures, MiEI, UMinho, 2017/18 1 Advaced Architectures Master Iformatics Eg. 2017/18 A.J.Proeça Memory Hierarchy (most slides are borrowed) AJProeça, Advaced Architectures, MiEI, UMiho, 2017/18 1 Itroductio Programmers wat ulimited amouts

More information

Multi-Threading. Hyper-, Multi-, and Simultaneous Thread Execution

Multi-Threading. Hyper-, Multi-, and Simultaneous Thread Execution Multi-Threadig Hyper-, Multi-, ad Simultaeous Thread Executio 1 Performace To Date Icreasig processor performace Pipeliig. Brach predictio. Super-scalar executio. Out-of-order executio. Caches. Hyper-Threadig

More information

COP4020 Programming Languages. Functional Programming Prof. Robert van Engelen

COP4020 Programming Languages. Functional Programming Prof. Robert van Engelen COP4020 Programmig Laguages Fuctioal Programmig Prof. Robert va Egele Overview What is fuctioal programmig? Historical origis of fuctioal programmig Fuctioal programmig today Cocepts of fuctioal programmig

More information

Chapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 9. Pointers and Dynamic Arrays. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 9 Poiters ad Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 9.1 Poiters 9.2 Dyamic Arrays Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Slide 9-3

More information

Custom single-purpose processors: Hardware. 4.1 Introduction. 4.2 Combinational logic design 4-1

Custom single-purpose processors: Hardware. 4.1 Introduction. 4.2 Combinational logic design 4-1 Chapter 4: Custom sigle-purpose processors: Hardware 4- Chapter 4 Custom sigle-purpose processors: Hardware 4. Itroductio As metioed i the previous chapter, a sigle-purpose processor is a digital sstem

More information

Solutions to Final COMS W4115 Programming Languages and Translators Monday, May 4, :10-5:25pm, 309 Havemeyer

Solutions to Final COMS W4115 Programming Languages and Translators Monday, May 4, :10-5:25pm, 309 Havemeyer Departmet of Computer ciece Columbia Uiversity olutios to Fial COM W45 Programmig Laguages ad Traslators Moday, May 4, 2009 4:0-5:25pm, 309 Havemeyer Closed book, o aids. Do questios 5. Each questio is

More information

Algorithm Design Techniques. Divide and conquer Problem

Algorithm Design Techniques. Divide and conquer Problem Algorithm Desig Techiques Divide ad coquer Problem Divide ad Coquer Algorithms Divide ad Coquer algorithm desig works o the priciple of dividig the give problem ito smaller sub problems which are similar

More information

Chapter 4 Topics C S. D A 2/e

Chapter 4 Topics C S. D A 2/e Chapter 4 Topics The esign Process 1-bus Microarchitecture for RC ata Path Implementation Logic esign for the 1-bus RC The Control Unit The 2- and 3-bus Processor esigns The Machine Reset Process Machine

More information

System and Software Architecture Description (SSAD)

System and Software Architecture Description (SSAD) System ad Software Architecture Descriptio (SSAD) Diabetes Health Platform Team #6 Jasmie Berry (Cliet) Veerav Naidu (Project Maager) Mukai Nog (Architect) Steve South (IV&V) Vijaya Prabhakara (Quality

More information

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe CHAPTER 22 Database Recovery Techiques Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe Itroductio Recovery algorithms Recovery cocepts Write-ahead

More information

ELEG 5173L Digital Signal Processing Introduction to TMS320C6713 DSK

ELEG 5173L Digital Signal Processing Introduction to TMS320C6713 DSK Departmet of Electrical Egieerig Uiversity of Arasas ELEG 5173L Digital Sigal Processig Itroductio to TMS320C6713 DSK Dr. Jigia Wu wuj@uar.edu ANALOG V.S DIGITAL 2 Aalog sigal processig ASP Aalog sigal

More information

Basic allocator mechanisms The course that gives CMU its Zip! Memory Management II: Dynamic Storage Allocation Mar 6, 2000.

Basic allocator mechanisms The course that gives CMU its Zip! Memory Management II: Dynamic Storage Allocation Mar 6, 2000. 5-23 The course that gives CM its Zip Memory Maagemet II: Dyamic Storage Allocatio Mar 6, 2000 Topics Segregated lists Buddy system Garbage collectio Mark ad Sweep Copyig eferece coutig Basic allocator

More information

. Written in factored form it is easy to see that the roots are 2, 2, i,

. Written in factored form it is easy to see that the roots are 2, 2, i, CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or

More information

CIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19

CIS 121 Data Structures and Algorithms with Java Spring Stacks, Queues, and Heaps Monday, February 18 / Tuesday, February 19 CIS Data Structures ad Algorithms with Java Sprig 09 Stacks, Queues, ad Heaps Moday, February 8 / Tuesday, February 9 Stacks ad Queues Recall the stack ad queue ADTs (abstract data types from lecture.

More information

Arquitectura de Computadores

Arquitectura de Computadores Arquitectura de Computadores Capítulo 2. Procesadores segmetados Based o the origial material of the book: D.A. Patterso y J.L. Heessy Computer Orgaizatio ad Desig: The Hardware/Software Iterface 4 th

More information

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 1 Itroductio to Computers ad C++ Programmig Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 1.1 Computer Systems 1.2 Programmig ad Problem Solvig 1.3 Itroductio to C++ 1.4 Testig

More information

Bluespec-3: Modules & Interfaces. Bluespec: State and Rules organized into modules

Bluespec-3: Modules & Interfaces. Bluespec: State and Rules organized into modules Bluespec-3: Modules & Iterfaces Arvid Computer Sciece & Artificial Itelligece Lab Massachusetts Istitute of Techology Based o material prepared by Bluespec Ic, Jauary 2005 February 28, 2005 L09-1 Bluespec:

More information

A Flexible Programmable Memory BIST for Embedded Single-Port Memory and Dual-Port Memory

A Flexible Programmable Memory BIST for Embedded Single-Port Memory and Dual-Port Memory A Flexible Programmable Memory BIST for Embedded Sigle-Port Memory ad Dual-Port Memory Yougkyu Park, Hog-Sik Kim, Ihyuk Choi, ad Sugho Kag Programmable memory built-i self-test (PMBIST) is a attractive

More information

How do we evaluate algorithms?

How do we evaluate algorithms? F2 Readig referece: chapter 2 + slides Algorithm complexity Big O ad big Ω To calculate ruig time Aalysis of recursive Algorithms Next time: Litterature: slides mostly The first Algorithm desig methods:

More information

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 4 Procedural Abstractio ad Fuctios That Retur a Value Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 4.1 Top-Dow Desig 4.2 Predefied Fuctios 4.3 Programmer-Defied Fuctios 4.4

More information

Pseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance

Pseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Pseudocode ( 1.1) High-level descriptio of a algorithm More structured

More information

CMSC Computer Architecture Lecture 10: Caches. Prof. Yanjing Li University of Chicago

CMSC Computer Architecture Lecture 10: Caches. Prof. Yanjing Li University of Chicago CMSC 22200 Computer Architecture Lecture 10: Caches Prof. Yajig Li Uiversity of Chicago Midterm Recap Overview ad fudametal cocepts ISA Uarch Datapath, cotrol Sigle cycle, multi cycle Pipeliig Basic idea,

More information

Lecture 28: Data Link Layer

Lecture 28: Data Link Layer Automatic Repeat Request (ARQ) 2. Go ack N ARQ Although the Stop ad Wait ARQ is very simple, you ca easily show that it has very the low efficiecy. The low efficiecy comes from the fact that the trasmittig

More information

Improvement of the Orthogonal Code Convolution Capabilities Using FPGA Implementation

Improvement of the Orthogonal Code Convolution Capabilities Using FPGA Implementation Improvemet of the Orthogoal Code Covolutio Capabilities Usig FPGA Implemetatio Naima Kaabouch, Member, IEEE, Apara Dhirde, Member, IEEE, Saleh Faruque, Member, IEEE Departmet of Electrical Egieerig, Uiversity

More information

Data diverse software fault tolerance techniques

Data diverse software fault tolerance techniques Data diverse software fault tolerace techiques Complemets desig diversity by compesatig for desig diversity s s limitatios Ivolves obtaiig a related set of poits i the program data space, executig the

More information

Introduction to Computing Systems: From Bits and Gates to C and Beyond 2 nd Edition

Introduction to Computing Systems: From Bits and Gates to C and Beyond 2 nd Edition Lecture Goals Itroductio to Computig Systems: From Bits ad Gates to C ad Beyod 2 d Editio Yale N. Patt Sajay J. Patel Origial slides from Gregory Byrd, North Carolia State Uiversity Modified slides by

More information

CIS 121. Introduction to Trees

CIS 121. Introduction to Trees CIS 121 Itroductio to Trees 1 Tree ADT Tree defiitio q A tree is a set of odes which may be empty q If ot empty, the there is a distiguished ode r, called root ad zero or more o-empty subtrees T 1, T 2,

More information

Course Site: Copyright 2012, Elsevier Inc. All rights reserved.

Course Site:   Copyright 2012, Elsevier Inc. All rights reserved. Course Site: http://cc.sjtu.edu.c/g2s/site/aca.html 1 Computer Architecture A Quatitative Approach, Fifth Editio Chapter 2 Memory Hierarchy Desig 2 Outlie Memory Hierarchy Cache Desig Basic Cache Optimizatios

More information

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5 Morga Kaufma Publishers 26 February, 28 COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 5 Set-Associative Cache Architecture Performace Summary Whe CPU performace icreases:

More information

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe

Copyright 2016 Ramez Elmasri and Shamkant B. Navathe Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe CHAPTER 18 Strategies for Query Processig Copyright 2016 Ramez Elmasri ad Shamkat B. Navathe Itroductio DBMS techiques to process a query Scaer idetifies

More information

One advantage that SONAR has over any other music-sequencing product I ve worked

One advantage that SONAR has over any other music-sequencing product I ve worked *gajedra* D:/Thomso_Learig_Projects/Garrigus_163132/z_productio/z_3B2_3D_files/Garrigus_163132_ch17.3d, 14/11/08/16:26:39, 16:26, page: 647 17 CAL 101 Oe advatage that SONAR has over ay other music-sequecig

More information

APPLICATION NOTE PACE1750AE BUILT-IN FUNCTIONS

APPLICATION NOTE PACE1750AE BUILT-IN FUNCTIONS APPLICATION NOTE PACE175AE BUILT-IN UNCTIONS About This Note This applicatio brief is iteded to explai ad demostrate the use of the special fuctios that are built ito the PACE175AE processor. These powerful

More information

System Overview. Hardware Concept. s Introduction to the Features of MicroAutoBox t

System Overview. Hardware Concept. s Introduction to the Features of MicroAutoBox t s Itroductio to the Features of MicroAutoBox t System Overview Objective Where to go from here dspace provides the MicroAutoBox i differet variats. This sectio gives you a overview o the MicroAutoBox's

More information

A New Morphological 3D Shape Decomposition: Grayscale Interframe Interpolation Method

A New Morphological 3D Shape Decomposition: Grayscale Interframe Interpolation Method A ew Morphological 3D Shape Decompositio: Grayscale Iterframe Iterpolatio Method D.. Vizireau Politehica Uiversity Bucharest, Romaia ae@comm.pub.ro R. M. Udrea Politehica Uiversity Bucharest, Romaia mihea@comm.pub.ro

More information

The following algorithms have been tested as a method of converting an I.F. from 16 to 512 MHz to 31 real 16 MHz USB channels:

The following algorithms have been tested as a method of converting an I.F. from 16 to 512 MHz to 31 real 16 MHz USB channels: DBE Memo#1 MARK 5 MEMO #18 MASSACHUSETTS INSTITUTE OF TECHNOLOGY HAYSTACK OBSERVATORY WESTFORD, MASSACHUSETTS 1886 November 19, 24 Telephoe: 978-692-4764 Fax: 781-981-59 To: From: Mark 5 Developmet Group

More information

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor Advanced Issues

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor Advanced Issues COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 4 The Processor Advaced Issues Review: Pipelie Hazards Structural hazards Desig pipelie to elimiate structural hazards.

More information

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Determined by ISA and compiler. Determined by CPU hardware

COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Determined by ISA and compiler. Determined by CPU hardware COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface ARM Editio Chapter 4 The Processor Itroductio CPU performace factors Istructio cout Determied by ISA ad compiler CPI ad Cycle time Determied

More information

Our Learning Problem, Again

Our Learning Problem, Again Noparametric Desity Estimatio Matthew Stoe CS 520, Sprig 2000 Lecture 6 Our Learig Problem, Agai Use traiig data to estimate ukow probabilities ad probability desity fuctios So far, we have depeded o describig

More information

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5.

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5. Morga Kaufma Publishers 26 February, 208 COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 5 Virtual Memory Review: The Memory Hierarchy Take advatage of the priciple

More information

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS)

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS) CSC165H1, Witer 018 Learig Objectives By the ed of this worksheet, you will: Aalyse the ruig time of fuctios cotaiig ested loops. 1. Nested loop variatios. Each of the followig fuctios takes as iput a

More information

The number n of subintervals times the length h of subintervals gives length of interval (b-a).

The number n of subintervals times the length h of subintervals gives length of interval (b-a). Simulator with MadMath Kit: Riema Sums (Teacher s pages) I your kit: 1. GeoGebra file: Ready-to-use projector sized simulator: RiemaSumMM.ggb 2. RiemaSumMM.pdf (this file) ad RiemaSumMMEd.pdf (educator's

More information

Control Unit Implementation

Control Unit Implementation Control Unit Implementation Moore Machine Implementation Reset RES PC IF PC MAR, PC + PC Note capture of MBR in these states IF Wait/ IF2 Wait/ Wait/ MAR Mem, Read/Write, Request, Mem MBR Wait/ IF3 Wait/

More information

BGP Attributes and Path Selection. ISP Training Workshops

BGP Attributes and Path Selection. ISP Training Workshops BGP Attributes ad Path Selectio ISP Traiig Workshops 1 BGP Attributes The tools available for the job 2 What Is a Attribute?... Next Hop AS Path MED...... p Part of a BGP Update p Describes the characteristics

More information

CMSC Computer Architecture Lecture 5: Pipelining. Prof. Yanjing Li University of Chicago

CMSC Computer Architecture Lecture 5: Pipelining. Prof. Yanjing Li University of Chicago CMSC 22200 Computer Architecture Lecture 5: Pipeliig Prof. Yajig Li Uiversity of Chicago Admiistrative Stuff Lab1 Due toight Lab2: out later today; due 2 weeks from ow Review sessio this Friday Turig award

More information

Computer Systems - HS

Computer Systems - HS What have we leared so far? Computer Systems High Level ENGG1203 2d Semester, 2017-18 Applicatios Sigals Systems & Cotrol Systems Computer & Embedded Systems Digital Logic Combiatioal Logic Sequetial Logic

More information

K-NET bus. When several turrets are connected to the K-Bus, the structure of the system is as showns

K-NET bus. When several turrets are connected to the K-Bus, the structure of the system is as showns K-NET bus The K-Net bus is based o the SPI bus but it allows to addressig may differet turrets like the I 2 C bus. The K-Net is 6 a wires bus (4 for SPI wires ad 2 additioal wires for request ad ackowledge

More information

Investigation Monitoring Inventory

Investigation Monitoring Inventory Ivestigatio Moitorig Ivetory Name Period Date Art Smith has bee providig the prits of a egravig to FieArt Gallery. He plas to make just 2000 more prits. FieArt has already received 70 of Art s prits. The

More information

Guide to Applying Online

Guide to Applying Online Guide to Applyig Olie Itroductio Respodig to requests for additioal iformatio Reportig: submittig your moitorig or ed of grat Pledges: submittig your Itroductio This guide is to help charities submit their

More information

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures Uiversity of Waterloo Departmet of Electrical ad Computer Egieerig ECE 250 Algorithms ad Data Structures Midterm Examiatio ( pages) Istructor: Douglas Harder February 7, 2004 7:30-9:00 Name (last, first)

More information

CS 11 C track: lecture 1

CS 11 C track: lecture 1 CS 11 C track: lecture 1 Prelimiaries Need a CMS cluster accout http://acctreq.cms.caltech.edu/cgi-bi/request.cgi Need to kow UNIX IMSS tutorial liked from track home page Track home page: http://courses.cms.caltech.edu/courses/cs11/material

More information

1 Enterprise Modeler

1 Enterprise Modeler 1 Eterprise Modeler Itroductio I BaaERP, a Busiess Cotrol Model ad a Eterprise Structure Model for multi-site cofiguratios are itroduced. Eterprise Structure Model Busiess Cotrol Models Busiess Fuctio

More information

Lecture 11: PI/T parallel I/O, part I

Lecture 11: PI/T parallel I/O, part I Lecture 11: PI/T parallel I/O, part I Geeral descriptio of the parallel I/O fuctio Bufferi Hadshaki Iput ad Output trasfers Timi Diarams Reister model of the 68230 Port Geeral Cotrol Reister (PGCR) Port

More information

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately.

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately. Workflow model GM AR Gumpy RM Dyagump At a very high level, this is what gump does. We ll be lookig at each of the items described here seperately. User edits project descriptor ad commits s maitai their

More information

Reversible Realization of Quaternary Decoder, Multiplexer, and Demultiplexer Circuits

Reversible Realization of Quaternary Decoder, Multiplexer, and Demultiplexer Circuits Egieerig Letters, :, EL Reversible Realizatio of Quaterary Decoder, Multiplexer, ad Demultiplexer Circuits Mozammel H.. Kha, Member, ENG bstract quaterary reversible circuit is more compact tha the correspodig

More information

Section 7.2: Direction Fields and Euler s Methods

Section 7.2: Direction Fields and Euler s Methods Sectio 7.: Directio ields ad Euler s Methods Practice HW from Stewart Tetbook ot to had i p. 5 # -3 9-3 odd or a give differetial equatio we wat to look at was to fid its solutio. I this chapter we will

More information