Multiplexers and Demultiplexers

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Multiplexers and Demultiplexers"

Transcription

1 I this lesso, you will lear about: Multiplexers ad Demultiplexers 1. Multiplexers 2. Combiatioal circuit implemetatio with multiplexers 3. Demultiplexers 4. Some examples Multiplexer A Multiplexer (see Figure 1) is a combiatioal circuit that selects oe of the 2 iput sigals (D, D 1, D 2,, D 2-1 ) to be passed to the sigle output lie Y. Q. How to select the iput lie (out of the possible 2 iput sigals) to be passed to the output lie? A. Selectio of the particular iput to be passed to the output is cotrolled by a set of iput sigals called Select Iputs (S, S 1, S 2,., S -1 ). Figure 1: Multiplexer Example 1: 2x1 Mux A 2x1 Mux has 2 iput lies (D & D 1 ), oe select iput (S), ad oe output lie (Y). (see Figure 2) IF S=, the Y= D Else (S=1) Y= D 1

2 D MUX Y D1 S Figure 2: A 2 X 1 Multiplexer Thus, the output sigal Y ca be expressed as: Y = S D + S D 1 Example 2: 4x1 Mux A 4x1 Mux has 4 iput lies (D, D 1, D 2, D 3 ), two select iputs (S & S 1 ), ad oe output lie Y. (see Figure 3) IF S 1 S =, the Y= D IF S 1 S =1, the Y= D 1 IF S 1 S =1, the Y= D 2 IF S 1 S =11, the Y= D 3 Thus, the output sigal Y ca be expressed as: miterm miterm miterm miterm m m1 m2 m3 Obviously, the iput selected to be passed to the output depeds o the miterm expressios of the select iputs. Figure 3: A 4 X 1 Multiplexer

3 I Geeral, For MUXes with select iputs, the output Y is give by Y = m D + m 1 D 1 + m 2 D m 2-1D 2 1 Where m i = i th miterm of the Select Iputs Thus Y = 2 1 i= m i D i Example 3: Quad 2X1 Mux Give two 4-bit umbers A ad B, desig a multiplexer that selects oe of these 2 umbers based o some select sigal S. Obviously, the output (Y) is a 4-bit umber. A A 1 A 2 A 3 Quad 2-1 MUX Y Y 1 B B 1 Y 2 Y 3 B 2 B 3 S Figure 4: Quad 2 X 1 Multiplexer The 4-bit output umber Y is defied as follows: Y = A IF S=, otherwise Y = B The circuit is implemeted usig four 2x1 Muxes, where the output of each of the Muxes gives oe of the outputs (Y i ). Combiatioal Circuit Implemetatio usig Muxes Problem Statemet: Give a fuctio of -variables, show how to use a MUX to implemet this fuctio. This ca be accomplished i oe of 2 ways: Usig a Mux with -select iputs Usig a Mux with -1 select iputs Method 1: Usig a Mux with -select iputs variables eed to be coected to select iputs. For a MUX with select iputs, the output Y is give by:

4 Y = m D + m 1 D 1 + m 2 D m 2-1 D 2 1 Alteratively, Y = Where m i = i th 2 1 i= m i D i miterm of the Select Iputs The MUX output expressio is a SUM of miterms expressio for all miterms (m i ) which have their correspodig iputs (D i ) equal to 1. Thus, it is possible to implemet ay fuctio of -variables usig a MUX with -select iputs by proper assigmet of the iput values (D i {, 1}). Y(S -1.. S 1 S ) = (miterms) Example 4: Implemet the fuctio F (A, B, C) = (1, 3, 5, 6) (see Figure 5) Sice umber of variables = 3, this requires a Mux with 3 select iputs, i.e. a 8x1 Mux The most sigificat variable A is coected to the most sigificat select iput S 2 while the least sigificat variable C is coected to the least sigificat select iput S, thus: S 2 = A, S 1 = B, ad S = C For the MUX output expressio (sum of miterms) to iclude miterm 1 we assig D 1 =1 Likewise, to iclude miterms 3, 5, ad 6 i the sum of miterms expressio while excludig miterms, 2, 4, ad 7, the followig iput (D i ) assigmets are made D 1 = D 3 = D 5 = D 6 = 1 D = D 2 = D 4 = D 7 = D 1 D1 D2 1 D3 1 D4 D5 Y F(A,B, C) = (1,3,5,6 ) 1 D6 D7 S 1 S 2 S A B C Figure 5: Implemetig fuctio with Mux with select iputs

5 Method 2: Usig a Mux with (-1) select iputs Ay -variable logic fuctio ca be implemeted usig a Mux with oly (-1) select iputs (e.g 4-to-1 mux to implemet ay 3 variable fuctio) This ca be accomplished as follows: Express fuctio i caoical sum-of-miterms form. Choose -1 variables to be coected to the mux select lies. Costruct the truth table of the fuctio, but groupig the -1 select iput variables together (e.g. by makig the -1 select variables as most sigificat iputs). The values of D i (mux iput lie) will be, or 1, or th variable or complemet of th variable of value of fuctio F, as will be clarified by the followig example. Example 5: Implemet the fuctio F (A, B, C) = (1, 2, 6, 7) (see figure 6) This fuctio ca be implemeted with a 4-to-1 lie MUX. A ad B are applied to the select lie, that is A S 1, B S The truth table of the fuctio ad the implemetatio are as show: Figure 6: Implemetig fuctio with Mux with -1 select iputs

6 Example 6: Cosider the fuctio F(A,B,C,D)= (1,3,4,11,12,13,14,15) This fuctio ca be implemeted with a 8-to-1 lie MUX (see Figure 7) A, B, ad C are applied to the select iputs as follows: A S 2, B S 1, C S The truth table ad implemetatio are show. Figure 7: Implemetig fuctio of Example 6 Demultiplexer It is a digital fuctio that performs iverse of the multiplexig operatio. It has oe iput lie (E) ad trasmits it to oe of 2 possible output lies (D, D 1, D 2,, D 2-1 ). The selectio of the specific output is cotrolled by the bit combiatio of select iputs.

7 D D 1 D 2 Movig Arm D 3 D 4 E D 5 D 2-1 Figure 8: A demultiplexer Example 7: A 1-to-4 lie Demux The iput E is directed to oe of the outputs, as specified by the two select lies S 1 ad S. D = E if S 1 S = D = S 1 S E D 1 = E if S 1 S = 1 D 1 = S 1 S E D 2 = E if S 1 S = 1 D 2 = S 1 S E D 3 = E if S 1 S = 11 D 3 = S 1 S E A careful ispectio of the Demux circuit shows that it is idetical to a 2 to 4 decoder with eable iput. E A 1 A D D 1 D 2 D 3 Figure 8: A 1-to-4 lie demultiplexer For the decoder, the iputs are A 1 ad A, ad the eable is iput E. (see figure 9) For demux, iput E provides the data, while other iputs accept the selectio variables. Although the two circuits have differet applicatios, their logic diagrams are exactly the same.

8 Decimal Eable Iputs Outputs value E A 1 A D D 1 D 2 D 3 X X Figure 9: Table for 1-to-4 lie demultiplexer

Chapter 10 Computer Design Basics

Chapter 10 Computer Design Basics Logic ad Computer Desig Fudametals Chapter 10 Computer Desig Basics Part 1 Datapaths Charles Kime & Thomas Kamiski 2004 Pearso Educatio, Ic. Terms of Use (Hyperliks are active i View Show mode) Overview

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

Searching Algorithm Efficiencies

Searching Algorithm Efficiencies Efficiecy of Liear Search Searchig Algorithm Efficiecies Havig implemeted the liear search algorithm, how would you measure its efficiecy? A useful measure (or metric) should be geeral, applicable to ay

More information

{{1}, {2, 4}, {3}} {{1, 3, 4}, {2}} {{1}, {2}, {3, 4}} 5.4 Stirling Numbers

{{1}, {2, 4}, {3}} {{1, 3, 4}, {2}} {{1}, {2}, {3, 4}} 5.4 Stirling Numbers . Stirlig Numbers Whe coutig various types of fuctios from., we quicly discovered that eumeratig the umber of oto fuctios was a difficult problem. For a domai of five elemets ad a rage of four elemets,

More information

Programmable Logic Devices Verilog Design Examples CMPE 415

Programmable Logic Devices Verilog Design Examples CMPE 415 Buildig Blocks Digital systems cosist of 2 mai parts: the datapath ad cotrol circuits. Datapath: stores ad maipulates data ad icludes compoets such as registers, shift registers, couters, multiplexers,

More information

L6: FSMs and Synchronization

L6: FSMs and Synchronization L6: FSMs ad Sychroizatio Lecture material courtesy of Rex Mi L6: 6. Sprig 24 Itroductory igital Systems Laboratory Asychroous Iputs i Sequetial Systems What about exteral sigals? Clock Sequetial System

More information

TILE PATTERNS & GRAPHING

TILE PATTERNS & GRAPHING TILE PATTERNS & GRAPHING LESSON 1 THE BIG IDEA Tile patters provide a meaigful cotext i which to geerate equivalet algebraic expressios ad develop uderstadig of the cocept of a variable. Such patters are

More information

Lesson 12. Sequences and Series

Lesson 12. Sequences and Series Retur to List of Lessos Lesso. Sequeces ad Series A ifiite sequece { a, a, a,... a,...} ca be thought of as a list of umbers writte i defiite order ad certai patter. It is usually deoted by { a } =, or

More information

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation

hp calculators HP 12C Statistics - average and standard deviation Average and standard deviation concepts HP12C average and standard deviation HP 1C Statistics - average ad stadard deviatio Average ad stadard deviatio cocepts HP1C average ad stadard deviatio Practice calculatig averages ad stadard deviatios with oe or two variables HP 1C Statistics

More information

CS100: Introduction to Computer Science

CS100: Introduction to Computer Science Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage -- Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of

More information

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling

Taking DCOP to the Real World: Efficient Complete Solutions for Distributed Multi-Event Scheduling Taig DCOP to the Real World: Efficiet Complete Solutios for Distributed Multi-Evet Schedulig Rajiv T. Maheswara, Milid Tambe, Emma Bowrig, Joatha P. Pearce, ad Pradeep araatham Uiversity of Souther Califoria

More information

Chapter Suppose you wish to use the Principle of Mathematical Induction to prove that 1 1! + 2 2! + 3 3! n n! = (n + 1)! 1 for all n 1.

Chapter Suppose you wish to use the Principle of Mathematical Induction to prove that 1 1! + 2 2! + 3 3! n n! = (n + 1)! 1 for all n 1. Chapter 4. Suppose you wish to prove that the followig is true for all positive itegers by usig the Priciple of Mathematical Iductio: + 3 + 5 +... + ( ) =. (a) Write P() (b) Write P(7) (c) Write P(73)

More information

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis

Running Time ( 3.1) Analysis of Algorithms. Experimental Studies ( 3.1.1) Limitations of Experiments. Pseudocode ( 3.1.2) Theoretical Analysis Ruig Time ( 3.) Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects.

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Engineering Data Management

Engineering Data Management BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

Chapter Gaussian Elimination

Chapter Gaussian Elimination Chapter 04.06 Gaussia Elimiatio After readig this chapter, you should be able to:. solve a set of simultaeous liear equatios usig Naïve Gauss elimiatio,. lear the pitfalls of the Naïve Gauss elimiatio

More information

0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5

0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5 Sectio 13 Kolmogorov-Smirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.

More information

Lecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009)

Lecture 13. Lecturer: Jonathan Kelner Scribe: Jonathan Pines (2009) 18.409 A Algorithmist s Toolkit October 27, 2009 Lecture 13 Lecturer: Joatha Keler Scribe: Joatha Pies (2009) 1 Outlie Last time, we proved the Bru-Mikowski iequality for boxes. Today we ll go over the

More information

Learning outcomes. Algorithms and Data Structures. Time Complexity Analysis. Time Complexity Analysis How fast is the algorithm? Prof. Dr.

Learning outcomes. Algorithms and Data Structures. Time Complexity Analysis. Time Complexity Analysis How fast is the algorithm? Prof. Dr. Algorithms ad Data Structures Algorithm efficiecy Learig outcomes Able to carry out simple asymptotic aalysisof algorithms Prof. Dr. Qi Xi 2 Time Complexity Aalysis How fast is the algorithm? Code the

More information

1 State-Space Canonical Forms

1 State-Space Canonical Forms State-Space Caoical Forms For ay give system, there are essetially a ifiite umber of possible state space models that will give the idetical iput/output dyamics Thus, it is desirable to have certai stadardized

More information

SAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx

SAMPLE QUESTIONS FOR FINAL EXAM. (1) (2) (3) (4) Find the following using the definition of the Riemann integral: (2x + 1)dx SAMPLE QUESTIONS FOR FINAL EXAM REAL ANALYSIS I FALL 006 3 4 Fid the followig usig the defiitio of the Riema itegral: a 0 x + dx 3 Cosider the partitio P x 0 3, x 3 +, x 3 +,......, x 3 3 + 3 of the iterval

More information

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find

Approximating Area under a curve with rectangles. To find the area under a curve we approximate the area using rectangles and then use limits to find 1.8 Approximatig Area uder a curve with rectagles 1.6 To fid the area uder a curve we approximate the area usig rectagles ad the use limits to fid 1.4 the area. Example 1 Suppose we wat to estimate 1.

More information

Desktop Management. Desktop Management Tools

Desktop Management. Desktop Management Tools Desktop Maagemet 9 Desktop Maagemet Tools Mac OS X icludes three desktop maagemet tools that you might fid helpful to work more efficietly ad productively: u Stacks puts expadable folders i the Dock. Clickig

More information

Cooley-Tukey. Tukey FFT Algorithms. FFT Algorithms. Cooley

Cooley-Tukey. Tukey FFT Algorithms. FFT Algorithms. Cooley Cooley Cooley-Tuey Tuey FFT Algorithms FFT Algorithms Cosider a legth- sequece x[ with a -poit DFT X[ where Represet the idices ad as +, +, Cooley Cooley-Tuey Tuey FFT Algorithms FFT Algorithms Usig these

More information

(VCP-310) 1-800-418-6789

(VCP-310) 1-800-418-6789 Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.

More information

One-step equations. Vocabulary

One-step equations. Vocabulary Review solvig oe-step equatios with itegers, fractios, ad decimals. Oe-step equatios Vocabulary equatio solve solutio iverse operatio isolate the variable Additio Property of Equality Subtractio Property

More information

Section 9.2 Series and Convergence

Section 9.2 Series and Convergence Sectio 9. Series ad Covergece Goals of Chapter 9 Approximate Pi Prove ifiite series are aother importat applicatio of limits, derivatives, approximatio, slope, ad cocavity of fuctios. Fid challegig atiderivatives

More information

Domain 1 - Describe Cisco VoIP Implementations

Domain 1 - Describe Cisco VoIP Implementations Maual ONT (642-8) 1-800-418-6789 Domai 1 - Describe Cisco VoIP Implemetatios Advatages of VoIP Over Traditioal Switches Voice over IP etworks have may advatages over traditioal circuit switched voice etworks.

More information

Section 8.3 : De Moivre s Theorem and Applications

Section 8.3 : De Moivre s Theorem and Applications The Sectio 8 : De Moivre s Theorem ad Applicatios Let z 1 ad z be complex umbers, where z 1 = r 1, z = r, arg(z 1 ) = θ 1, arg(z ) = θ z 1 = r 1 (cos θ 1 + i si θ 1 ) z = r (cos θ + i si θ ) ad z 1 z =

More information

Overview on S-Box Design Principles

Overview on S-Box Design Principles Overview o S-Box Desig Priciples Debdeep Mukhopadhyay Assistat Professor Departmet of Computer Sciece ad Egieerig Idia Istitute of Techology Kharagpur INDIA -721302 What is a S-Box? S-Boxes are Boolea

More information

5.3. Generalized Permutations and Combinations

5.3. Generalized Permutations and Combinations 53 GENERALIZED PERMUTATIONS AND COMBINATIONS 73 53 Geeralized Permutatios ad Combiatios 53 Permutatios with Repeated Elemets Assume that we have a alphabet with letters ad we wat to write all possible

More information

1 The Binomial Theorem: Another Approach

1 The Binomial Theorem: Another Approach The Biomial Theorem: Aother Approach Pascal s Triagle I class (ad i our text we saw that, for iteger, the biomial theorem ca be stated (a + b = c a + c a b + c a b + + c ab + c b, where the coefficiets

More information

Security Functions and Purposes of Network Devices and Technologies (SY0-301) 1-800-418-6789. Firewalls. Audiobooks

Security Functions and Purposes of Network Devices and Technologies (SY0-301) 1-800-418-6789. Firewalls. Audiobooks Maual Security+ Domai 1 Network Security Every etwork is uique, ad architecturally defied physically by its equipmet ad coectios, ad logically through the applicatios, services, ad idustries it serves.

More information

ARITHMETIC AND GEOMETRIC PROGRESSIONS

ARITHMETIC AND GEOMETRIC PROGRESSIONS Arithmetic Ad Geometric Progressios Sequeces Ad ARITHMETIC AND GEOMETRIC PROGRESSIONS Successio of umbers of which oe umber is desigated as the first, other as the secod, aother as the third ad so o gives

More information

if A S, then X \ A S, and if (A n ) n is a sequence of sets in S, then n A n S,

if A S, then X \ A S, and if (A n ) n is a sequence of sets in S, then n A n S, Lecture 5: Borel Sets Topologically, the Borel sets i a topological space are the σ-algebra geerated by the ope sets. Oe ca build up the Borel sets from the ope sets by iteratig the operatios of complemetatio

More information

Review for College Algebra Final Exam

Review for College Algebra Final Exam Review for College Algebra Fial Exam (Please remember that half of the fial exam will cover chapters 1-4. This review sheet covers oly the ew material, from chapters 5 ad 7.) 5.1 Systems of equatios i

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich faf@cam.ac.uk dot@dotat.at Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

Realization of Different Multiplexers by Using COG Reversible Gate

Realization of Different Multiplexers by Using COG Reversible Gate Iteratioal Joural of Electroics ad Electrical Egieerig Vol., No. 5, October 25 Realizatio of Differet Multiplexers by Usig COG Reversible Gate S. Mamataj ECE Departmet, Murshidabad College of Egieerig

More information

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here). BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly

More information

The Binomial Multi- Section Transformer

The Binomial Multi- Section Transformer 4/15/21 The Bioial Multisectio Matchig Trasforer.doc 1/17 The Bioial Multi- Sectio Trasforer Recall that a ulti-sectio atchig etwork ca be described usig the theory of sall reflectios as: where: Γ ( ω

More information

B1. Fourier Analysis of Discrete Time Signals

B1. Fourier Analysis of Discrete Time Signals B. Fourier Aalysis of Discrete Time Sigals Objectives Itroduce discrete time periodic sigals Defie the Discrete Fourier Series (DFS) expasio of periodic sigals Defie the Discrete Fourier Trasform (DFT)

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites Gregory Carey, 1998 Liear Trasformatios & Composites - 1 Liear Trasformatios ad Liear Composites I Liear Trasformatios of Variables Meas ad Stadard Deviatios of Liear Trasformatios A liear trasformatio

More information

A Gentle Introduction to Algorithms: Part II

A Gentle Introduction to Algorithms: Part II A Getle Itroductio to Algorithms: Part II Cotets of Part I:. Merge: (to merge two sorted lists ito a sigle sorted list.) 2. Bubble Sort 3. Merge Sort: 4. The Big-O, Big-Θ, Big-Ω otatios: asymptotic bouds

More information

CS103X: Discrete Structures Homework 4 Solutions

CS103X: Discrete Structures Homework 4 Solutions CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible six-figure salaries i whole dollar amouts are there that cotai at least

More information

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is 0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values

More information

Memory Interface. CEN433 King Saud University Dr. Mohammed Amer Arafah

Memory Interface. CEN433 King Saud University Dr. Mohammed Amer Arafah Memory Iterface CEN433 Kig Saud Uiversity Dr. 1 Address Decodig Whe iterfaced to a microprocessor with 20 address sigals there is a mismatch. The extra 9 address pis (A11-A19) are decoded usig a decoder

More information

Hybrid Electronics Laboratory

Hybrid Electronics Laboratory Hybrid Electronics Laboratory Design and Simulation of Decoders, Encoders, Multiplexer and Demultiplexer Aim: To study decoders, encoders, multiplexer and demultiplexer. Objectives: 1. Implement and simulate

More information

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

Module 4: Mathematical Induction

Module 4: Mathematical Induction Module 4: Mathematical Iductio Theme 1: Priciple of Mathematical Iductio Mathematical iductio is used to prove statemets about atural umbers. As studets may remember, we ca write such a statemet as a predicate

More information

Baan Service Master Data Management

Baan Service Master Data Management Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :

More information

Design with Multiplexers

Design with Multiplexers Design with Multiplexers Consider the following design, taken from the 5 th edition of my textbook. This is a correct implementation of the Carry Out of a Full Adder. In terms of Boolean expressions, this

More information

hp calculators HP 12C Platinum Statistics - correlation coefficient The correlation coefficient HP12C Platinum correlation coefficient

hp calculators HP 12C Platinum Statistics - correlation coefficient The correlation coefficient HP12C Platinum correlation coefficient HP 1C Platium Statistics - correlatio coefficiet The correlatio coefficiet HP1C Platium correlatio coefficiet Practice fidig correlatio coefficiets ad forecastig HP 1C Platium Statistics - correlatio coefficiet

More information

Fourier Analysis. f () t = + cos[5 t] + cos[10 t] + sin[5 t] + sin[10 t] x10 Pa

Fourier Analysis. f () t = + cos[5 t] + cos[10 t] + sin[5 t] + sin[10 t] x10 Pa Fourier Aalysis I our Mathematics classes, we have bee taught that complicated uctios ca ote be represeted as a log series o terms whose sum closely approximates the actual uctio. aylor series is oe very

More information

I. Harmonic Components of Periodic Signals Consider that signal

I. Harmonic Components of Periodic Signals Consider that signal ECE Sigals ad Systems Sprig, UMD Experimet 5: Fourier Series Cosider the cotiuous time sigal give by y(t) = A + A cos (π f ) + A cos (π f ) + A cos (6π f ) +.. where A is the DC compoet of the sigal, A

More information

when n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on.

when n = 1, 2, 3, 4, 5, 6, This list represents the amount of dollars you have after n days. Note: The use of is read as and so on. Geometric eries Before we defie what is meat by a series, we eed to itroduce a related topic, that of sequeces. Formally, a sequece is a fuctio that computes a ordered list. uppose that o day 1, you have

More information

Does the problem need access to data files or data bases?

Does the problem need access to data files or data bases? 19 PROGRAM DESIGN INTRODUCTION Although there are may desig techiques that we could discuss we shall keep thigs simple ad talk about oly two geeric techiques based o two major ideas i programmig: procedures,

More information

E-Plex Enterprise Access Control System

E-Plex Enterprise Access Control System Eterprise Access Cotrol System Egieered for Flexibility Modular Solutio The Eterprise Access Cotrol System is a modular solutio for maagig access poits. Employig a variety of hardware optios, system maagemet

More information

represented by 4! different arrangements of boxes, divide by 4! to get ways

represented by 4! different arrangements of boxes, divide by 4! to get ways Problem Set #6 solutios A juggler colors idetical jugglig balls red, white, ad blue (a I how may ways ca this be doe if each color is used at least oce? Let us preemptively color oe ball i each color,

More information

Asymptotic Growth of Functions

Asymptotic Growth of Functions CMPS Itroductio to Aalysis of Algorithms Fall 3 Asymptotic Growth of Fuctios We itroduce several types of asymptotic otatio which are used to compare the performace ad efficiecy of algorithms As we ll

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

Distributions of Order Statistics

Distributions of Order Statistics Chapter 2 Distributios of Order Statistics We give some importat formulae for distributios of order statistics. For example, where F k: (x)=p{x k, x} = I F(x) (k, k + 1), I x (a,b)= 1 x t a 1 (1 t) b 1

More information

Lecture Notes CMSC 251

Lecture Notes CMSC 251 We have this messy summatio to solve though First observe that the value remais costat throughout the sum, ad so we ca pull it out frot Also ote that we ca write 3 i / i ad (3/) i T () = log 3 (log ) 1

More information

EUROCONTROL PRISMIL. EUROCONTROL civil-military performance monitoring system

EUROCONTROL PRISMIL. EUROCONTROL civil-military performance monitoring system EUROCONTROL PRISMIL EUROCONTROL civil-military performace moitorig system Itroductio What is PRISMIL? PRISMIL is a olie civil-military performace moitorig system which facilitates the combied performace

More information

Power Factor in Electrical Power Systems with Non-Linear Loads

Power Factor in Electrical Power Systems with Non-Linear Loads Power Factor i Electrical Power Systems with No-Liear Loads By: Gozalo Sadoval, ARTECHE / INELAP S.A. de C.V. Abstract. Traditioal methods of Power Factor Correctio typically focus o displacemet power

More information

Ekkehart Schlicht: Economic Surplus and Derived Demand

Ekkehart Schlicht: Economic Surplus and Derived Demand Ekkehart Schlicht: Ecoomic Surplus ad Derived Demad Muich Discussio Paper No. 2006-17 Departmet of Ecoomics Uiversity of Muich Volkswirtschaftliche Fakultät Ludwig-Maximilias-Uiversität Müche Olie at http://epub.ub.ui-mueche.de/940/

More information

Safety Requirements engineering and Proof of implementation

Safety Requirements engineering and Proof of implementation Presetatio to DVClub commuity October 20 th 2015 Safety Requiremets egieerig ad Proof of implemetatio Test ad Verificatio Solutios Deliverig Tailored Solutios for Hardware Verificatio ad Software Testig

More information

ISOLATION TRANSFORMER. FOR 3 rd HARMONIC FILTERING TSA INSTRUCTIONS MANUAL M A

ISOLATION TRANSFORMER. FOR 3 rd HARMONIC FILTERING TSA INSTRUCTIONS MANUAL M A ISOLATION TRANSFORMER FOR 3 rd HARMONIC FILTERING TSA INSTRUCTIONS MANUAL M-983-0A INTRODUCTION There is a lot of electrical supply istallatios where most of the loads are sigle phase, supplyig a rectifier

More information

Chapter 5 An Introduction to Vector Searching and Sorting

Chapter 5 An Introduction to Vector Searching and Sorting Chapter 5 A Itroductio to Vector Searchig ad Sortig Searchig ad sortig are two of the most frequetly performed computig tasks. I this chapter we will examie several elemetary searchig ad sortig algorithms

More information

Algebra Work Sheets. Contents

Algebra Work Sheets. Contents The work sheets are grouped accordig to math skill. Each skill is the arraged i a sequece of work sheets that build from simple to complex. Choose the work sheets that best fit the studet s eed ad will

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Measurable Functions

Measurable Functions Measurable Fuctios Dug Le 1 1 Defiitio It is ecessary to determie the class of fuctios that will be cosidered for the Lebesgue itegratio. We wat to guaratee that the sets which arise whe workig with these

More information

8.1 Arithmetic Sequences

8.1 Arithmetic Sequences MCR3U Uit 8: Sequeces & Series Page 1 of 1 8.1 Arithmetic Sequeces Defiitio: A sequece is a comma separated list of ordered terms that follow a patter. Examples: 1, 2, 3, 4, 5 : a sequece of the first

More information

Section IV.5: Recurrence Relations from Algorithms

Section IV.5: Recurrence Relations from Algorithms Sectio IV.5: Recurrece Relatios from Algorithms Give a recursive algorithm with iput size, we wish to fid a Θ (best big O) estimate for its ru time T() either by obtaiig a explicit formula for T() or by

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

Engineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51

Engineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51 Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log

More information

Chapter 5: Inner Product Spaces

Chapter 5: Inner Product Spaces Chapter 5: Ier Product Spaces Chapter 5: Ier Product Spaces SECION A Itroductio to Ier Product Spaces By the ed of this sectio you will be able to uderstad what is meat by a ier product space give examples

More information

Lesson 15 ANOVA (analysis of variance)

Lesson 15 ANOVA (analysis of variance) Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

More information

Authentication - Access Control Default Security Active Directory Trusted Authentication Guest User or Anonymous (un-authenticated) Logging Out

Authentication - Access Control Default Security Active Directory Trusted Authentication Guest User or Anonymous (un-authenticated) Logging Out FME Server Security Table of Cotets FME Server Autheticatio - Access Cotrol Default Security Active Directory Trusted Autheticatio Guest User or Aoymous (u-autheticated) Loggig Out Authorizatio - Roles

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

ORDERS OF GROWTH KEITH CONRAD

ORDERS OF GROWTH KEITH CONRAD ORDERS OF GROWTH KEITH CONRAD Itroductio Gaiig a ituitive feel for the relative growth of fuctios is importat if you really wat to uderstad their behavior It also helps you better grasp topics i calculus

More information

A probabilistic proof of a binomial identity

A probabilistic proof of a binomial identity A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two

More information

Lecture 10: Ray Tracing and Constructive Solid Geometry. Interactive Computer Graphics. Ray tracing with secondary rays. Ray tracing: Shadows

Lecture 10: Ray Tracing and Constructive Solid Geometry. Interactive Computer Graphics. Ray tracing with secondary rays. Ray tracing: Shadows Iteractive Computer Graphics Lecture 10: Ray Tracig ad Costructive Solid Geometry Ray tracig with secodary rays Ray tracig usig just primary rays produces images similar to ormal polygo rederig techiques

More information

x(x 1)(x 2)... (x k + 1) = [x] k n+m 1

x(x 1)(x 2)... (x k + 1) = [x] k n+m 1 1 Coutig mappigs For every real x ad positive iteger k, let [x] k deote the fallig factorial ad x(x 1)(x 2)... (x k + 1) ( ) x = [x] k k k!, ( ) k = 1. 0 I the sequel, X = {x 1,..., x m }, Y = {y 1,...,

More information

Mathematical goals. Starting points. Materials required. Time needed

Mathematical goals. Starting points. Materials required. Time needed Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

More information

Message Exchange in the Utility Market Using SAP for Utilities. Point of View by Marc Metz and Maarten Vriesema

Message Exchange in the Utility Market Using SAP for Utilities. Point of View by Marc Metz and Maarten Vriesema Eergy, Utilities ad Chemicals the way we see it Message Exchage i the Utility Market Usig SAP for Utilities Poit of View by Marc Metz ad Maarte Vriesema Itroductio Liberalisatio of utility markets has

More information

A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design

A Combined Continuous/Binary Genetic Algorithm for Microstrip Antenna Design A Combied Cotiuous/Biary Geetic Algorithm for Microstrip Atea Desig Rady L. Haupt The Pesylvaia State Uiversity Applied Research Laboratory P. O. Box 30 State College, PA 16804-0030 haupt@ieee.org Abstract:

More information

T R A N S F O R M E R A C C E S S O R I E S SAM REMOTE CONTROL SYSTEM

T R A N S F O R M E R A C C E S S O R I E S SAM REMOTE CONTROL SYSTEM REMOTE CONTROL SYSTEM REMOTE CONTROL SYSTEM TYPE MRCS T R A N S F O R M E R A C C E S S O R I E S PLN.03.08 CODE NO: 720 (20A.) CODE NO: 72400 / 800 (400/800A.) CODE NO: 73000 (000A.). GENERAL This system

More information

Finding the circle that best fits a set of points

Finding the circle that best fits a set of points Fidig the circle that best fits a set of poits L. MAISONOBE October 5 th 007 Cotets 1 Itroductio Solvig the problem.1 Priciples............................... Iitializatio.............................

More information

Configuring Additional Active Directory Server Roles

Configuring Additional Active Directory Server Roles Maual Upgradig your MCSE o Server 2003 to Server 2008 (70-649) 1-800-418-6789 Cofigurig Additioal Active Directory Server Roles Active Directory Lightweight Directory Services Backgroud ad Cofiguratio

More information

Combinational Circuits (Part II) Notes

Combinational Circuits (Part II) Notes Combinational Circuits (Part II) Notes This part of combinational circuits consists of the class of circuits based on data transmission and code converters. These circuits are multiplexers, de multiplexers,

More information

Chapter 25. Waveforms

Chapter 25. Waveforms Chapter 5 Nosiusoidal Waveforms Waveforms Used i electroics except for siusoidal Ay periodic waveform may be expressed as Sum of a series of siusoidal waveforms at differet frequecies ad amplitudes 1 Waveforms

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

Lecture 16: Address decoding

Lecture 16: Address decoding Lecture 16: Address decodi Itroductio to address decodi Full address decodi Partial address decodi Implemeti address decoders Examples Microprocessor-based System Desi Ricardo Gutierrez-Osua Wriht State

More information

Properties of MLE: consistency, asymptotic normality. Fisher information.

Properties of MLE: consistency, asymptotic normality. Fisher information. Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout

More information

Infinite Sequences and Series

Infinite Sequences and Series CHAPTER 4 Ifiite Sequeces ad Series 4.1. Sequeces A sequece is a ifiite ordered list of umbers, for example the sequece of odd positive itegers: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...

More information