Questions About Numbers. Number Systems and Arithmetic. Introduction to Binary Numbers. Negative Numbers?
|
|
- Myles Arnold
- 6 years ago
- Views:
Transcription
1 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? identify errors (e.g. overflow)? Wht is n nd wht does it look klik like? =rithmetic logic unit Introduction to Binry Numbers Consider 4-bit binry number Deciml Binry Deciml Binry Exmples of binry rithmetic: = 5 = 6 Negtive Numbers? We would like number system tht provides obvious representtion of,,... uses dder for ddition single vlue of equl coverge of positive nd negtive numbers esy detection of sign esy negtion
2 Some Alterntives Sign Mgnitude -- MSB is sign bit, rest the sme - == -5 == One s complement -- flip ll bits to negte - == -5 == Two s Complement Representtion s complement representtion ti of negtive numbers Tke the bitwise inverse nd dd Biggest 4-bit Binry Number: 7 Smllest 4-bit Binry Number: -8 Deciml Two s Complement Binry Two s Complement Arithmetic Deciml s Complement Binry Deciml s Complement Binry Exmples: 7-6 = 7 (- 6) = - 5 = (- 5) = - Some Things We Wnt To Know About Our Number System negtion sign extension =>,, - =>,, overflow detection 5 6
3 Detection Instruction Fetch Arithmetic -- The hert of finstruction ti execution -4 Instruction Decode Opernd Fetch opertion Execute Store b result So how do we detect overflow? Next Instruction Designing n Arithmetic Logic Unit A B N N op N Zero Control Lines (op) Function And Or Add Subtrct Set-on-less-thn A One Bit This -bit will perform AND, OR, nd ADD b
4 A -bit -bit -bit b b How About Subtrction? Keep in mind the following: (A - B) is the sme s: A (-B) s s Complement negte: Tke the inverse of every bit nd dd Bit-wise inverse of B is!b: A - B = A (-B) = A (!B ) = A!B Binvert b b b b Detection Logic Crry into MSB! = Crry out of MSB For N-bit : = [N - ] XOR [N - ] A -bit B A -bit B A -bit B A -bit B X Y X XOR Y Zero Detection Logic Zero Detection Logic is just one BIG NOR gte Any non-zero input to the NOR gte will cuse its output to be zero A B A B A B A B -bit -bit -bit -bit
5 Set-on-less-thn Binvert b Binvert Full Bnegte Do subtrct use sign bit route to bit of result ll other bits zero. Binvert b b b b b b b wht signls ccomplish: Binvert CIn Oper dd? sub? nd? or? beq? slt? Zero Set b. detection b b Set Set sign bit (dder output from bit ) The Disdvntge of Ripple Crry MULTIPLY The dder we just built is clled Ripple Crry Adder The crry bit my hve to propgte from LSB to MSB Worst cse dely for n N-bit RC dder: N-gte dely A -bit B A -bit B A -bit B A -bit B A B Pper nd pencil exmple: Multiplicnd Multiplier x Product =? m bits x n bits = mn bit product Binry mkes it esy: => plce ( x multiplicnd) => plce multiplicnd ( x multiplicnd) The point -> ripple crry dders re slow. Fster ddition schemes re possible tht ccelerte the movement of the crry from one end to the other.
6 MULTIPLY HARDWARE Observtions on Multiply 64-bit Multiplicnd reg, 64-bit, 64-bit Product reg, -bit multiplier reg 64-bit Multiplicnd Shift left 64 bits Multiplier Shift right bits MIPS registers Hi nd Lo re left nd right hlf of Product Gives us MIPS instruction MultU Wht bout signed multipliction? esiest solution is to mke both positive & remember whether to complement product when done. Product 64 bits Write Control test Divide: Pper & Pencil DIVIDE HARDWARE Divisor Quotient Dividend 64-bit Divisor reg, 64-bit, 64-bit Reminder reg, -bit Quotient reg Divisor 64 bits Shift right Reminder See how big number cn be subtrcted, creting quotient bit on ech step Binry => * divisor or * divisor Dividend = Quotient x Divisor Reminder 64-bit Reminder 64 bits Write Control test Quotient Shift left bits
7 Divide Hrdwre Hi nd Lo registers in MIPS combine to ct s 64-bit register for multiply nd divide Signed Divides: id Simplest is to remember signs, mke positive, nd complement quotient nd reminder if necessry Note: Dividend nd Reminder must hve sme sign Note: Quotient negted if Divisor sign & Dividend sign disgree Key Points Instruction Set drives the design performnce, CPU clock speed driven by dder dely Multipliction nd division tke much longer thn ddition, requiring multiple ddition steps. Binry Frctions = x x x x so.... = x x x x - x - x - e.g.,.75 = /4 = / = / /4 =. sign Recll Scientific Nottion deciml point Mntiss exponent x.67 x rdix (bse) Issues: Arithmetic (, -, *, / ) Representtion, Norml form Rnge nd Precision Rounding Exceptions (e.g., divide by zero, overflow, underflow) Errors Properties ( negtion, inversion, if A = B then A - B = )
8 Floting-Point Numbers Representtion of floting point numbers in IEEE 754 stndrd: 8 single precision sign S E M exponent: excess 7 binry integer (ctul exponent is e = E - 7) mntiss: sign mgnitude, normlized binry significnd w/ hidden integer bit:.m N = (-) S E-7(.M) < E < 55 = =... 5 = X =. X 8 =. =... X =... X - =... rnge of bout X -8 to X 8 lwys normlized (so lwys leding, thus never shown) specil representtion of (E = ) (why?) cn do integer compre for greter-thn, sign Wht do you notice?.5 * -.75 * -.5 *.75* Does this work with negtive numbers, s well? Double Precision Floting Point Floting Point Addition Representtion of floting point numbers in IEEE 754 stndrd: double precision sign S E M M exponent: mntiss: excess binry integer sign mgnitude, normlized binry significnd w/ hidden ctul exponent is e = E - integer bit:.m N = (-) S E-(.M) < E < 48 5 () bit mntiss rnge of bout X -8 to X 8 How do you dd in scientific nottion? 9.96 x 4 5. x Bsic Algorithm. Align. Add. Normlize 4. Round
9 FP Addition Hrdwre Sign Exponent Significnd Sign Exponent Significnd Floting Point Multipliction Smll Exponent difference Compre exponents How do you multiply in scientific nottion? (9.9 x 4 )(5. x ) = 5.48 x 7 Control Increment or decrement Shift right Rounding hrdwre Big Shift left or right Shift smller number right Add Normlize Round Bsic Algorithm. Add exponents. Multiply. Normlize 4. Round 5. Set Sign Sign Exponent Significnd FP Accurcy Extremely importnt in scientific clcultions Very tiny errors cn ccumulte over time IEEE 754 FP stndrd hs four rounding modes lwys round up (towrd ) lwys round down (towrd - ) truncte round dto nerest => in cse of tie, round to nerest even Requires extr bits in intermedite representtions Key Points Floting Point extends the rnge of numbers tht cn be represented, t the expense of precision (ccurcy). FP opertions re very similr il to integer, but with pre- nd post-processing. Rounding implementtion is criticl to ccurcy over time.
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 informationWhat 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 informationNumber Systems and Computer Arithmetic
Number Systems and Computer Arithmetic Counting to four billion two fingers at a time What do all those bits mean now? bits (011011011100010...01) instruction R-format I-format... integer data number text
More informationRepresentation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation
Representtion of Numbers Number Representtion Computer represent ll numbers, other thn integers nd some frctions with imprecision. Numbers re stored in some pproximtion which cn be represented by fixed
More informationCourse Administration
/4/7 Spring 7 EE 363: Computer Orgniztion Arithmetic for Computers Numer Representtion & ALU Avinsh Kodi Deprtment of Electricl Engineering & Computer Science Ohio University, Athens, Ohio 457 E-mil: kodi@ohio.edu
More informationDivide: Paper & Pencil
Divide: Paper & Pencil 1001 Quotient Divisor 1000 1001010 Dividend -1000 10 101 1010 1000 10 Remainder See how big a number can be subtracted, creating quotient bit on each step Binary => 1 * divisor or
More informationStack Manipulation. Other Issues. How about larger constants? Frame Pointer. PowerPC. Alternative Architectures
Other Issues Stck Mnipultion support for procedures (Refer to section 3.6), stcks, frmes, recursion mnipulting strings nd pointers linkers, loders, memory lyout Interrupts, exceptions, system clls nd conventions
More informationComputer 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 information12-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 informationBasics of Logic Design Arithmetic Logic Unit (ALU)
Bsics of Logic Design Arithmetic Logic Unit (ALU) CPS 4 Lecture 9 Tody s Lecture Homework #3 Assigned Due Mrch 3 Project Groups ssigned & posted to lckord. Project Specifiction is on We Due April 9 Building
More informationEngineer 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 informationParallel Square and Cube Computations
Prllel Squre nd Cube Computtions Albert A. Liddicot nd Michel J. Flynn Computer Systems Lbortory, Deprtment of Electricl Engineering Stnford University Gtes Building 5 Serr Mll, Stnford, CA 945, USA liddicot@stnford.edu
More informationSystems 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 informationSubtracting 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 informationFloating Point Numbers and Interval Arithmetic
480: 05092008 -- floting point; intervl rith Floting Point Numbers nd Intervl Arithmetic Are floting point numbers just broken? (from http://www.cs.princeton.edu/introcs) To mthemticin like me floting
More information10.5 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 informationUnit 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 informationSection 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 informationECEN 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 informationCOMP 303 Computer Architecture Lecture 6
COMP 303 Computer Architecture Lecture 6 MULTIPLY (unsigned) Paper and pencil example (unsigned): Multiplicand 1000 = 8 Multiplier x 1001 = 9 1000 0000 0000 1000 Product 01001000 = 72 n bits x n bits =
More information9 4. CISC - Curriculum & Instruction Steering Committee. California County Superintendents Educational Services Association
9. CISC - Curriculum & Instruction Steering Committee The Winning EQUATION A HIGH QUALITY MATHEMATICS PROFESSIONAL DEVELOPMENT PROGRAM FOR TEACHERS IN GRADES THROUGH ALGEBRA II STRAND: NUMBER SENSE: Rtionl
More information1. 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 information5 Regular 4-Sided Composition
Xilinx-Lv User Guide 5 Regulr 4-Sided Composition This tutoril shows how regulr circuits with 4-sided elements cn be described in Lv. The type of regulr circuits tht re discussed in this tutoril re those
More informationSIMPLIFYING 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 informationConcepts Introduced. A 1-Bit Logical Unit. 1-Bit Half Adder (cont.) 1-Bit Half Adder
oncepts Introduced A -Bit Logicl Unit sic rithmetic/logic unit clocks ltches nd ip-ops registers SRAMs nd RAMs nite stte mchines Below is -it logicl unit tht performs AN nd OR opertions Both the AN nd
More informationDigital Design. Chapter 1: Introduction. Digital Design. Copyright 2006 Frank Vahid
Chpter : Introduction Copyright 6 Why Study?. Look under the hood of computers Solid understnding --> confidence, insight, even better progrmmer when wre of hrdwre resource issues Electronic devices becoming
More informationRational Numbers---Adding Fractions With Like Denominators.
Rtionl Numbers---Adding Frctions With Like Denomintors. A. In Words: To dd frctions with like denomintors, dd the numertors nd write the sum over the sme denomintor. B. In Symbols: For frctions c nd b
More informationDigital Design. Chapter 4: Datapath Components
Digitl Design Chpter 4: Dtpth Components Slides to ccompny the textbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com Copyright
More information9.1 apply the distance and midpoint formulas
9.1 pply the distnce nd midpoint formuls DISTANCE FORMULA MIDPOINT FORMULA To find the midpoint between two points x, y nd x y 1 1,, we Exmple 1: Find the distnce between the two points. Then, find the
More informationTailoring the 32-Bit ALU to MIPS
Tailoring the 32-Bit ALU to MIPS MIPS ALU extensions Overflow detection: Carry into MSB XOR Carry out of MSB Branch instructions Shift instructions Slt instruction Immediate instructions ALU performance
More informationSmall 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 informationChapter 4: Datapath Components. Instructor: Dr. Hyunyoung Lee. Copyright Based on slides by Frank Vahid. Frank Vahid
Chpter 4: Dtpth Components Instructor: Dr. Hyunyoung Lee Bsed on slides by Copyright 2 Instructors of courses requiring Vhid's Digitl Design textbook (published by John Wiley nd Sons) hve permission to
More information10/9/2012. Operator is an operation performed over data at runtime. Arithmetic, Logical, Comparison, Assignment, Etc. Operators have precedence
/9/22 P f Performing i Si Simple l Clcultions C l l ti with ith C#. Opertors in C# nd Opertor Precedence 2. Arithmetic Opertors 3. Logicl Opertors 4. Bitwise Opertors 5. Comprison Opertors 6. Assignment
More informationCOMPUTER SCIENCE 123. Foundations of Computer Science. 6. Tuples
COMPUTER SCIENCE 123 Foundtions of Computer Science 6. Tuples Summry: This lecture introduces tuples in Hskell. Reference: Thompson Sections 5.1 2 R.L. While, 2000 3 Tuples Most dt comes with structure
More informationVerification of Floating-Point Adders
Verifiction of Floting-Point Adders Yirng-An Chen nd Rndl E. Brynt ychen+@cs.cmu.edu brynt+@cs.cmu.edu Computer cience Dept. Crnegie Mellon Univ. Pittsburgh PA 15213 Abstrct. The floting-point(fp) division
More informationGeorge Boole. IT 3123 Hardware and Software Concepts. Switching Algebra. Boolean Functions. Boolean Functions. Truth Tables
George Boole IT 3123 Hrdwre nd Softwre Concepts My 28 Digitl Logic The Little Mn Computer 1815 1864 British mthemticin nd philosopher Mny contriutions to mthemtics. Boolen lger: n lger over finite sets
More informationEECS 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 informationReview: MIPS Organization
1 MIPS Arithmetic Review: MIPS Organization Processor Memory src1 addr 5 src2 addr 5 dst addr 5 write data Register File registers ($zero - $ra) bits src1 data src2 data read/write addr 1 1100 2 30 words
More informationx )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 informationGeometric transformations
Geometric trnsformtions Computer Grphics Some slides re bsed on Shy Shlom slides from TAU mn n n m m T A,,,,,, 2 1 2 22 12 1 21 11 Rows become columns nd columns become rows nm n n m m A,,,,,, 1 1 2 22
More information2 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 informationCSE 141 Computer Architecture Summer Session Lecture 3 ALU Part 2 Single Cycle CPU Part 1. Pramod V. Argade
CSE 141 Computer Architecture Summer Session 1 2004 Lecture 3 ALU Part 2 Single Cycle CPU Part 1 Pramod V. Argade Reading Assignment Announcements Chapter 5: The Processor: Datapath and Control, Sec. 5.3-5.4
More informationEngineer-to-Engineer Note
Engineer-to-Engineer Note EE-270 Technicl notes on using Anlog Devices DSPs, processors nd development tools Contct our technicl support t processor.support@nlog.com nd dsptools.support@nlog.com Or visit
More informationComputer Organization and Structure. Bing-Yu Chen National Taiwan University
Computer Organization and Structure Bing-Yu Chen National Taiwan University Arithmetic for Computers Addition and Subtraction Gate Logic and K-Map Method Constructing a Basic ALU Arithmetic Logic Unit
More informationMIPS Integer ALU Requirements
MIPS Integer ALU Requirements Add, AddU, Sub, SubU, AddI, AddIU: 2 s complement adder/sub with overflow detection. And, Or, Andi, Ori, Xor, Xori, Nor: Logical AND, logical OR, XOR, nor. SLTI, SLTIU (set
More informationMIPS 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 informationToday s Lecture. Basics of Logic Design: Boolean Algebra, Logic Gates. Recursive Example. Review: The C / C++ code. Recursive Example (Continued)
Tod s Lecture Bsics of Logic Design: Boolen Alger, Logic Gtes Alvin R. Leeck CPS 4 Lecture 8 Homework #2 Due Ferur 3 Outline Review (sseml recursion) Building the uilding locks Logic Design Truth tles,
More informationSmall 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 informationChapter 1: Introduction
Chpter : Introduction Slides to ccompny the textbook, First Edition, by, John Wiley nd Sons Publishers, 7. http://www.ddvhid.com Copyright 7 Instructors of courses requiring Vhid's textbook (published
More informationMA1008. 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 informationCMU 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 informationΕΠΛ323 - 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 informationBefore We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1):
Overview (): Before We Begin Administrtive detils Review some questions to consider Winter 2006 Imge Enhncement in the Sptil Domin: Bsics of Sptil Filtering, Smoothing Sptil Filters, Order Sttistics Filters
More informationModule 2: Computer Arithmetic
Module 2: Computer Arithmetic 1 B O O K : C O M P U T E R O R G A N I Z A T I O N A N D D E S I G N, 3 E D, D A V I D L. P A T T E R S O N A N D J O H N L. H A N N E S S Y, M O R G A N K A U F M A N N
More informationSection 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 informationDynamic 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 informationSmall 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 information4452 Mathematical Modeling Lecture 4: Lagrange Multipliers
Mth Modeling Lecture 4: Lgrnge Multipliers Pge 4452 Mthemticl Modeling Lecture 4: Lgrnge Multipliers Lgrnge multipliers re high powered mthemticl technique to find the mximum nd minimum of multidimensionl
More informationSmall 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 informationSmall 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 informationComputer Architecture. Chapter 3: Arithmetic for Computers
182.092 Computer Architecture Chapter 3: Arithmetic for Computers Adapted from Computer Organization and Design, 4 th Edition, Patterson & Hennessy, 2008, Morgan Kaufmann Publishers and Mary Jane Irwin
More information6.2 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 informationToday. CS 188: Artificial Intelligence Fall Recap: Search. Example: Pancake Problem. Example: Pancake Problem. General Tree Search.
CS 88: Artificil Intelligence Fll 00 Lecture : A* Serch 9//00 A* Serch rph Serch Tody Heuristic Design Dn Klein UC Berkeley Multiple slides from Sturt Russell or Andrew Moore Recp: Serch Exmple: Pncke
More informationEE260: Logic Design, Spring n Integer multiplication. n Booth s algorithm. n Integer division. n Restoring, non-restoring
EE 260: Introduction to Digital Design Arithmetic II Yao Zheng Department of Electrical Engineering University of Hawaiʻi at Mānoa Overview n Integer multiplication n Booth s algorithm n Integer division
More informationSmall 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 informationDigital Signal Processing: A Hardware-Based Approach
Digitl Signl Processing: A Hrdwre-Bsed Approch Roert Esposito Electricl nd Computer Engineering Temple University troduction Teching Digitl Signl Processing (DSP) hs included the utilition of simultion
More informationIntegration. September 28, 2017
Integrtion September 8, 7 Introduction We hve lerned in previous chpter on how to do the differentition. It is conventionl in mthemtics tht we re supposed to lern bout the integrtion s well. As you my
More informationLAB L Hardware Building Blocks
LAB L Hrdwre Building Blocks Perform the following groups of tsks: LL1.v 1. In previous l we creted the 2-to-1 mux shown in the left prt of the figure elow nd found tht it cts s n if sttement. c c 0 1
More informationSmall 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 informationSmall 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 informationMATH 25 CLASS 5 NOTES, SEP
MATH 25 CLASS 5 NOTES, SEP 30 2011 Contents 1. A brief diversion: reltively prime numbers 1 2. Lest common multiples 3 3. Finding ll solutions to x + by = c 4 Quick links to definitions/theorems Euclid
More informationAccelerating 3D convolution using streaming architectures on FPGAs
Accelerting 3D convolution using streming rchitectures on FPGAs Hohun Fu, Robert G. Clpp, Oskr Mencer, nd Oliver Pell ABSTRACT We investigte FPGA rchitectures for ccelerting pplictions whose dominnt cost
More information50 AMC LECTURES Lecture 2 Analytic Geometry Distance and Lines. can be calculated by the following formula:
5 AMC LECTURES Lecture Anlytic Geometry Distnce nd Lines BASIC KNOWLEDGE. Distnce formul The distnce (d) between two points P ( x, y) nd P ( x, y) cn be clculted by the following formul: d ( x y () x )
More informationEECS150 - 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 informationStudy Guide for Exam 3
Mth 05 Elementry Algebr Fll 00 Study Guide for Em Em is scheduled for Thursdy, November 8 th nd ill cover chpters 5 nd. You my use "5" note crd (both sides) nd scientific clcultor. You re epected to no
More informationLecture 10 Evolutionary Computation: Evolution strategies and genetic programming
Lecture 10 Evolutionry Computtion: Evolution strtegies nd genetic progrmming Evolution strtegies Genetic progrmming Summry Negnevitsky, Person Eduction, 2011 1 Evolution Strtegies Another pproch to simulting
More informationa < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1
Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the
More informationSimplifying 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 informationCOMPUTER ORGANIZATION AND DESIGN
COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface 5 th Edition Chapter 3 Arithmetic for Computers Arithmetic for Computers Operations on integers Addition and subtraction Multiplication
More information6/23/2011. Review: IEEE-754. CSE 2021: Computer Organization. Exercises. Examples. Shakil M. Khan (adapted from Profs. Roumani & Asif)
6/23/2 CSE 22: Computer Orgniztion Lecture-8() Floting point computing (IEEE 754) Review: IEEE-754 single: 8 its doule: its single: 23 its doule: 52 its S Exponent Frction S x ( ) ( Frction) 2 (Exponent
More informationTransparent neutral-element elimination in MPI reduction operations
Trnsprent neutrl-element elimintion in MPI reduction opertions Jesper Lrsson Träff Deprtment of Scientific Computing University of Vienn Disclimer Exploiting repetition nd sprsity in input for reducing
More informationCSE 401 Midterm Exam 11/5/10 Sample Solution
Question 1. egulr expressions (20 points) In the Ad Progrmming lnguge n integer constnt contins one or more digits, but it my lso contin embedded underscores. Any underscores must be preceded nd followed
More informationApproximate computations
Living with floting-point numers Stndrd normlized representtion (sign + frction + exponent): Approximte computtions Rnges of vlues: Representtions for:, +, +0, 0, NN (not numer) Jordi Cortdell Deprtment
More informationDigital Design. Chapter 6: Optimizations and Tradeoffs
Digitl Design Chpter 6: Optimiztions nd Trdeoffs Slides to ccompny the tetbook Digitl Design, with RTL Design, VHDL, nd Verilog, 2nd Edition, by Frnk Vhid, John Wiley nd Sons Publishers, 2. http://www.ddvhid.com
More informationFault injection attacks on cryptographic devices and countermeasures Part 2
Fult injection ttcks on cryptogrphic devices nd countermesures Prt Isrel Koren Deprtment of Electricl nd Computer Engineering University of Msschusetts Amherst, MA Countermesures - Exmples Must first detect
More informationAngle properties of lines and polygons
chievement Stndrd 91031 pply geometric resoning in solving problems Copy correctly Up to 3% of workbook Copying or scnning from ES workbooks is subject to the NZ Copyright ct which limits copying to 3%
More informationRay surface intersections
Ry surfce intersections Some primitives Finite primitives: polygons spheres, cylinders, cones prts of generl qudrics Infinite primitives: plnes infinite cylinders nd cones generl qudrics A finite primitive
More informationa(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 informationLecture Topics. Announcements. Today: Integer Arithmetic (P&H ) Next: The MIPS ISA (P&H ) Consulting hours. Milestone #1 (due 1/26)
Lecture Topics Today: Integer Arithmetic (P&H 3.1-3.4) Next: The MIPS ISA (P&H 2.1-2.14) 1 Announcements Consulting hours Milestone #1 (due 1/26) Milestone #2 (due 2/2) 2 1 Review: Integer Operations Internal
More informationMatrices 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 information361 div.1. Computer Architecture EECS 361 Lecture 7: ALU Design : Division
361 div.1 Computer Architecture EECS 361 Lecture 7: ALU Design : Division Outline of Today s Lecture Introduction to Today s Lecture Divide Questions and Administrative Matters Introduction to Single cycle
More informationALU Design. 1-bit Full Adder 4-bit Arithmetic circuits. Arithmetic and Logic Unit Flags. Add/Subtract/Increament/Decrement Circuit
LU Design -bit Full dder 4-bit rithmetic circuits dd/subtract/increament/decrement Circuit rithmetic and Logic Unit Flags Carry-Out, Sign, Zero, Overflow Shift and Rotate t Operations COE2 (Fall27) LU
More informationComputer Architecture Set Four. Arithmetic
Computer Architecture Set Four Arithmetic Arithmetic Where we ve been: Performance (seconds, cycles, instructions) Abstractions: Instruction Set Architecture Assembly Language and Machine Language What
More informationAn Efficient Divide and Conquer Algorithm for Exact Hazard Free Logic Minimization
An Efficient Divide nd Conquer Algorithm for Exct Hzrd Free Logic Minimiztion J.W.J.M. Rutten, M.R.C.M. Berkelr, C.A.J. vn Eijk, M.A.J. Kolsteren Eindhoven University of Technology Informtion nd Communiction
More informationPYTHON PROGRAMMING. The History of Python. Features of Python. This Course
The History of Python PYTHON PROGRAMMING Dr Christin Hill 7 9 November 2016 Invented by Guido vn Rossum* t the Centrum Wiskunde & Informtic in Amsterdm in the erly 1990s Nmed fter Monty Python s Flying
More informationCPE300: Digital System Architecture and Design
CPE300: Digital System Architecture and Design Fall 2011 MW 17:30-18:45 CBC C316 Arithmetic Unit 10122011 http://www.egr.unlv.edu/~b1morris/cpe300/ 2 Outline Recap Fixed Point Arithmetic Addition/Subtraction
More informationIntegration. October 25, 2016
Integrtion October 5, 6 Introduction We hve lerned in previous chpter on how to do the differentition. It is conventionl in mthemtics tht we re supposed to lern bout the integrtion s well. As you my hve
More informationTiming for Ripple Carry Adder
Timing for Ripple Carry Adder 1 2 3 Look Ahead Method 5 6 7 8 9 Look-Ahead, bits wide 10 11 Multiplication Simple Gradeschool Algorithm for 32 Bits (6 Bit Result) Multiplier Multiplicand AND gates 32
More informationUnit #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 information2-3 search trees red-black BSTs B-trees
2-3 serch trees red-lck BTs B-trees 3 2-3 tree llow 1 or 2 keys per node. 2-node: one key, two children. 3-node: two keys, three children. ymmetric order. Inorder trversl yields keys in scending order.
More information