What do all those bits mean now? Number Systems and Arithmetic. Introduction to Binary Numbers. Questions About Numbers
|
|
- Rolf Short
- 5 years ago
- Views:
Transcription
1 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 precision double precision Questions About Numbers 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 like? =rithmetic logic unit Introduction to Binry Numbers Consider 4-bit binry number Deciml Binry Deciml Binry Exmples of binry rithmetic: = 5 = 6
2 Negtive Numbers? Some Alterntives 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 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 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) = -
3 Some Things We Wnt To Know About Our Number System Detection negtion sign extension =>,, - =>,, overflow detection So how do we detect overflow? Instruction Fetch Instruction Decode Opernd Fetch Execute Store Next Instruction Arithmetic -- The hert of instruction execution b opertion result Designing n Arithmetic Logic Unit A B N N op Control Lines (op) Function And Or Add Subtrct Set-on-less-thn N Zero
4 A One Bit -bit A -bit -bit This -bit will perform AND, OR, nd ADD b b - b b b b How About Subtrction? Keep in mind the following: (A - B) is the sme s: A (-B) 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 b Binvert Detection Logic Crry into MSB! = Crry out of MSB For N-bit : = [N - ] XOR [N - ] A B A B A B A B -bit -bit -bit -bit X Y X XOR Y
5 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 Set-on-less-thn A B A B A B A B -bit -bit -bit -bit Do subtrct use sign bit route to bit of result ll other bits zero Binvert b. Binvert b detection b. Set Binvert b b b b Full Bnegte b b b b Set Set wht signls ccomplish: neg oper dd? sub? nd? Zero or? beq? slt? The Disdvntge of Ripple Crry 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 sign bit (dder output from bit ) 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 Pper nd pencil exmple: Multiplicnd Multiplier x MULTIPLY HARDWARE Version 64-bit Multiplicnd reg, 64-bit, 64-bit Product reg, -bit multiplier reg Multiplicnd Shift left Product =? m bits x n bits = mn bit product Binry mkes it esy: => plce ( x multiplicnd) => plce multiplicnd ( x multiplicnd) we ll look t couple of versions of multipliction hrdwre 64-bit Product Write Control test Multiplier Shift right bits Multiply Algorithm Version Multiplier Multiplicnd Product Multiplier =. Add multiplicnd to product nd plce the result in Product register Strt. Test Multiplier. Shift the Multiplicnd register left bit. Shift the Multiplier register right bit nd repetition? Multiplier = No: < repetitions Observtions on Multiply Version clock per cycle => clocks per multiply Rtio of multiply to dd : / bits in multiplicnd lwys => 64-bit dder is wsted s inserted in left of multiplicnd s shifted => lest significnt bits of product never chnged once formed Insted of shifting multiplicnd to left, shift product to right? Wsted spce (zeroes) in product register exctly mtches meningful bits of multiplier t ll times. Combine? Yes: repetitions Done
7 MULTIPLY HARDWARE Version -bit Multiplicnd reg, -bit, 64-bit Product reg, (-bit Multiplier reg) -bit Multiplicnd bits Product Shift right Write Multiplicnd Product Control test Product =. Add multiplicnd to the left hlf of the product nd plce the result in the left hlf of the Product register Strt. Test Product. Shift the Product register right bit nd repetition? Done Product = No: < repetitions Yes: repetitions Observtions on Multiply Version steps per bit becuse Multiplier & Product combined -bit dder 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. Divide: Pper & Pencil DIVIDE HARDWARE Version Divisor Quotient Dividend 64-bit Divisor reg, 64-bit, 64-bit Reminder reg, -bit Quotient reg Divisor 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 Write Control test Quotient Shift left bits
8 Divide Algorithm Version Tkes n steps for n-bit Quotient & Rem. Quotient Divisor Reminder Reminder >= Strt. Subtrct the Divisor register from the Reminder register, nd plce the result in the Reminder register. Test Reminder Reminder < DIVIDE HARDWARE Version -bit Divisor reg, -bit, 64-bit Reminder reg, (-bit Quotient reg) Divisor Strt. Shift the Reminder register left bit. Subtrct the Divisor register from the left hlf of the Reminder register nd plce the result in the left hlf of the Reminder register. Shift the Quotient register to the left setting the new rightmost bit to.. Shift the Divisor register right bit. rd repetition? b. Restore the originl vlue by dding the Divisor register to the Reminder register, nd plce the sum in the Reminder register. Also shift the Quotient register to the left, setting the new lest significnt bit to. No: < repetitions bits -bit Reminder Shift right Shift left Write Control test Reminder > Reminder < Test Reminder. Shift the Reminder register to the b. Restore the originl vlue by dding left, setting the new rightmost bit to the Divisor register to the left hlf of the Reminder register nd plce the sum in the left hlf of the Reminder register. Also shift the Reminder register to the left, setting the new rightmost bit to No: < repetitions nd repetition? Yes: repetitions Yes: repetitions Done. Shift left hlf of Reminder right bit Done Observtions on Divide Version Sme Hrdwre s Multiply: just need to dd or subtrct, nd 6-bit register to shift left or shift right Hi nd Lo registers in MIPS combine to ct s 64-bit register for multiply nd divide Signed Divides: 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.
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 informationQuestions About Numbers. Number Systems and Arithmetic. Introduction to Binary Numbers. Negative Numbers?
Questions About Numbers Number Systems nd Arithmetic or Computers go to elementry school How do you represent negtive numbers? frctions? relly lrge numbers? relly smll numbers? How do you do rithmetic?
More 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationEECS150 - Digital Design Lecture 13 - Combinational Logic & Arithmetic Circuits Part 3
EECS15 - Digital Design Lecture 13 - Combinational Logic & Arithmetic Circuits Part 3 October 8, 22 John Wawrzynek Fall 22 EECS15 - Lec13-cla3 Page 1 Multiplication a 3 a 2 a 1 a Multiplicand b 3 b 2 b
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 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 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 informationHomework 3. Assigned on 02/15 Due time: midnight on 02/21 (1 WEEK only!) B.2 B.11 B.14 (hint: use multiplexors) CSCI 402: Computer Architectures
Homework 3 Assigned on 02/15 Due time: midnight on 02/21 (1 WEEK only!) B.2 B.11 B.14 (hint: use multiplexors) 1 CSCI 402: Computer Architectures Arithmetic for Computers (2) Fengguang Song Department
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 informationEEC 483 Computer Organization
EEC 483 Computer Organization Chapter 3. Arithmetic for Computers Chansu Yu Table of Contents Ch.1 Introduction Ch. 2 Instruction: Machine Language Ch. 3-4 CPU Implementation Ch. 5 Cache and VM Ch. 6-7
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 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 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 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 informationInteger Multiplication and Division
Integer Multiplication and Division COE 301 Computer Organization Prof. Muhamed Mudawar College of Computer Sciences and Engineering King Fahd University of Petroleum and Minerals Presentation Outline
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 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 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 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 informationCS 241. Fall 2017 Midterm Review Solutions. October 24, Bits and Bytes 1. 3 MIPS Assembler 6. 4 Regular Languages 7.
CS 241 Fll 2017 Midterm Review Solutions Octoer 24, 2017 Contents 1 Bits nd Bytes 1 2 MIPS Assemly Lnguge Progrmming 2 3 MIPS Assemler 6 4 Regulr Lnguges 7 5 Scnning 9 1 Bits nd Bytes 1. Give two s complement
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 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 informationLecture 8: Addition, Multiplication & Division
Lecture 8: Addition, Multiplication & Division Today s topics: Signed/Unsigned Addition Multiplication Division 1 Signed / Unsigned The hardware recognizes two formats: unsigned (corresponding to the C
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 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 informationLecture Topics. Announcements. Today: Integer Arithmetic (P&H ) Next: continued. Consulting hours. Introduction to Sim. Milestone #1 (due 1/26)
Lecture Topics Today: Integer Arithmetic (P&H 3.1-3.4) Next: continued 1 Announcements Consulting hours Introduction to Sim Milestone #1 (due 1/26) 2 1 Overview: Integer Operations Internal representation
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 informationOutline. EEL-4713 Computer Architecture Multipliers and shifters. Deriving requirements of ALU. MIPS arithmetic instructions
Outline EEL-4713 Computer Architecture Multipliers and shifters Multiplication and shift registers Chapter 3, section 3.4 Next lecture Division, floating-point 3.5 3.6 EEL-4713 Ann Gordon-Ross.1 EEL-4713
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 informationReview of Last lecture. Review ALU Design. Designing a Multiplier Shifter Design Review. Booth s algorithm. Today s Outline
Today s Outline San Jose State University EE176-SJSU Computer Architecture and Organization Lecture 5 HDL, ALU, Shifter, Booth Algorithm Multiplier & Divider Instructor: Christopher H. Pham Review of Last
More informationCOMPUTER ARITHMETIC (Part 1)
Eastern Mediterranean University School of Computing and Technology ITEC255 Computer Organization & Architecture COMPUTER ARITHMETIC (Part 1) Introduction The two principal concerns for computer arithmetic
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 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 informationAlgorithm Design (5) Text Search
Algorithm Design (5) Text Serch Tkshi Chikym School of Engineering The University of Tokyo Text Serch Find sustring tht mtches the given key string in text dt of lrge mount Key string: chr x[m] Text Dt:
More 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 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 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 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 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 informationStack. A list whose end points are pointed by top and bottom
4. Stck Stck A list whose end points re pointed by top nd bottom Insertion nd deletion tke plce t the top (cf: Wht is the difference between Stck nd Arry?) Bottom is constnt, but top grows nd shrinks!
More 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 informationCS/COE 0447 Example Problems for Exam 2 Spring 2011
CS/COE 0447 Example Problems for Exam 2 Spring 2011 1) Show the steps to multiply the 4-bit numbers 3 and 5 with the fast shift-add multipler. Use the table below. List the multiplicand (M) and product
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 informationChapter 3 Arithmetic for Computers
Chapter 3 Arithmetic for Computers 1 Arithmetic Where we've been: Abstractions: Instruction Set Architecture Assembly Language and Machine Language What's up ahead: Implementing the Architecture operation
More informationCPS 104 Computer Organization and Programming
CPS 104 Computer Organization and Programming Lecture 9: Integer Arithmetic. Robert Wagner CPS104 IMD.1 RW Fall 2000 Overview of Today s Lecture: Integer Multiplication and Division. Read Appendix B CPS104
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 informationCS311H: Discrete Mathematics. Graph Theory IV. A Non-planar Graph. Regions of a Planar Graph. Euler s Formula. Instructor: Işıl Dillig
CS311H: Discrete Mthemtics Grph Theory IV Instructor: Işıl Dillig Instructor: Işıl Dillig, CS311H: Discrete Mthemtics Grph Theory IV 1/25 A Non-plnr Grph Regions of Plnr Grph The plnr representtion of
More 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 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 informationDigital Design using HDLs EE 4755 Final Examination
Nme Solution Digitl Design using HDLs EE 4755 Finl Exmintion Thursdy, 8 Decemer 6 :3-4:3 CST Alis The Hottest Plce in Hell Prolem Prolem Prolem 3 Prolem 4 Prolem 5 Prolem 6 Exm Totl (3 pts) ( pts) (5 pts)
More information1 Quad-Edge Construction Operators
CS48: Computer Grphics Hndout # Geometric Modeling Originl Hndout #5 Stnford University Tuesdy, 8 December 99 Originl Lecture #5: 9 November 99 Topics: Mnipultions with Qud-Edge Dt Structures Scribe: Mike
More informationGrade 7/8 Math Circles Geometric Arithmetic October 31, 2012
Fculty of Mthemtics Wterloo, Ontrio N2L 3G1 Grde 7/8 Mth Circles Geometric Arithmetic Octoer 31, 2012 Centre for Eduction in Mthemtics nd Computing Ancient Greece hs given irth to some of the most importnt
More 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 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 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 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 informationEnginner To Engineer Note
Technicl Notes on using Anlog Devices DSP components nd development tools from the DSP Division Phone: (800) ANALOG-D, FAX: (781) 461-3010, EMAIL: dsp_pplictions@nlog.com, FTP: ftp.nlog.com Using n ADSP-2181
More 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 informationUnion-Find Problem. Using Arrays And Chains. A Set As A Tree. Result Of A Find Operation
Union-Find Problem Given set {,,, n} of n elements. Initilly ech element is in different set. ƒ {}, {},, {n} An intermixed sequence of union nd find opertions is performed. A union opertion combines two
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 informationChapter 3 Arithmetic for Computers. ELEC 5200/ From P-H slides
Chapter 3 Arithmetic for Computers 1 Arithmetic for Computers Operations on integers Addition and subtraction Multiplication and division Dealing with overflow Floating-point real numbers Representation
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 informationNUMBER OPERATIONS. Mahdi Nazm Bojnordi. CS/ECE 3810: Computer Organization. Assistant Professor School of Computing University of Utah
NUMBER OPERATIONS Mahdi Nazm Bojnordi Assistant Professor School of Computing University of Utah CS/ECE 3810: Computer Organization Overview Homework 4 is due tonight Verify your uploaded file before the
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 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 informationLecture T4: Pattern Matching
Introduction to Theoreticl CS Lecture T4: Pttern Mtching Two fundmentl questions. Wht cn computer do? How fst cn it do it? Generl pproch. Don t tlk bout specific mchines or problems. Consider miniml bstrct
More informationHyperbolas. Definition of Hyperbola
CHAT Pre-Clculus Hyperols The third type of conic is clled hyperol. For n ellipse, the sum of the distnces from the foci nd point on the ellipse is fixed numer. For hyperol, the difference of the distnces
More informationCS201 Discussion 10 DRAWTREE + TRIES
CS201 Discussion 10 DRAWTREE + TRIES DrwTree First instinct: recursion As very generic structure, we could tckle this problem s follows: drw(): Find the root drw(root) drw(root): Write the line for the
More informationCOMP 423 lecture 11 Jan. 28, 2008
COMP 423 lecture 11 Jn. 28, 2008 Up to now, we hve looked t how some symols in n lphet occur more frequently thn others nd how we cn sve its y using code such tht the codewords for more frequently occuring
More informationRATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING
RATIONAL EQUATION: APPLICATIONS & PROBLEM SOLVING When finding the LCD of problem involving the ddition or subtrction of frctions, it my be necessry to fctor some denomintors to discover some restricted
More 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 informationT insn-mem T regfile T ALU T data-mem T regfile
This Unit: rithmetic CI 371 Computer Organization and Design Unit 3: rithmetic pp pp pp ystem software Mem CPU I/O! little review! Binary + 2s complement! Ripple-carry addition (RC)! Fast integer addition!
More informationZZ - Advanced Math Review 2017
ZZ - Advnced Mth Review Mtrix Multipliction Given! nd! find the sum of the elements of the product BA First, rewrite the mtrices in the correct order to multiply The product is BA hs order x since B is
More information