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

Size: px
Start display at page:

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

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 relly lrge numbers? relly smll numbers? How do you do rithmetic? identify (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 + +

2 Negtive Numbers? Some Alterntives We would like 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 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) = - + +

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: s s Complement negte: Tke the 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 = m+n 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 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. So Fr Binry Frctions Cn do logicl, dd, subtrct, multiply, divide,... But... wht bout frctions? wht bout relly lrge numbers? = x + x + x + x so.... = x + x + x + x - + x - + x - e.g.,.75 = /4 = / = / + /4 =.

8 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 = ) 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 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 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.

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

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

More information

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

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

More information

Number Systems and Computer Arithmetic

Number 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 information

Representation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation

Representation 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 information

Course Administration

Course 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 information

Computer Arithmetic Logical, Integer Addition & Subtraction Chapter

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

More information

Divide: Paper & Pencil

Divide: 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 information

Stack Manipulation. Other Issues. How about larger constants? Frame Pointer. PowerPC. Alternative Architectures

Stack 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 information

12-B FRACTIONS AND DECIMALS

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

More information

Basics of Logic Design Arithmetic Logic Unit (ALU)

Basics 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 information

Engineer To Engineer Note

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

More information

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

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

More information

Parallel Square and Cube Computations

Parallel 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 information

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

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

More information

Floating Point Numbers and Interval Arithmetic

Floating 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 information

Subtracting Fractions

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

More information

COMP 303 Computer Architecture Lecture 6

COMP 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 information

ECEN 468 Advanced Logic Design Lecture 36: RTL Optimization

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

More information

Section 10.4 Hyperbolas

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

More information

COMPUTER SCIENCE 123. Foundations of Computer Science. 6. Tuples

COMPUTER 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 information

10/9/2012. Operator is an operation performed over data at runtime. Arithmetic, Logical, Comparison, Assignment, Etc. Operators have precedence

10/9/2012. 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 information

9 4. CISC - Curriculum & Instruction Steering Committee. California County Superintendents Educational Services Association

9 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 information

Digital Design. Chapter 1: Introduction. Digital Design. Copyright 2006 Frank Vahid

Digital 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 information

Concepts Introduced. A 1-Bit Logical Unit. 1-Bit Half Adder (cont.) 1-Bit Half Adder

Concepts 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 information

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

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

More information

5 Regular 4-Sided Composition

5 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 information

10.5 Graphing Quadratic Functions

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

More information

1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)

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

More information

Tailoring the 32-Bit ALU to MIPS

Tailoring 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 information

9.1 apply the distance and midpoint formulas

9.1 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 information

SIMPLIFYING ALGEBRA PASSPORT.

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

More information

Small Business Networking

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

More information

George Boole. IT 3123 Hardware and Software Concepts. Switching Algebra. Boolean Functions. Boolean Functions. Truth Tables

George 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 information

Rational Numbers---Adding Fractions With Like Denominators.

Rational 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 information

Verification of Floating-Point Adders

Verification 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 information

Digital Design. Chapter 4: Datapath Components

Digital 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 information

x )Scales are the reciprocal of each other. e

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

More information

Engineer-to-Engineer Note

Engineer-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 information

Chapter 4: Datapath Components. Instructor: Dr. Hyunyoung Lee. Copyright Based on slides by Frank Vahid. Frank Vahid

Chapter 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 information

Chapter 1: Introduction

Chapter 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 information

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

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

More information

Lecture 10 Evolutionary Computation: Evolution strategies and genetic programming

Lecture 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 information

MIPS Integer ALU Requirements

MIPS 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 information

Small Business Networking

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

More information

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

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

More information

MIPS I/O and Interrupt

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

More information

Geometric transformations

Geometric 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 information

ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών

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

More information

CSE 141 Computer Architecture Summer Session Lecture 3 ALU Part 2 Single Cycle CPU Part 1. Pramod V. Argade

CSE 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 information

Today s Lecture. Basics of Logic Design: Boolean Algebra, Logic Gates. Recursive Example. Review: The C / C++ code. Recursive Example (Continued)

Today 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 information

Computer Organization and Structure. Bing-Yu Chen National Taiwan University

Computer 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 information

Review: MIPS Organization

Review: 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 information

Small Business Networking

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

More information

Digital Signal Processing: A Hardware-Based Approach

Digital 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 information

Small Business Networking

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

More information

CMU Fall VLSI CAD

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

More information

Before We Begin. Introduction to Spatial Domain Filtering. Introduction to Digital Image Processing. Overview (1): Administrative Details (1):

Before 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 information

Small Business Networking

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

More information

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

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

More information

Section 3.1: Sequences and Series

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

More information

4452 Mathematical Modeling Lecture 4: Lagrange Multipliers

4452 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 information

Transparent neutral-element elimination in MPI reduction operations

Transparent 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 information

Module 2: Computer Arithmetic

Module 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 information

Small Business Networking

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

More information

Small Business Networking

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

More information

Small Business Networking

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

More information

Study Guide for Exam 3

Study 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 information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < 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 information

Accelerating 3D convolution using streaming architectures on FPGAs

Accelerating 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 information

6.2 Volumes of Revolution: The Disk Method

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

More information

Computer Architecture. Chapter 3: Arithmetic for Computers

Computer 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 information

Slides for Data Mining by I. H. Witten and E. Frank

Slides for Data Mining by I. H. Witten and E. Frank Slides for Dt Mining y I. H. Witten nd E. Frnk Simplicity first Simple lgorithms often work very well! There re mny kinds of simple structure, eg: One ttriute does ll the work All ttriutes contriute eqully

More information

Today. CS 188: Artificial Intelligence Fall Recap: Search. Example: Pancake Problem. Example: Pancake Problem. General Tree Search.

Today. 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 information

EE260: Logic Design, Spring n Integer multiplication. n Booth s algorithm. n Integer division. n Restoring, non-restoring

EE260: 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 information

COMPUTER ORGANIZATION AND DESIGN

COMPUTER 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 information

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

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

More information

LAB L Hardware Building Blocks

LAB 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 information

Lecture Topics. Announcements. Today: Integer Arithmetic (P&H ) Next: The MIPS ISA (P&H ) Consulting hours. Milestone #1 (due 1/26)

Lecture 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 information

Fault injection attacks on cryptographic devices and countermeasures Part 2

Fault 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 information

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

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

More information

PYTHON PROGRAMMING. The History of Python. Features of Python. This Course

PYTHON 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 information

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

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

More information

MATH 25 CLASS 5 NOTES, SEP

MATH 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 information

CPSC 213. Polymorphism. Introduction to Computer Systems. Readings for Next Two Lectures. Back to Procedure Calls

CPSC 213. Polymorphism. Introduction to Computer Systems. Readings for Next Two Lectures. Back to Procedure Calls Redings for Next Two Lectures Text CPSC 213 Switch Sttements, Understnding Pointers - 2nd ed: 3.6.7, 3.10-1st ed: 3.6.6, 3.11 Introduction to Computer Systems Unit 1f Dynmic Control Flow Polymorphism nd

More information

Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Lecture 3

Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Lecture 3 Floating-Point Data Representation and Manipulation 198:231 Introduction to Computer Organization Instructor: Nicole Hynes nicole.hynes@rutgers.edu 1 Fixed Point Numbers Fixed point number: integer part

More information

Simplifying Algebra. Simplifying Algebra. Curriculum Ready.

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

More information

CPE300: Digital System Architecture and Design

CPE300: 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 information

6/23/2011. Review: IEEE-754. CSE 2021: Computer Organization. Exercises. Examples. Shakil M. Khan (adapted from Profs. Roumani & Asif)

6/23/2011. 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 information

CSE 401 Midterm Exam 11/5/10 Sample Solution

CSE 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 information

Approximate computations

Approximate 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 information

Digital Design. Chapter 6: Optimizations and Tradeoffs

Digital 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 information

Angle properties of lines and polygons

Angle 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 information

Integration. September 28, 2017

Integration. 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 information

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

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

More information

CS 241. Fall 2017 Midterm Review Solutions. October 24, Bits and Bytes 1. 3 MIPS Assembler 6. 4 Regular Languages 7.

CS 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 information

2-3 search trees red-black BSTs B-trees

2-3 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

1 Quad-Edge Construction Operators

1 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 information

ZZ - Advanced Math Review 2017

ZZ - 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

COMMON HALF YEARLY EXAMINATION DECEMBER 2018

COMMON HALF YEARLY EXAMINATION DECEMBER 2018 li.net i.net li.net i.net li.net i.net li.net i.net li.net i.net li.net i.net li.net i.net li.net i.net li.net i.net.pds.pds COMMON HALF YEARLY EXAMINATION DECEMBER 2018 STD : XI SUBJECT: COMPUTER SCIENCE

More information

Small Business Networking

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

More information