Homework 1 graded and returned in class today. Solutions posted online. Request regrades by next class period. Question 10 treated as extra credit

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Homework 1 graded and returned in class today. Solutions posted online. Request regrades by next class period. Question 10 treated as extra credit"

Transcription

1 Announcements Homework 1 graded and returned in class today. Solutions posted online. Request regrades by next class period. Question 10 treated as extra credit Quiz 2 Monday on Number System Conversions Covers lectures on computer number systems Covers all types of problems in Homework 1 Try practice problems (posted to class schedule) CSC Computer Organization 1

2 Representing Real Numbers: Floating Point Finale CSC 242 Computer Organization Dr. Lucas Layman January 31, 2018

3 IEEE 754 Standard for Floating-Point Arithmetic Defines a different format for storing real numbers Specify rules for communicating real numbers between components Rounding rules Arithmetic operations Exception handling (division by zero, overflow, etc) CSC Computer Organization 3

4 IEEE 754 generalized process 1) Convert the integer and significand from decimal to binary 2) Normalize the binary, a.k.a., convert it to scientific notation in binary 3) Store the key values of the normalized binary this is the floating point representation CSC Computer Organization 4

5 1) Convert the integer and significand from decimal to binary Example: convert to 8-bit binary Algorithm: a) Convert the integer part (2) to binary using successive division. b) Convert the significand (.625) to binary using successive multiplication: 1) Multiply only the significand by 2 2) Note the integer value (1 or 0). These are your binary significands starting with the MSB. 3) Repeat steps 1-2 until your significand is 0 or you hit the maximum number of bits c) Write the binary CSC Computer Organization 5

6 2) Normalize the binary Move the radix point so that it is one bit from the left. Adjust the exponent so that the value does not change = = = = = = CSC Computer Organization 6

7 3) Store the key values of the normalized binary 1) the sign 3) the exponent = ± x 2 1 2) the significand CSC Computer Organization 7

8 3) Store the key values of the normalized binary exponent 3 bits An 8-bit float (1 byte): sign bit significand 4 bits Note: 8-bit floats aren t very useful, but they illustrate the process. Modern computers use 32- and 64-bit floats. CSC Computer Organization 8

9 3) Store the key values of the normalized binary (cont.) = x 2 1 exponent 3 bits Sign bit: 1 = negative, 0 = non-negative Exponent bits: sign bit Take the exponent and add the bias to it. The bias is always 2 k-1-1 where k is the number of bits in the exponent field. Convert the exponent (with added bias) to binary. Significand bits: take the first m bits of your normalized binary s significand significand 4 bits CSC Computer Organization 9

10 3) Store the key values of the normalized binary (cont.) = ± x 2 1 exponent 3 bits Sign bit: Exponent bits: We have dropped this 1. It is implied. sign bit mantissa 4 bits Significand bits: CSC Computer Organization 10

11 3) Store the key values of the normalized binary (cont.) = x 2-2 exponent 3 bits Sign bit: Exponent bits: We have dropped this 1. It is implied. sign bit significand 4 bits Significand bits: CSC Computer Organization 11

12 Once more, beginning to end Convert to 8-bit IEEE 754 floating point 1) to binary: 2) Normalize: 3) Store values: 1) Sign bit: 2) Exponent: 3) Significand: Answer: exponent 3 bits sign bit significand 4 bits CSC Computer Organization 12

13 Floats in modern computers A single-precision float is 4 bytes, or 32 bits: exponent 8 bits sign bit significand 23 bits CSC Computer Organization 13

14 Floats in modern computers (cont.) A double-precision float is 8 bytes, or 64 bits. Python uses this by default. 8 bit 32 bit 64 bit exponent 11 bits significand 52 bits CSC Computer Organization 14

15 Converting to IEEE 32-bit floating point format Convert (process is the same as 8-bit) 1) Convert the integer and significand from decimal to binary (example 3) -> ) Normalize: x ) Store the key values of the normalized binary: Sign bit: 1 Exponent: = = Note: The bias for a 32 bit floating point # is always 127 Significand: CSC Computer Organization 15

16 Converting to IEEE 32-bit floating point format (cont.) = Sign bit: 1 Exponent: = = Significand: exponent 8 bits sign bit significand 23 bits CSC Computer Organization 16

17 Another 32-bit example Convert to 32-bit floating point 1) Convert the integer and significand from decimal to binary 2) Normalize the binary 3) Store the key values of the normalized binary 1) sign bit 2) exponent (remember the bias is 127) 3) the significand to 23 bits CSC Computer Organization 17

18 Review on computer representations of numbers Name Base Range Purpose Decimal 10 [0,9] The number system most humans use Binary 2 [0,1] The language of all computers Octal 8 [0,7] Rarely used. Common in early computers Hex 16 [0,F] user-friendly representation of binary data CSC Computer Organization 18

19 Review on computer representations of numbers Name Base Purpose Two s complement 2 A way to represent signed integers Floating point Any A way to represent real numbers CSC Computer Organization 19

20 Storing other types of data We ve discussed storing integers and real numbers But binary bits/bytes can also store: Pixel data for images (e.g., color codes) Digital audio (e.g., compressed or uncompressed waveforms) Program instructions (e.g., from Python or Java) Alphabet characters for display on the monitor Everything is stored in binary, but what the binary represents depends on how the binary is used CSC Computer Organization 20

21 One example ASCII ASCII American Standard Code for Information Interchange 128 characters (including null) represented by 2 7 bits. Characters are usually referred to by their 2-digit hex: 00-7F. Developed in the 60 s when Bell telephone created a digital telegraph CSC Computer Organization 21

22 CSC Computer Organization 22

23 Unicode There are other characters than in ASCII Unicode consortium handles all the characters in the world. Unicode specifies the international standard for representing characters, including emojis CSC Computer Organization 23

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1 IT 1204 Section 2.0 Data Representation and Arithmetic 2009, University of Colombo School of Computing 1 What is Analog and Digital The interpretation of an analog signal would correspond to a signal whose

More information

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng.

CS 265. Computer Architecture. Wei Lu, Ph.D., P.Eng. CS 265 Computer Architecture Wei Lu, Ph.D., P.Eng. 1 Part 1: Data Representation Our goal: revisit and re-establish fundamental of mathematics for the computer architecture course Overview: what are bits

More information

Inf2C - Computer Systems Lecture 2 Data Representation

Inf2C - Computer Systems Lecture 2 Data Representation Inf2C - Computer Systems Lecture 2 Data Representation Boris Grot School of Informatics University of Edinburgh Last lecture Moore s law Types of computer systems Computer components Computer system stack

More information

Floating-point Arithmetic. where you sum up the integer to the left of the decimal point and the fraction to the right.

Floating-point Arithmetic. where you sum up the integer to the left of the decimal point and the fraction to the right. Floating-point Arithmetic Reading: pp. 312-328 Floating-Point Representation Non-scientific floating point numbers: A non-integer can be represented as: 2 4 2 3 2 2 2 1 2 0.2-1 2-2 2-3 2-4 where you sum

More information

The type of all data used in a C (or C++) program must be specified

The type of all data used in a C (or C++) program must be specified The type of all data used in a C (or C++) program must be specified A data type is a description of the data being represented That is, a set of possible values and a set of operations on those values

More information

Chapter 03: Computer Arithmetic. Lesson 09: Arithmetic using floating point numbers

Chapter 03: Computer Arithmetic. Lesson 09: Arithmetic using floating point numbers Chapter 03: Computer Arithmetic Lesson 09: Arithmetic using floating point numbers Objective To understand arithmetic operations in case of floating point numbers 2 Multiplication of Floating Point Numbers

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

Digital Computers and Machine Representation of Data

Digital Computers and Machine Representation of Data Digital Computers and Machine Representation of Data K. Cooper 1 1 Department of Mathematics Washington State University 2013 Computers Machine computation requires a few ingredients: 1 A means of representing

More information

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation Course Schedule CS 221 Computer Architecture Week 3: Information Representation (2) Fall 2001 W1 Sep 11- Sep 14 Introduction W2 Sep 18- Sep 21 Information Representation (1) (Chapter 3) W3 Sep 25- Sep

More information

Floating Point. The World is Not Just Integers. Programming languages support numbers with fraction

Floating Point. The World is Not Just Integers. Programming languages support numbers with fraction 1 Floating Point The World is Not Just Integers Programming languages support numbers with fraction Called floating-point numbers Examples: 3.14159265 (π) 2.71828 (e) 0.000000001 or 1.0 10 9 (seconds in

More information

Floating Point Arithmetic

Floating Point Arithmetic Floating Point Arithmetic CS 365 Floating-Point What can be represented in N bits? Unsigned 0 to 2 N 2s Complement -2 N-1 to 2 N-1-1 But, what about? very large numbers? 9,349,398,989,787,762,244,859,087,678

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

l l l l l l l Base 2; each digit is 0 or 1 l Each bit in place i has value 2 i l Binary representation is used in computers

l l l l l l l Base 2; each digit is 0 or 1 l Each bit in place i has value 2 i l Binary representation is used in computers 198:211 Computer Architecture Topics: Lecture 8 (W5) Fall 2012 Data representation 2.1 and 2.2 of the book Floating point 2.4 of the book Computer Architecture What do computers do? Manipulate stored information

More information

Data Representation and Networking

Data Representation and Networking Data Representation and Networking Instructor: Dmitri A. Gusev Spring 2007 CSC 120.02: Introduction to Computer Science Lecture 3, January 30, 2007 Data Representation Topics Covered in Lecture 2 (recap+)

More information

10.1. Unit 10. Signed Representation Systems Binary Arithmetic

10.1. Unit 10. Signed Representation Systems Binary Arithmetic 0. Unit 0 Signed Representation Systems Binary Arithmetic 0.2 BINARY REPRESENTATION SYSTEMS REVIEW 0.3 Interpreting Binary Strings Given a string of s and 0 s, you need to know the representation system

More information

Chapter 4: Data Representations

Chapter 4: Data Representations Chapter 4: Data Representations Integer Representations o unsigned o sign-magnitude o one's complement o two's complement o bias o comparison o sign extension o overflow Character Representations Floating

More information

CS101 Lecture 04: Binary Arithmetic

CS101 Lecture 04: Binary Arithmetic CS101 Lecture 04: Binary Arithmetic Binary Number Addition Two s complement encoding Briefly: real number representation Aaron Stevens (azs@bu.edu) 25 January 2013 What You ll Learn Today Counting in binary

More information

Floating Point Numbers. Lecture 9 CAP

Floating Point Numbers. Lecture 9 CAP Floating Point Numbers Lecture 9 CAP 3103 06-16-2014 Review of Numbers Computers are made to deal with numbers What can we represent in N bits? 2 N things, and no more! They could be Unsigned integers:

More information

D I G I T A L C I R C U I T S E E

D I G I T A L C I R C U I T S E E D I G I T A L C I R C U I T S E E Digital Circuits Basic Scope and Introduction This book covers theory solved examples and previous year gate question for following topics: Number system, Boolean algebra,

More information

Number Systems & Encoding

Number Systems & Encoding Number Systems & Encoding Lecturer: Sri Parameswaran Author: Hui Annie Guo Modified: Sri Parameswaran Week2 1 Lecture overview Basics of computing with digital systems Binary numbers Floating point numbers

More information

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010 Contents Number systems and conversion Binary arithmetic Representation of negative numbers Addition of two s complement numbers Addition of one s complement numbers Binary s Readings Unit.~. UNIT NUMBER

More information

Computer Systems C S Cynthia Lee

Computer Systems C S Cynthia Lee Computer Systems C S 1 0 7 Cynthia Lee 2 Today s Topics LECTURE: Floating point! Real Numbers and Approximation MATH TIME! Some preliminary observations on approximation We know that some non-integer numbers

More information

Characters, Strings, and Floats

Characters, Strings, and Floats Characters, Strings, and Floats CS 350: Computer Organization & Assembler Language Programming 9/6: pp.8,9; 9/28: Activity Q.6 A. Why? We need to represent textual characters in addition to numbers. Floating-point

More information

IEEE Standard for Floating-Point Arithmetic: 754

IEEE Standard for Floating-Point Arithmetic: 754 IEEE Standard for Floating-Point Arithmetic: 754 G.E. Antoniou G.E. Antoniou () IEEE Standard for Floating-Point Arithmetic: 754 1 / 34 Floating Point Standard: IEEE 754 1985/2008 Established in 1985 (2008)

More information

Chapter 4: Computer Codes. In this chapter you will learn about:

Chapter 4: Computer Codes. In this chapter you will learn about: Ref. Page Slide 1/30 Learning Objectives In this chapter you will learn about: Computer data Computer codes: representation of data in binary Most commonly used computer codes Collating sequence Ref. Page

More information

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

QUIZ ch.1. 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law

QUIZ ch.1. 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law QUIZ ch.1 1 st generation 2 nd generation 3 rd generation 4 th generation 5 th generation Rock s Law Moore s Law Integrated circuits Density of silicon chips doubles every 1.5 yrs. Multi-core CPU Transistors

More information

15213 Recitation 2: Floating Point

15213 Recitation 2: Floating Point 15213 Recitation 2: Floating Point 1 Introduction This handout will introduce and test your knowledge of the floating point representation of real numbers, as defined by the IEEE standard. This information

More information

Chapter 2 Bits, Data Types, and Operations

Chapter 2 Bits, Data Types, and Operations Chapter 2 Bits, Data Types, and Operations How do we represent data in a computer? At the lowest level, a computer is an electronic machine. works by controlling the flow of electrons Easy to recognize

More information

CSC201, SECTION 002, Fall 2000: Homework Assignment #2

CSC201, SECTION 002, Fall 2000: Homework Assignment #2 1 of 7 11/8/2003 7:34 PM CSC201, SECTION 002, Fall 2000: Homework Assignment #2 DUE DATE Monday, October 2, at the start of class. INSTRUCTIONS FOR PREPARATION Neat, in order, answers easy to find. Staple

More information

3.5 Floating Point: Overview

3.5 Floating Point: Overview 3.5 Floating Point: Overview Floating point (FP) numbers Scientific notation Decimal scientific notation Binary scientific notation IEEE 754 FP Standard Floating point representation inside a computer

More information

IEEE-754 floating-point

IEEE-754 floating-point IEEE-754 floating-point Real and floating-point numbers Real numbers R form a continuum - Rational numbers are a subset of the reals - Some numbers are irrational, e.g. π Floating-point numbers are an

More information

Floating Point Numbers

Floating Point Numbers Floating Point Numbers Summer 8 Fractional numbers Fractional numbers fixed point Floating point numbers the IEEE 7 floating point standard Floating point operations Rounding modes CMPE Summer 8 Slides

More information

CMPS 10 Introduction to Computer Science Lecture Notes

CMPS 10 Introduction to Computer Science Lecture Notes CMPS Introduction to Computer Science Lecture Notes Binary Numbers Until now we have considered the Computing Agent that executes algorithms to be an abstract entity. Now we will be concerned with techniques

More information

DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.

DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors. Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic 0 (0 volts) and one for logic

More information

Data Representation. DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.

Data Representation. DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors. Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic ( volts) and one for logic (3.3

More information

SE311: Design of Digital Systems

SE311: Design of Digital Systems SE311: Design of Digital Systems Lecture 3: Complements and Binary arithmetic Dr. Samir Al-Amer (Term 041) SE311_Lec3 (c) 2004 AL-AMER ١ Outlines Complements Signed Numbers Representations Arithmetic Binary

More information

Five classic components

Five classic components CS/COE0447: Computer Organization and Assembly Language Chapter 3 modified by Bruce Childers original slides by Sangyeun Cho Dept. of Computer Science Five classic components I am like a control tower

More information

Administrivia. CMSC 216 Introduction to Computer Systems Lecture 24 Data Representation and Libraries. Representing characters DATA REPRESENTATION

Administrivia. CMSC 216 Introduction to Computer Systems Lecture 24 Data Representation and Libraries. Representing characters DATA REPRESENTATION Administrivia CMSC 216 Introduction to Computer Systems Lecture 24 Data Representation and Libraries Jan Plane & Alan Sussman {jplane, als}@cs.umd.edu Project 6 due next Friday, 12/10 public tests posted

More information

ECE 2020B Fundamentals of Digital Design Spring problems, 6 pages Exam Two 26 February 2014

ECE 2020B Fundamentals of Digital Design Spring problems, 6 pages Exam Two 26 February 2014 Instructions: This is a closed book, closed note exam. Calculators are not permitted. If you have a question, raise your hand and I will come to you. Please work the exam in pencil and do not separate

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

Digital Fundamentals

Digital Fundamentals Digital Fundamentals Tenth Edition Floyd Chapter 1 Modified by Yuttapong Jiraraksopakun Floyd, Digital Fundamentals, 10 th 2008 Pearson Education ENE, KMUTT ed 2009 Analog Quantities Most natural quantities

More information

Lecture 2: Number Systems

Lecture 2: Number Systems Lecture 2: Number Systems Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Prof. Russell Tessier of University of Massachusetts Aby George of Wayne State University Contents

More information

Signed umbers. Sign/Magnitude otation

Signed umbers. Sign/Magnitude otation Signed umbers So far we have discussed unsigned number representations. In particular, we have looked at the binary number system and shorthand methods in representing binary codes. With m binary digits,

More information

CMSC 313 Lecture 03 Multiple-byte data big-endian vs little-endian sign extension Multiplication and division Floating point formats Character Codes

CMSC 313 Lecture 03 Multiple-byte data big-endian vs little-endian sign extension Multiplication and division Floating point formats Character Codes Multiple-byte data CMSC 313 Lecture 03 big-endian vs little-endian sign extension Multiplication and division Floating point formats Character Codes UMBC, CMSC313, Richard Chang 4-5 Chapter

More information

Co-processor Math Processor. Richa Upadhyay Prabhu. NMIMS s MPSTME February 9, 2016

Co-processor Math Processor. Richa Upadhyay Prabhu. NMIMS s MPSTME February 9, 2016 8087 Math Processor Richa Upadhyay Prabhu NMIMS s MPSTME richa.upadhyay@nmims.edu February 9, 2016 Introduction Need of Math Processor: In application where fast calculation is required Also where there

More information

Number Representation 3/2/01 Lecture #

Number Representation 3/2/01 Lecture # Number Representation 3/2/01 Lecture #11 16.070 How are numbers represented in a computer? Data come in two basic types! Numbers Whole/Integer (1, -3, 0) Natural, Positive (1, 2, 3) Real/Floating-point

More information

Programming Studio #1 ECE 190

Programming Studio #1 ECE 190 Programming Studio #1 ECE 190 Programming Studio #1 Announcements In Studio Assignment Introduction to Linux Command-Line Operations Recitation Floating Point Representation Binary & Hexadecimal 2 s Complement

More information

QUIZ: Generations of computer technology. Hardware:

QUIZ: Generations of computer technology. Hardware: QUIZ: Generations of computer technology Hardware: 1. 2. 3. 4. 5. 1 QUIZ: Generations of computer technology Software: 1. 2. 3. 4. 5. 6. 2 Chapter 2 Binary Values and Number Systems Numbers Natural numbers,

More information

Number Systems. Binary Numbers. Appendix. Decimal notation represents numbers as powers of 10, for example

Number Systems. Binary Numbers. Appendix. Decimal notation represents numbers as powers of 10, for example Appendix F Number Systems Binary Numbers Decimal notation represents numbers as powers of 10, for example 1729 1 103 7 102 2 101 9 100 decimal = + + + There is no particular reason for the choice of 10,

More information

Floating point. Today! IEEE Floating Point Standard! Rounding! Floating Point Operations! Mathematical properties. Next time. !

Floating point. Today! IEEE Floating Point Standard! Rounding! Floating Point Operations! Mathematical properties. Next time. ! Floating point Today! IEEE Floating Point Standard! Rounding! Floating Point Operations! Mathematical properties Next time! The machine model Chris Riesbeck, Fall 2011 Checkpoint IEEE Floating point Floating

More information

The Sign consists of a single bit. If this bit is '1', then the number is negative. If this bit is '0', then the number is positive.

The Sign consists of a single bit. If this bit is '1', then the number is negative. If this bit is '0', then the number is positive. IEEE 754 Standard - Overview Frozen Content Modified by on 13-Sep-2017 Before discussing the actual WB_FPU - Wishbone Floating Point Unit peripheral in detail, it is worth spending some time to look at

More information

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning 4 Operations On Data 4.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List the three categories of operations performed on data.

More information

Floating Point. EE 109 Unit 20. Floating Point Representation. Fixed Point

Floating Point. EE 109 Unit 20. Floating Point Representation. Fixed Point 2.1 Floating Point 2.2 EE 19 Unit 2 IEEE 754 Floating Point Representation Floating Point Arithmetic Used to represent very numbers (fractions) and very numbers Avogadro s Number: +6.247 * 1 23 Planck

More information

CS/EE1012 INTRODUCTION TO COMPUTER ENGINEERING SPRING 2013 HOMEWORK I. Solve all homework and exam problems as shown in class and sample solutions

CS/EE1012 INTRODUCTION TO COMPUTER ENGINEERING SPRING 2013 HOMEWORK I. Solve all homework and exam problems as shown in class and sample solutions CS/EE2 INTRODUCTION TO COMPUTER ENGINEERING SPRING 23 DUE : February 22, 23 HOMEWORK I READ : Related portions of the following chapters : È Chapter È Chapter 2 È Appendix E ASSIGNMENT : There are eight

More information

CS61C L10 MIPS Instruction Representation II, Floating Point I (6)

CS61C L10 MIPS Instruction Representation II, Floating Point I (6) CS61C L1 MIPS Instruction Representation II, Floating Point I (1) inst.eecs.berkeley.edu/~cs61c CS61C : Machine Structures Lecture #1 Instruction Representation II, Floating Point I 25-1-3 There is one

More information

Numeric Variable Storage Pattern

Numeric Variable Storage Pattern Numeric Variable Storage Pattern Sreekanth Middela Srinivas Vanam Rahul Baddula Percept Pharma Services, Bridgewater, NJ ABSTRACT This paper presents the Storage pattern of Numeric Variables within the

More information

Computer Arithmetic Ch 8

Computer Arithmetic Ch 8 Computer Arithmetic Ch 8 ALU Integer Representation Integer Arithmetic Floating-Point Representation Floating-Point Arithmetic 1 Arithmetic Logical Unit (ALU) (2) Does all work in CPU (aritmeettis-looginen

More information

Giving credit where credit is due

Giving credit where credit is due CSCE 230J Computer Organization Floating Point Dr. Steve Goddard goddard@cse.unl.edu http://cse.unl.edu/~goddard/courses/csce230j Giving credit where credit is due Most of slides for this lecture are based

More information

ecture 25 Floating Point Friedland and Weaver Computer Science 61C Spring 2017 March 17th, 2017

ecture 25 Floating Point Friedland and Weaver Computer Science 61C Spring 2017 March 17th, 2017 ecture 25 Computer Science 61C Spring 2017 March 17th, 2017 Floating Point 1 New-School Machine Structures (It s a bit more complicated!) Software Hardware Parallel Requests Assigned to computer e.g.,

More information

System Programming CISC 360. Floating Point September 16, 2008

System Programming CISC 360. Floating Point September 16, 2008 System Programming CISC 360 Floating Point September 16, 2008 Topics IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties Powerpoint Lecture Notes for Computer Systems:

More information

CS321. Introduction to Numerical Methods

CS321. Introduction to Numerical Methods CS31 Introduction to Numerical Methods Lecture 1 Number Representations and Errors Professor Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 40506 0633 August 5, 017 Number

More information

DATA REPRESENTATION. Data Types. Complements. Fixed Point Representations. Floating Point Representations. Other Binary Codes. Error Detection Codes

DATA REPRESENTATION. Data Types. Complements. Fixed Point Representations. Floating Point Representations. Other Binary Codes. Error Detection Codes 1 DATA REPRESENTATION Data Types Complements Fixed Point Representations Floating Point Representations Other Binary Codes Error Detection Codes 2 Data Types DATA REPRESENTATION Information that a Computer

More information

Chapter 2 Float Point Arithmetic. Real Numbers in Decimal Notation. Real Numbers in Decimal Notation

Chapter 2 Float Point Arithmetic. Real Numbers in Decimal Notation. Real Numbers in Decimal Notation Chapter 2 Float Point Arithmetic Topics IEEE Floating Point Standard Fractional Binary Numbers Rounding Floating Point Operations Mathematical properties Real Numbers in Decimal Notation Representation

More information

Python Input, output and variables. Lecture 23 COMPSCI111/111G SS 2018

Python Input, output and variables. Lecture 23 COMPSCI111/111G SS 2018 Python Input, output and variables Lecture 23 COMPSCI111/111G SS 2018 1 Today s lecture What is Python? Displaying text on screen using print() Variables Numbers and basic arithmetic Getting input from

More information

Floating Point. CSC207 Fall 2017

Floating Point. CSC207 Fall 2017 Floating Point CSC207 Fall 2017 Ariane 5 Rocket Launch Ariane 5 rocket explosion In 1996, the European Space Agency s Ariane 5 rocket exploded 40 seconds after launch. During conversion of a 64-bit to

More information

Dr. Chuck Cartledge. 3 June 2015

Dr. Chuck Cartledge. 3 June 2015 Miscellanea 8224 Revisited Break 1.5 1.6 Conclusion References Backup slides CSC-205 Computer Organization Lecture #002 Section 1.5 Dr. Chuck Cartledge 3 June 2015 1/30 Table of contents I 5 1.6 1 Miscellanea

More information

Building a Test Suite

Building a Test Suite Program #3 Is on the web Exam #1 Announcements Today, 6:00 7:30 in Armory 0126 Makeup Exam Friday March 9, 2:00 PM room TBA Reading Notes (Today) Chapter 16 (Tuesday) 1 API: Building a Test Suite Int createemployee(char

More information

ECE 372 Microcontroller Design Assembly Programming Arrays. ECE 372 Microcontroller Design Assembly Programming Arrays

ECE 372 Microcontroller Design Assembly Programming Arrays. ECE 372 Microcontroller Design Assembly Programming Arrays Assembly Programming Arrays Assembly Programming Arrays Array For Loop Example: unsigned short a[]; for(j=; j

More information

CS 430 Spring Mike Lam, Professor. Data Types and Type Checking

CS 430 Spring Mike Lam, Professor. Data Types and Type Checking CS 430 Spring 2015 Mike Lam, Professor Data Types and Type Checking Type Systems Type system Rules about valid types, type compatibility, and how data values can be used Benefits of a robust type system

More information

Chapter 2. Binary Values and Number Systems

Chapter 2. Binary Values and Number Systems Chapter 2 Binary Values and Number Systems Numbers Natural numbers, a.k.a. positive integers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645, 32 Negative numbers A

More information

1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM

1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1.1 Introduction Given that digital logic and memory devices are based on two electrical states (on and off), it is natural to use a number

More information

CS61C : Machine Structures

CS61C : Machine Structures inst.eecs.berkeley.edu/~cs61c CS61C : Machine Structures Lecture #10 Instruction Representation II, Floating Point I 2005-10-03 Lecturer PSOE, new dad Dan Garcia www.cs.berkeley.edu/~ddgarcia #9 bears

More information

COSC 243 (Computer Architecture)

COSC 243 (Computer Architecture) COSC 243 Computer Architecture And Operating Systems 1 Dr. Andrew Trotman Instructors Office: 123A, Owheo Phone: 479-7842 Email: andrew@cs.otago.ac.nz Dr. Zhiyi Huang (course coordinator) Office: 126,

More information

P( Hit 2nd ) = P( Hit 2nd Miss 1st )P( Miss 1st ) = (1/15)(15/16) = 1/16. P( Hit 3rd ) = (1/14) * P( Miss 2nd and 1st ) = (1/14)(14/15)(15/16) = 1/16

P( Hit 2nd ) = P( Hit 2nd Miss 1st )P( Miss 1st ) = (1/15)(15/16) = 1/16. P( Hit 3rd ) = (1/14) * P( Miss 2nd and 1st ) = (1/14)(14/15)(15/16) = 1/16 CODING and INFORMATION We need encodings for data. How many questions must be asked to be certain where the ball is. (cases: avg, worst, best) P( Hit 1st ) = 1/16 P( Hit 2nd ) = P( Hit 2nd Miss 1st )P(

More information

IBM 370 Basic Data Types

IBM 370 Basic Data Types IBM 370 Basic Data Types This lecture discusses the basic data types used on the IBM 370, 1. Two s complement binary numbers 2. EBCDIC (Extended Binary Coded Decimal Interchange Code) 3. Zoned Decimal

More information

EE 109 Unit 3. Analog vs. Digital. Analog vs. Digital. Binary Representation Systems ANALOG VS. DIGITAL

EE 109 Unit 3. Analog vs. Digital. Analog vs. Digital. Binary Representation Systems ANALOG VS. DIGITAL 3. 3. EE 9 Unit 3 Binary Representation Systems ANALOG VS. DIGITAL 3.3 3. Analog vs. Digital The analog world is based on continuous events. Observations can take on any (real) value. The digital world

More information

Representing and Manipulating Floating Points

Representing and Manipulating Floating Points Representing and Manipulating Floating Points Jin-Soo Kim (jinsookim@skku.edu) Computer Systems Laboratory Sungkyunkwan University http://csl.skku.edu The Problem How to represent fractional values with

More information

Computers and programming languages introduction

Computers and programming languages introduction Computers and programming languages introduction Eugeniy E. Mikhailov The College of William & Mary Lecture 01 Eugeniy Mikhailov (W&M) Practical Computing Lecture 01 1 / 19 Class goals and structure Primary

More information

ECE2049 E17 Lecture 2: Data Representations & C Programming Basics

ECE2049 E17 Lecture 2: Data Representations & C Programming Basics ECE2049 E17 Lecture 2: Data Representations & C Programming Basics Administrivia Lab 0 after class today! o Get your MSP430 board! Install instructions for CCS are on course website under Resources o You

More information

Arithmetic. Chapter 3 Computer Organization and Design

Arithmetic. Chapter 3 Computer Organization and Design Arithmetic Chapter 3 Computer Organization and Design Addition Addition is similar to decimals 0000 0111 + 0000 0101 = 0000 1100 Subtraction (negate) 0000 0111 + 1111 1011 = 0000 0010 Over(under)flow For

More information

Floating Point Puzzles The course that gives CMU its Zip! Floating Point Jan 22, IEEE Floating Point. Fractional Binary Numbers.

Floating Point Puzzles The course that gives CMU its Zip! Floating Point Jan 22, IEEE Floating Point. Fractional Binary Numbers. class04.ppt 15-213 The course that gives CMU its Zip! Topics Floating Point Jan 22, 2004 IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties Floating Point Puzzles For

More information

Unit 3. Analog vs. Digital. Analog vs. Digital ANALOG VS. DIGITAL. Binary Representation

Unit 3. Analog vs. Digital. Analog vs. Digital ANALOG VS. DIGITAL. Binary Representation 3.1 3.2 Unit 3 Binary Representation ANALOG VS. DIGITAL 3.3 3.4 Analog vs. Digital The analog world is based on continuous events. Observations can take on (real) any value. The digital world is based

More information

IEEE Floating Point Numbers Overview

IEEE Floating Point Numbers Overview COMP 40: Machine Structure and Assembly Language Programming (Fall 2015) IEEE Floating Point Numbers Overview Noah Mendelsohn Tufts University Email: noah@cs.tufts.edu Web: http://www.cs.tufts.edu/~noah

More information

Lecture 1. Course Overview, Python Basics

Lecture 1. Course Overview, Python Basics Lecture 1 Course Overview, Python Basics We Are Very Full! Lectures and Labs are at fire-code capacity We cannot add sections or seats to lectures You may have to wait until someone drops No auditors are

More information

DATA 301 Introduction to Data Analytics Data Representation. Dr. Ramon Lawrence University of British Columbia Okanagan

DATA 301 Introduction to Data Analytics Data Representation. Dr. Ramon Lawrence University of British Columbia Okanagan DATA 301 Introduction to Data Analytics Data Representation Dr. Ramon Lawrence University of British Columbia Okanagan ramon.lawrence@ubc.ca DATA 301: Data Analytics (2) Computer Terminology There is a

More information

UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS

UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS UNIT - I: COMPUTER ARITHMETIC, REGISTER TRANSFER LANGUAGE & MICROOPERATIONS (09 periods) Computer Arithmetic: Data Representation, Fixed Point Representation, Floating Point Representation, Addition and

More information

1.1. Unit 1. Integer Representation

1.1. Unit 1. Integer Representation 1.1 Unit 1 Integer Representation 1.2 Skills & Outcomes You should know and be able to apply the following skills with confidence Convert an unsigned binary number to and from decimal Understand the finite

More information

umber Systems bit nibble byte word binary decimal

umber Systems bit nibble byte word binary decimal umber Systems Inside today s computers, data is represented as 1 s and 0 s. These 1 s and 0 s might be stored magnetically on a disk, or as a state in a transistor. To perform useful operations on these

More information

CS429: Computer Organization and Architecture

CS429: Computer Organization and Architecture CS429: Computer Organization and Architecture Dr. Bill Young Department of Computer Sciences University of Texas at Austin Last updated: September 18, 2017 at 12:48 CS429 Slideset 4: 1 Topics of this Slideset

More information

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning

4 Operations On Data 4.1. Foundations of Computer Science Cengage Learning 4 Operations On Data 4.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List the three categories of operations performed on data.

More information

Chapter 2: Number Systems

Chapter 2: Number Systems Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This two-valued number system is called binary. As presented earlier, there are many

More information

Systems I. Floating Point. Topics IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties

Systems I. Floating Point. Topics IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties Systems I Floating Point Topics IEEE Floating Point Standard Rounding Floating Point Operations Mathematical properties IEEE Floating Point IEEE Standard 754 Established in 1985 as uniform standard for

More information

Floating Point. What can be represented in N bits? 0 to 2N-1. 9,349,398,989,787,762,244,859,087, x 1067

Floating Point. What can be represented in N bits? 0 to 2N-1. 9,349,398,989,787,762,244,859,087, x 1067 MIPS Floating Point Operations Cptr280 Dr Curtis Nelson Floating Point What can be represented in N bits? Unsigned 2 s Complement 0 to 2N-1-2N-1 to 2N-1-1 But, what about- Very large numbers? 9,349,398,989,787,762,244,859,087,678

More information

Introduction to Computer Science. Homework 1

Introduction to Computer Science. Homework 1 Introduction to Computer Science Homework. In each circuit below, the rectangles represent the same type of gate. Based on the input and output information given, identify whether the gate involved is

More information

Data Representation Floating Point

Data Representation Floating Point Data Representation Floating Point CSCI 2400 / ECE 3217: Computer Architecture Instructor: David Ferry Slides adapted from Bryant & O Hallaron s slides via Jason Fritts Today: Floating Point Background:

More information

8/30/2016. In Binary, We Have A Binary Point. ECE 120: Introduction to Computing. Fixed-Point Representations Support Fractions

8/30/2016. In Binary, We Have A Binary Point. ECE 120: Introduction to Computing. Fixed-Point Representations Support Fractions University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing Fixed- and Floating-Point Representations In Binary, We Have A Binary Point Let

More information

Lecture Notes: Floating-Point Numbers

Lecture Notes: Floating-Point Numbers Lecture Notes: Floating-Point Numbers CS227-Scientific Computing September 8, 2010 What this Lecture is About How computers represent numbers How this affects the accuracy of computation Positional Number

More information

Floating Point Representation. CS Summer 2008 Jonathan Kaldor

Floating Point Representation. CS Summer 2008 Jonathan Kaldor Floating Point Representation CS3220 - Summer 2008 Jonathan Kaldor Floating Point Numbers Infinite supply of real numbers Requires infinite space to represent certain numbers We need to be able to represent

More information