Agenda EE 224: INTRODUCTION TO DIGITAL CIRCUITS & COMPUTER DESIGN. Lecture 1: Introduction. Go over the syllabus 3/31/2010


 Susan Turner
 2 years ago
 Views:
Transcription
1 // EE : INTRODUCTION TO DIGITAL CIRCUITS & COMPUTER DESIGN Lecture : Introduction /9/ Avinash Kodi, Agenda Go over the syllabus Introduction ti to Digital it Systems
2 // Why Digital Systems? Obvious reason Implementation ti basis for all modern computing, communication and control devices (C ) Building larger things from smaller components Faster, cheaper, more efficient than analog More reasons Inherent parallelism in hardware In addition to serial software design Binary Representation Binary Information digits (BITS) or n bits specify M = n different values Or M values specified by n = log M bits
3 // The DigitalBinary World 5 Easy to process binary data Digital logic where voltage <.5 V is a and >. 5 V is a Easy to store binary data Fast disk and CDROM storage devices, cheap and small Memory stick Easy to transmit and protect Data protection well developed (parity) Easy to describe mathematically Discrete mathematics (boolean algebra) Design of Computers Hierarchical Design Hardware Computerbased system design Design in which a computer is interfaced with and/or embedded in a larger system with a specific function, System design Design in which components such as the CPU. Memory, and I/O chips are interfaced to build a computer, Gate or Logic level Design of higherlevel components with chips containing logical gates Device level Design of logic gates using transistors
4 // Abstraction Levels 7 Hardware: Levels of Detail  (topdown) x y ALU s, s z Block diagram x y Arithmetic Unit Logic Unit MUX z s s Magnified processor topography
5 // Hardware: Levels of Detail  Block diagram Logic diagram x y Arithmetic Unit Logic Unit MUX z x y MUX g x y MUX g s s x y MUX g x y MUX g Hardware: Levels of Detail & x Logic diagram y MUX g x y MUX g x y MUX g x y MUX g A B Electric circuit diagram NAND NOT C s 5
6 // Design of Computers Hierarchical Design Software (topdown) High Level Language Program (e.g., C) Compiler Assembly Language Program Assembler Machine Language g Program // Swap A and B temp = A; A = B; B = temp; mov AX,A mov BX,B mov A,BX mov B,AX D D D D or Machine Interpretation Control Signal Specification History of Computers Vacuum Tubes Transistors VLSI ENIAC Eckert and Mauchly 96 8, vacuum tubes,,8 instructions/sec,, ft Intel Microprocessor Introduced in 97,5 transistors, mm, 8 KHz Processor speed doubles every 8 months (Moore s Law) Memory speed doubles every 5 years 6
7 // Pentium  55,, Transistors 6 mm Ghz Introduced in Intel Core Duo E66 65nm technology node 9 Million transistors mm 7
8 // Number System  Definition 5 A set of values to represent quantity We apply numbers everyday and knowing how numbers work will give us insight into how computer manipulates and stores numbers Example: Roman Numerals ( = I, 5 = V, = X, 5 = L, = C, 5 = D, = M) History 6 The number system in most common use today is the Arabic system. It was first developed in India and was used as early as the rd century BC. The introduction of the symbol, used to indicate the positional value of digits was very important. We thus became familiar with the concept of groups of units, tens of units, hundreds of units, and so on. In number systems, it is often helpful to think of y, p recurring sets, where a set of values is repeated over and over again. We always write the digit with the largest value on the left of the number 8
9 // Base Values 7 The base (R=radix) value of a number system is the number of different values the set has before repeating itself Binary = (, ) Octal = 8 (  7) Decimal = ( 9) Hexadecimal = 6 ( 9, A F) A number at any base can be expanded in a power series (positional notation) ti N ) = ( aaaaa. a a a R = = a R + a R + a R + a R + a R + R + a R + a R a i R 7 a Decimal Number System (Base ) 8 Uses different symbols to represent values the greatest value (digit and column) the least value (digit and column) 96 = N ) = ( aaaaa. a a a R = = a R + a R + a R + a R + a R + + R + a R + a R a i R 8 a... 9
10 // Decimal Number System (Base ) 9 Uses only different symbols to represent values the greatest value (digit and column) the least value (digit and column) Columns are used identical to the decimal system, leftmost is used to represent the greatest value Increasing order of value Octal Number System (Base 8) Uses 8 different symbols to represent values the greatest value (digit and column) the least value (digit and column)
11 // Hexadecimal Number System (Base 6) Uses 6 different symbols to represent values A B C D E F the least value the greatest value A =, B =, C =, D =, E =, F = 5 Binary to Decimal Convert to Decimal = = = N ) = ( aaaaa. a a a R = = a R + a R + a R + a R + a R + + R + a R + a R a i R a...
12 // What about fraction conversion? Example:. = +. = = = N ) +. 5 = ( aaaaa. a a a R = = a R + a R + a R + a R + a R + + R + a R + a R a i R a... Decimal to Binary Divide the number by, then divide what s left by, and so on until there is nothing left (zero) 5 = 5/ = 7, Remainder = 7/ =, Remainder = / = 6, Remainder = 6/ =, Remainder = / =, Remainder = / =, Remainder =
13 // 5 What about decimal fractions into binary?.65 = F = (. a a a ) R F R = a + a R + a R = a. F Conversion of a decimal fraction to base R can be done using successive multiplications by R. F R = a + a R = a. F F =.65 F =.5 F =.5 x x x.5.5. =. a  = a  = a  = Class Problem 6 Convert 7. 8 into decimal Convert AF 6 into decimal Convert 5 into binary Convert.7 into binary
14 // InterBase Conversion 7 Conversion between bases other than decimal is generally easier if we use decimal as an intermediate base Example: Convert (.) to base 7 For Binary Hexadecimal, each hexadecimal digit represents binary bits, split the binary numbers into groups of bits, starting from right Example: Convert = (55B6.6) 6 BINHEXDEC Conversion Table 8 Decimal (base ) Binary (base ) Octal (base 8) Hexadecimal (base 6) A B C 5 D 6 E 5 7 F
15 // Binary Numbers & Coding 9 Flexibility of representation In principle, can assign any binary combination (called a code word) to any data as long as it is uniquely encoded Information Type Numeric Must represent the range of data needed Simple, straightforward computation for common arithmetic operations permitted Relation to binary numbers NonNumeric Greater flexibility since no arithmetic operations Not tied to binary numbers Binary Codes for Decimal Digits There are over 8, ways in which you can choose elements from 6 possible bit binary numbers. Decimal 8,,, Excess 8,,, Gray
16 // Binary Coded Decimal (BCD) BCD is the 8,,, code Referring to bit weights used Simplest, intuitive code for binary Uses powers of, but only encodes the first ten values from to 9 Eg: (9) = (8) + () There are invalid code words like or Decimal ,,, Gray Code Unweighted and nonarithmetic, arranged so that every transition from one value to the next involves only one bit change. Decimal Gray B B B (a) Binary Code for Positions through 7 G G G (b) Gray Code for Positions through 7 6
17 // Arithmetic: Binary, Octal, Hexadecimal, Binary Codes Addition Subtraction ti Multiplication Division Unsigned Binary Addition Just like in high school (carry s) Carry Out LSB CarryIn is the default CarryIn to the Least Significant Bit (LSB) 7
18 // Binary Subtraction 5 Just like in high school (borrow s) Minuend 5 8 Subtrahend Binary Multiplication 6 Binary Multiplication is simple x = ; x = ; x = ; x = Multiplicand Multiplier x Partial Products x xx Products 8
19 // Binary Division 7 Arithmetic Inversion of Multiplication Example: Divide id. with Octal Multiplication 8 Multiply 56 8 with 8 showing all intermediate steps 56 8 x x 6 8 = = x5 8 = = x 8 = = 8 8 x 6 8 = = x5 8 = = x 8 =6 =6 8 9
20 // Hexadecimal Subtraction 9 Subtract (A96B) 6 (9FC) 6 Minuend A 9 6 B 6 Subtrahend  9 F C 6 Difference A F 6 The partial differences were found a) BC =BC=(6+)=7=5=F BC produces a negative result, so a borrow is generated b) 5  = c) (9 + 6) F = A d) 9 9 = BCD Arithmetic Given a BCD code, we use binary arithmetic to add the digits: 8 Eight +5 + Plus 5 is (> 9) Note that the result is MORE THAN 9, so needs two digits! To correct the BCD digit, ADD 6, 8 Eight +5 + Plus 5 is (> 9) + so add 6 carry = leaving + carry Final answer (two digits)
21 // More BCD Arithmetic Add 8 BCD to 89 BCD showing carries and digit corrections Carry BCD Carry + Binary sum Add 6 + BCD Sum BCD Result 9 7
DIGITAL SYSTEM DESIGN
DIGITAL SYSTEM DESIGN UNIT I: Introduction to Number Systems and Boolean Algebra Digital and Analog Basic Concepts, Some history of Digital SystemsIntroduction to number systems, Binary numbers, Number
More informationChapter 1. Digital Systems and Binary Numbers
Chapter 1. Digital Systems and Binary Numbers Tong In Oh 1 1.1 Digital Systems Digital age Characteristic of digital system Generality and flexibility Represent and manipulate discrete elements of information
More informationBINARY SYSTEM. Binary system is used in digital systems because it is:
CHAPTER 2 CHAPTER CONTENTS 2.1 Binary System 2.2 Binary Arithmetic Operation 2.3 Signed & Unsigned Numbers 2.4 Arithmetic Operations of Signed Numbers 2.5 Hexadecimal Number System 2.6 Octal Number System
More informationLogic and Computer Design Fundamentals. Chapter 1 Digital Computers and Information
Logic and Computer Design Fundamentals Chapter 1 Digital Computers and Information Overview Digital Systems and Computer Systems Information Representation Number Systems [binary, octal and hexadecimal]
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd Chapter 2 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Decimal Numbers The position of each digit in a weighted
More informationDigital Systems COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals
Digital Systems COE 202 Digital Logic Design Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Welcome to COE 202 Course Webpage: http://faculty.kfupm.edu.sa/coe/mudawar/coe202/ Lecture
More informationCS 121 Digital Logic Design. Chapter 1. Teacher Assistant. Hadeel AlAteeq
CS 121 Digital Logic Design Chapter 1 Teacher Assistant Hadeel AlAteeq Announcement DON T forgot to SIGN your schedule OR you will not be allowed to attend next lecture. Communication Office hours (8
More informationCHW 261: Logic Design
CHW 261: Logic Design Instructors: Prof. Hala Zayed Dr. Ahmed Shalaby http://www.bu.edu.eg/staff/halazayed14 http://bu.edu.eg/staff/ahmedshalaby14# Slide 1 Slide 2 Slide 3 Digital Fundamentals CHAPTER
More informationLecture (02) Operations on numbering systems
Lecture (02) Operations on numbering systems By: Dr. Ahmed ElShafee ١ Dr. Ahmed ElShafee, ACU : Spring 2018, CSE202 Logic Design I Complements of a number Complements are used in digital computers to simplify
More informationKorea University of Technology and Education
MEC52 디지털공학 Binary Systems JeeHwan Ryu School of Mechanical Engineering Binary Numbers a 5 a 4 a 3 a 2 a a.a  a 2 a 3 base or radix = a n r n a n r n...a 2 r 2 a ra a  r  a 2 r 2...a m r m
More informationComputer Sc. & IT. Digital Logic. Computer Sciencee & Information Technology. 20 Rank under AIR 100. Postal Correspondence
GATE Postal Correspondence Computer Sc. & IT 1 Digital Logic Computer Sciencee & Information Technology (CS) 20 Rank under AIR 100 Postal Correspondence Examination Oriented Theory, Practice Set Key concepts,
More informationChapter 1 Review of Number Systems
1.1 Introduction Chapter 1 Review of Number Systems Before the inception of digital computers, the only number system that was in common use is the decimal number system which has a total of 10 digits
More informationNumeral Systems. Numeral System Positional systems Decimal Binary Octal. Subjects:
Numeral Systems Numeral System Positional systems Decimal Binary Octal Subjects: Introduction A numeral system (or system of numeration) is a writing system for expressing numbers, that is a mathematical
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers Mano & Ciletti Chapter 1 By Suleyman TOSUN Ankara University Outline Digital Systems Binary Numbers NumberBase Conversions Octal and Hexadecimal Numbers Complements
More informationLecture (03) Binary Codes Registers and Logic Gates
Lecture (03) Binary Codes Registers and Logic Gates By: Dr. Ahmed ElShafee Binary Codes Digital systems use signals that have two distinct values and circuit elements that have two stable states. binary
More informationEEM 232 Digital System I
EEM 232 Digital System I Instructor : Assist. Prof. Dr. Emin Germen egermen@anadolu.edu.tr Course Book : Logic and Computer Design Fundamentals by Mano & Kime Third Ed/Fourth Ed.. Pearson Grading 1 st
More informationMACHINE LEVEL REPRESENTATION OF DATA
MACHINE LEVEL REPRESENTATION OF DATA CHAPTER 2 1 Objectives Understand how integers and fractional numbers are represented in binary Explore the relationship between decimal number system and number systems
More informationD 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 informationIntroduction to Numbering Systems
NUMBER SYSTEM Introduction to Numbering Systems We are all familiar with the decimal number system (Base 10). Some other number systems that we will work with are Binary Base 2 Octal Base 8 Hexadecimal
More informationDigital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes
Digital Fundamentals CHAPTER 2 Number Systems, Operations, and Codes Decimal Numbers The decimal number system has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 The decimal numbering system has a base of
More informationChapter 3: Number Systems and Codes. Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc.
Chapter 3: Number Systems and Codes Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc., 5 th edition Decimal System The radix or base of a number system determines
More informationCOE 202: Digital Logic Design Number Systems Part 2. Dr. Ahmad Almulhem ahmadsm AT kfupm Phone: Office:
COE 0: Digital Logic Design Number Systems Part Dr. Ahmad Almulhem Email: ahmadsm AT kfupm Phone: 8607554 Office: 34 Objectives Arithmetic operations: Binary number system Other number systems Base Conversion
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:0011:15 SEB 1242 Lecture 22 121115 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Binary Number Representation Binary Arithmetic Combinatorial Logic
More informationNumber Systems CHAPTER Positional Number Systems
CHAPTER 2 Number Systems Inside computers, information is encoded as patterns of bits because it is easy to construct electronic circuits that exhibit the two alternative states, 0 and 1. The meaning of
More informationDIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM
COURSE / CODE DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) NUMBER SYSTEM A considerable subset of digital systems deals with arithmetic operations. To understand the
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers Prof. Wangrok Oh Dept. of Information Communications Eng. Chungnam National University Prof. Wangrok Oh(CNU) 1 / 51 Overview 1 Course Summary 2 Binary Numbers 3 NumberBase
More informationChapter 2: Number Systems
Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This twovalued number system is called binary. As presented earlier, there are many
More information2. MACHINE REPRESENTATION OF TYPICAL ARITHMETIC DATA FORMATS (NATURAL AND INTEGER NUMBERS).
2. MACHINE REPRESENTATION OF TYPICAL ARITHMETIC DATA FORMATS (NATURAL AND INTEGER NUMBERS). 2.. Natural Binary Code (NBC). The positional code with base 2 (B=2), introduced in Exercise, is used to encode
More informationDigital 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 informationNumbering systems. Dr Abu Arqoub
Numbering systems The decimal numbering system is widely used, because the people Accustomed (معتاد) to use the hand fingers in their counting. But with the development of the computer science another
More informationAssembly Language for IntelBased Computers, 4 th Edition. Chapter 1: Basic Concepts. Chapter Overview. Welcome to Assembly Language
Assembly Language for IntelBased Computers, 4 th Edition Kip R. Irvine Chapter 1: Basic Concepts Slides prepared by Kip R. Irvine Revision date: 09/15/2002 Chapter corrections (Web) Printing a slide show
More informationMs Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES. 1.1 Introduction
Ms Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES Structure 2.1 Introduction 2.2 Objectives 2.3 Binary Numbers 2.3.1 BinarytoDecimal conversion 2.3.2 DecimaltoBinary Conversion 2.4 Octal Numbers
More informationMicrocomputers. Outline. Number Systems and Digital Logic Review
Microcomputers Number Systems and Digital Logic Review Lecture 11 Outline Number systems and formats Common number systems Base Conversion Integer representation Signed integer representation Binary coded
More informationNumber Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris HuiRu 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 informationThe x86 Microprocessors. Introduction. The 80x86 Microprocessors. 1.1 Assembly Language
The x86 Microprocessors Introduction 1.1 Assembly Language Numbering and Coding Systems Human beings use the decimal system (base 10) Decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Computer systems use the
More informationETGG1801 Game Programming Foundations I Andrew Holbrook Fall Lecture 0  Introduction to Computers 1
ETGG1801 Game Programming Foundations I Andrew Holbrook Fall 2013 Lecture 0  Introduction to Computers 1 Introduction to Computers Vacuum Tubes and Transistors Electricallycontrolled switches Logic Gates
More informationLogic Circuits I ECE 1411 Thursday 4:45pm7:20pm. Nathan Pihlstrom.
Logic Circuits I ECE 1411 Thursday 4:45pm7:20pm Nathan Pihlstrom www.uccs.edu/~npihlstr My Background B.S.E.E. from Colorado State University M.S.E.E. from Colorado State University M.B.A. from UCCS Ford
More informationTOPIC: NUMBER SYSTEMS
Ministry of Secondary Education Progressive Comprehensive High School PCHS Mankon Bamenda Department of Computer Studies Republic of Cameroon Peace Work  Fatherland TOPIC: NUMBER SYSTEMS Class: Comp.
More informationNUMBER SYSTEMS AND CODES
C H A P T E R 69 Learning Objectives Number Systems The Decimal Number System Binary Number System Binary to Decimal Conversion Binary Fractions DoubleDadd Method Decimal to Binary Conversion Shifting
More informationMoodle WILLINGDON COLLEGE SANGLI. ELECTRONICS (B. Sc.I) Introduction to Number System
Moodle 1 WILLINGDON COLLEGE SANGLI ELECTRONICS (B. Sc.I) Introduction to Number System E L E C T R O N I C S Introduction to Number System and Codes Moodle developed By Dr. S. R. Kumbhar Department of
More informationSlide Set 1. for ENEL 339 Fall 2014 Lecture Section 02. Steve Norman, PhD, PEng
Slide Set 1 for ENEL 339 Fall 2014 Lecture Section 02 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2014 ENEL 353 F14 Section
More informationECE 20B, Winter Purpose of Course. Introduction to Electrical Engineering, II. Administration
ECE 20B, Winter 2003 Introduction to Electrical Engineering, II Instructor: Andrew B Kahng (lecture) Email: abk@eceucsdedu Telephone: 8588224884 office, 8583530550 cell Office: 3802 AP&M Lecture: TuThu
More informationELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE2700: Digital Logic Design Winter Notes  Unit 4. hundreds.
UNSIGNED INTEGER NUMBERS Notes  Unit 4 DECIMAL NUMBER SYSTEM A decimal digit can take values from to 9: Digitbydigit representation of a positive integer number (powers of ): DIGIT 3 4 5 6 7 8 9 Number:
More informationDLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR
UNIT I Digital Systems: Binary Numbers, Octal, Hexa Decimal and other base numbers, Number base conversions, complements, signed binary numbers, Floating point number representation, binary codes, error
More informationLOGIC DESIGN. Dr. Mahmoud Abo_elfetouh
LOGIC DESIGN Dr. Mahmoud Abo_elfetouh Course objectives This course provides you with a basic understanding of what digital devices are, how they operate, and how they can be designed to perform useful
More informationNumber System. Introduction. Decimal Numbers
Number System Introduction Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26
More informationHistory of Computing. Ahmed Sallam 11/28/2014 1
History of Computing Ahmed Sallam 11/28/2014 1 Outline Blast from the past Layered Perspective of Computing Why Assembly? Data Representation Base 2, 8, 10, 16 Number systems Boolean operations and algebra
More informationBinary. Hexadecimal BINARY CODED DECIMAL
Logical operators Common arithmetic operators, like plus, minus, multiply and divide, works in any number base but the binary number system provides some further operators, called logical operators. Meaning
More informationELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE278: Digital Logic Design Fall Notes  Unit 4. hundreds.
ECE78: Digital Logic Design Fall 6 UNSIGNED INTEGER NUMBERS Notes  Unit 4 DECIMAL NUMBER SYSTEM A decimal digit can take values from to 9: Digitbydigit representation of a positive integer number (powers
More informationLecture 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 informationUNIT 2 NUMBER SYSTEM AND PROGRAMMING LANGUAGES
UNIT 2 NUMBER SYSTEM AND PROGRAMMING LANGUAGES Structure 2.0 Introduction 2.1 Unit Objectives 2.2 Number Systems 2.3 Bits and Bytes 2.4 Binary Number System 2.5 Decimal Number System 2.6 Octal Number System
More informationQUIZ 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. Multicore CPU Transistors
More informationChapter 2. Data Representation in Computer Systems
Chapter 2 Data Representation in Computer Systems Chapter 2 Objectives Understand the fundamentals of numerical data representation and manipulation in digital computers. Master the skill of converting
More informationCHAPTER TWO. Data Representation ( M.MORRIS MANO COMPUTER SYSTEM ARCHITECTURE THIRD EDITION ) IN THIS CHAPTER
1 CHAPTER TWO Data Representation ( M.MORRIS MANO COMPUTER SYSTEM ARCHITECTURE THIRD EDITION ) IN THIS CHAPTER 21 Data Types 22 Complements 23 FixedPoint Representation 24 FloatingPoint Representation
More informationOctal & Hexadecimal Number Systems. Digital Electronics
Octal & Hexadecimal Number Systems Digital Electronics What, More Number Systems? Why do we need more number systems? Humans understand decimal Check out my ten digits! Digital electronics (computers)
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers & Number Systems
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers & Number Systems Introduction Numbers and Their Properties Multiples and Factors The Division Algorithm Prime and Composite Numbers Prime Factors
More informationLevel ISA3: Information Representation
Level ISA3: Information Representation 1 Information as electrical current At the lowest level, each storage unit in a computer s memory is equipped to contain either a high or low voltage signal Each
More informationReview of Number Systems
Review of Number Systems The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a digital computer.
More informationDIGITAL ARITHMETIC: OPERATIONS AND CIRCUITS
C H A P T E R 6 DIGITAL ARITHMETIC: OPERATIONS AND CIRCUITS OUTLINE 6 Binary Addition 62 Representing Signed Numbers 63 Addition in the 2 s Complement System 64 Subtraction in the 2 s Complement
More informationLogic Design: Part 2
Orange Coast College Business Division Computer Science Department CS 6 Computer Architecture Logic Design: Part 2 Where are we? Number systems Decimal Binary (and related Octal and Hexadecimal) Binary
More informationChapter Overview. Assembly Language for IntelBased Computers, 4 th Edition. Chapter 1: Basic Concepts. Printing this Slide Show
Assembly Language for IntelBased Computers, 4 th Edition Kip R. Irvine Chapter 1: Basic Concepts Chapter Overview Welcome to Assembly Language Virtual Machine Concept Data Representation Boolean Operations
More informationSlide Set 1. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary
Slide Set 1 for ENEL 353 Fall 2017 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2017 SN s ENEL 353 Fall 2017 Slide Set 1 slide
More informationBinary Systems and Codes
1010101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101010
More informationDLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 3 DLD P VIDYA SAGAR
DLD UNIT III Combinational Circuits (CC), Analysis procedure, Design Procedure, Combinational circuit for different code converters and other problems, Binary Adder Subtractor, Decimal Adder, Binary Multiplier,
More informationCMSC 313 COMPUTER ORGANIZATION & ASSEMBLY LANGUAGE PROGRAMMING LECTURE 01, SPRING 2013
CMSC 313 COMPUTER ORGANIZATION & ASSEMBLY LANGUAGE PROGRAMMING LECTURE 01, SPRING 2013 TOPICS TODAY Course overview Levels of machines Machine models: von Neumann & System Bus FetchExecute Cycle Base
More informationDigital Techniques. Lecture 1. 1 st Class
Digital Techniques Lecture 1 1 st Class Digital Techniques Digital Computer and Digital System: Digital computer is a part of digital system, it based on binary system. A block diagram of digital computer
More informationElectronics Engineering ECE / E & T
STUDENT COPY DIGITAL ELECTRONICS 1 SAMPLE STUDY MATERIAL Electronics Engineering ECE / E & T Postal Correspondence Course GATE, IES & PSUs Digital Electronics 2015 ENGINEERS INSTITUTE OF INDIA. All Rights
More informationChapter 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 informationPositional Number System
Positional Number System A number is represented by a string of digits where each digit position has an associated weight. The weight is based on the radix of the number system. Some common radices: Decimal.
More informationLearning the Binary System
Learning the Binary System www.brainlubeonline.com/counting_on_binary/ Formated to L A TEX: /25/22 Abstract This is a document on the base2 abstract numerical system, or Binary system. This is a VERY
More informationIT 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 information2 Number Systems 2.1. Foundations of Computer Science Cengage Learning
2 Number Systems 2.1 Foundations of Computer Science Cengage Learning 2.2 Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish between
More information9/3/2015. Data Representation II. 2.4 Signed Integer Representation. 2.4 Signed Integer Representation
Data Representation II CMSC 313 Sections 01, 02 The conversions we have so far presented have involved only unsigned numbers. To represent signed integers, computer systems allocate the highorder bit
More information1. 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 informationComputer Organization
Computer Organization Register Transfer Logic Number System Department of Computer Science Missouri University of Science & Technology hurson@mst.edu 1 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5,
More informationDigital Logic Design Exercises. Assignment 1
Assignment 1 For Exercises 15, match the following numbers with their definition A Number Natural number C Integer number D Negative number E Rational number 1 A unit of an abstract mathematical system
More informationMicroprocessors I MICROCOMPUTERS AND MICROPROCESSORS
Microprocessors I Outline of the Lecture Microcomputers and Microprocessors Evolution of Intel 80x86 Family Microprocessors Binary and Hexadecimal Number Systems MICROCOMPUTERS AND MICROPROCESSORS There
More informationCourse Syllabus [1/2]
Course Syllabus [1/2] Instructor 逄愛君, acpang@csie.ntu.edu.tw Office Number: 417, Office Hour: 15:00~17:00 (Thursday) Textbook Assembly Language for IntelBased Computers, Kip R. Irvine, Pearson Education,
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd Chapter 2 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Quiz 2 Agenda Lecture: Chapter 2 (27 through 211):
More informationLOGIC CIRCUITS. Kirti P_Didital Design 1
LOGIC CIRCUITS Kirti P_Didital Design 1 Introduction The digital system consists of two types of circuits, namely (i) Combinational circuits and (ii) Sequential circuit A combinational circuit consists
More informationCPE 323 REVIEW DATA TYPES AND NUMBER REPRESENTATIONS IN MODERN COMPUTERS
CPE 323 REVIEW DATA TYPES AND NUMBER REPRESENTATIONS IN MODERN COMPUTERS Aleksandar Milenković The LaCASA Laboratory, ECE Department, The University of Alabama in Huntsville Email: milenka@uah.edu Web:
More informationPositional notation Ch Conversions between Decimal and Binary. /continued. Binary to Decimal
Positional notation Ch.. /continued Conversions between Decimal and Binary Binary to Decimal  use the definition of a number in a positional number system with base  evaluate the definition formula using
More informationCPE 323 REVIEW DATA TYPES AND NUMBER REPRESENTATIONS IN MODERN COMPUTERS
CPE 323 REVIEW DATA TYPES AND NUMBER REPRESENTATIONS IN MODERN COMPUTERS Aleksandar Milenković The LaCASA Laboratory, ECE Department, The University of Alabama in Huntsville Email: milenka@uah.edu Web:
More informationFinal Labs and Tutors
ICT106 Fundamentals of Computer Systems  Topic 2 REPRESENTATION AND STORAGE OF INFORMATION Reading: Linux Assembly Programming Language, Ch 2.42.9 and 3.63.8 Final Labs and Tutors Venue and time South
More informationOutline. What Digit? => Number System. Decimal (base 10) Significant Digits. Lect 03 Number System, Gates, Boolean Algebra. CS221: Digital Design
Lect 3 Number System, Gates, Boolean Algebra CS22: Digital Design Dr. A. Sahu Dept of Comp. Sc. & Engg. Indian Institute of Technology Guwahati Outline Number System Decimal, Binary, Octal, Hex Conversions
More informationChap 1. Digital Computers and Information
Chap 1. Digital Computers and Information Spring 004 Overview Digital Systems and Computer Systems Information Representation Number Systems [binary, octal and hexadecimal] Arithmetic Operations Base Conversion
More informationCMPE223/CMSE222 Digital Logic Design. Positional representation
CMPE223/CMSE222 Digital Logic Design Number Representation and Arithmetic Circuits: Number Representation and Unsigned Addition Positional representation First consider integers Begin with positive only
More informationNumber representations
Number representations Number bases Three number bases are of interest: Binary, Octal and Hexadecimal. We look briefly at conversions among them and between each of them and decimal. Binary Basetwo, or
More informationBinary Addition. Add the binary numbers and and show the equivalent decimal addition.
Binary Addition The rules for binary addition are 0 + 0 = 0 Sum = 0, carry = 0 0 + 1 = 0 Sum = 1, carry = 0 1 + 0 = 0 Sum = 1, carry = 0 1 + 1 = 10 Sum = 0, carry = 1 When an input carry = 1 due to a previous
More informationUser. Application program. Interfaces. Operating system. Hardware
Operating Systems Introduction to Operating Systems and Computer Hardware Introduction and Overview The operating system is a set of system software routines that interface between an application program
More informationExcerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997
Excerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997 APPENDIX A.1 Number systems and codes Since tenfingered humans are addicted to the decimal system, and since computers
More informationQUIZ: 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 informationPrinciples of Computer Architecture. Chapter 3: Arithmetic
31 Chapter 3  Arithmetic Principles of Computer Architecture Miles Murdocca and Vincent Heuring Chapter 3: Arithmetic 32 Chapter 3  Arithmetic 3.1 Overview Chapter Contents 3.2 Fixed Point Addition
More informationComputer Logical Organization Tutorial
Computer Logical Organization Tutorial COMPUTER LOGICAL ORGANIZATION TUTORIAL Simply Easy Learning by tutorialspoint.com tutorialspoint.com i ABOUT THE TUTORIAL Computer Logical Organization Tutorial Computer
More informationENE 334 Microprocessors
Page 1 ENE 334 Microprocessors Lecture 10: MCS51: Logical and Arithmetic : Dejwoot KHAWPARISUTH http://webstaff.kmutt.ac.th/~dejwoot.kha/ ENE 334 MCS51 Logical & Arithmetic Page 2 Logical: Objectives
More informationMemory Addressing, Binary, and Hexadecimal Review
C++ By A EXAMPLE Memory Addressing, Binary, and Hexadecimal Review You do not have to understand the concepts in this appendix to become wellversed in C++. You can master C++, however, only if you spend
More informationChapter 1 Preliminaries
Chapter 1 Preliminaries This chapter discusses the major classes of programming languages and the relationship among them. It also discusses the binary and the hexadecimal number systems which are used
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Spring, 2018 ldvan@cs.nctu.edu.tw http://www.cs.nctu.edu.tw/~ldvan/ Outline
More informationLecture (01) Digital Systems and Binary Numbers By: Dr. Ahmed ElShafee
١ Lecture (01) Digital Systems and Binary Numbers By: Dr. Ahmed ElShafee Digital systems Digital systems are used in communication, business transactions, traffic control, spacecraft guidance, medical
More informationCHAPTER 2 Number Systems
CHAPTER 2 Number Systems Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish between nonpositional and positional number systems.
More information