Today s topics. Digital Computers. More on binary. Binary Digits (Bits)


 Domenic Griffith
 2 years ago
 Views:
Transcription
1 Today s topics! Binary Numbers! Brookshear..! Slides from Prof. Marti Hearst of UC Berkeley SIMS! Upcoming! Networks Interactive Introduction to Graph Theory Kearns, Michael. "Economics, Computer Science, and Policy." Issues in Science and Technology, Winter 5.! Problem Solving Digital Computers! What are computers made up of?! Lowest level of abstraction: atoms! Higher level: transistors! Transistors! Invented in 95 at Bell Labs! An electronic switch! Building block for all modern electronics! Transistors are packaged as Integrated Circuits (ICs)! million transistors in IC Compsci. Compsci. Binary Digits (Bits)! Yes or No! On or Off! One or Zero! More on binary! Byte! A sequence of bits! 8 bits = byte! bytes = word (sometimes or 8 bytes)! Powers of two! How do binary numbers work? Compsci. Compsci.
2 Data Encoding! Text: Each character (letter, punctuation, etc.) is assigned a unique bit pattern.! ASCII: Uses patterns of 7bits to represent most symbols used in written English text! Unicode: Uses patterns of bits to represent the major symbols used in languages world side! ISO standard: Uses patterns of bits to represent most symbols used in languages world wide! Numbers: Uses bits to represent a number in base two! Limitations of computer representations of numeric values! Overflow happens when a value is too big to be represented! Truncation happens when a value is between two representable values Images, Sound, & Compression! Images! Store as bit map: define each pixel RGB Luminance and chrominance! Vector techniques Scalable TrueType and PostScript! Audio! Sampling! Compression! Lossless: Huffman, LZW, GIF! Lossy: JPEG, MPEG, MP Compsci.5 Compsci. Decimal (Base ) Numbers Binary (Base ) Numbers! Each digit in a decimal number is chosen from ten symbols: {,,,,, 5,, 7, 8, 9 }! The position (right to left) of each digit represents a power of ten.! Example: Consider the decimal number 7 7!!!! position: 7 = " + " + " + 7"! Each digit in a binary number is chosen from two symbols: {, }! The position (right to left) of each digit represents a power of two.! Example: Convert binary number to decimal!!!! position: = " + " + " + " = "8 + " + " + " = = Compsci.7 Compsci.8
3 Powers of Two Famous Powers of Two Decimal 8 8 Binary Power of 5 7 Compsci.9 Compsci. Other Number Systems Binary Addition Also: + + = with a carry of Compsci. Compsci.
4 Adding Binary Numbers ! + = ( " + " + " ) + ( " + " ) = ( " + " + " ) + ( " + " )! Add like terms: There is one, one, one = " + " + " = Adding Binary Numbers $ carry ! + = ( " + " + " ) + (" + " + " ) = ( " + " + " ) + (" + " + " )! Add like terms: There are two s, two s, one = " + " + "! BinaryNumber Applet = "8 + " + " + " = Compsci. Compsci. Converting Decimal to Binary Converting Decimal to Binary Decimal # # conversion # # = " = " = " + " = + = " + " = " + " + " 5 = + = " + " + " = + = " + " + " 7 = ++ = " + " + " 8 = " + " + " + " Binary! Repeated division by two until the quotient is zero! Example: Convert decimal number 5 to binary 7 Binary representation of 5 is 5 remainder Compsci.5 Compsci.
5 Converting Decimal to Binary Problems 7 5! Subtracting highest power of two! s in positions 5,,,! = plus thirtytwo! 8s = plus sixteen! s = plus eights! s = 8s plus four! 7 s = s plus two! 5 = 7 s plus ones 55 =  =  =  = Compsci.7! Convert to decimal representation! Add the binary numbers and and express their sum in binary representation! Convert 77 to binary representation Compsci.8 Solutions! Convert to decimal representation Solutions! Convert 77 to binary representation = " + " 5 + " + " + " + " + " = " + " + " + "8 + " + " + " = = 88! Add the binary numbers and and express their sum in binary representation Binary representation of 77 is Compsci.9 Compsci.
6 Boolean Logic! AND, OR, NOT, NOR, NAND, XOR! Each operator has a set of rules for combining two binary inputs! These rules are defined in a Truth Table! (This term is from the field of Logic)! Each implemented in an electronic device called a gate! Gates operate on inputs of s and s! These are more basic than operations like addition! Gates are used to build up circuits that Compute addition, subtraction, etc Store values to be used later Translate values from one format to another Truth Tables Compsci. Compsci. InClass Questions. How many different bit patterns can be formed if each must consist of exactly bits?. Represent the bit pattern in hexadecimal notation.. Translate each of the following binary representations into its equivalent base ten representation..... Translate in decimal to binary Compsci.
1. Which of the following Boolean operations produces the output 1 for the fewest number of input patterns?
Test Bank Chapter One (Data Representation) Multiple Choice Questions 1. Which of the following Boolean operations produces the output 1 for the fewest number of input patterns? ANSWER: A A. AND B. OR
More informationActivity 1: Bits and Bytes
ICS3U (Java): Introduction to Computer Science, Grade 11, University Preparation Activity 1: Bits and Bytes The Binary Number System Computers use electrical circuits that include many transistors and
More informationSection 1.4 Place Value Systems of Numeration in Other Bases
Section.4 Place Value Systems of Numeration in Other Bases Other Bases The HinduArabic system that is used in most of the world today is a positional value system with a base of ten. The simplest reason
More informationLogic Design. Dr. Yosry A. Azzam
Logic Design Dr. Yosry A. Azzam Binary systems Chapter 1 Agenda Binary Systems : Binary Numbers, Binary Codes, Binary Logic ASCII Code (American Standard Code for Information Interchange) Boolean Algebra
More informationDigital Fundamentals
Digital Fundamentals with PLD Programming Floyd Chapter 2 29 Pearson Education Decimal Numbers The position of each digit in a weighted number system is assigned a weight based on the base or radix of
More informationData Storage. Chapter 3. Objectives. 31 Data Types. Data Inside the Computer. After studying this chapter, students should be able to:
Chapter 3 Data Storage Objectives After studying this chapter, students should be able to: List five different data types used in a computer. Describe how integers are stored in a computer. Describe how
More informationReview of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement
Review of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement Topic 1: Binary, Octal, and Hexadecimal Numbers The number system we generally use in our everyday lives is a decimal
More informationPart 1 Theory Fundamentals
Part 1 Theory Fundamentals 2 Chapter 1 Information Representation Learning objectives By the end of this chapter you should be able to: show understanding of the basis of different number systems show
More informationDigital System Design Prof. D. Roychoudhury Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Digital System Design Prof. D. Roychoudhury Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture  03 Digital Logic  I Today, we will start discussing on Digital
More informationData Representation. Data Representation, Storage, and Retrieval. Data Representation. Data Representation. Data Representation. Data Representation
, Storage, and Retrieval ULM/HHIM Summer Program Project 3, Day 3, Part 3 Digital computers convert the data they process into a digital value. Text Audio Images/Graphics Video Digitizing 00000000... 6/8/20
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: 10/27/2002 Chapter corrections (Web) Printing a slide show
More informationBinary Adders: Half Adders and Full Adders
Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order
More informationNumber System. Some important number systems are as follows. Decimal number system Binary number system Octal number system Hexadecimal number system
Number System When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only
More informationLecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor
Lecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor During that lecture we learnt about the function of the central component of a computer, the microprocessor
More informationChapter II Binary Data Representation
Chapter II Binary Data Representation The atomic unit of data in computer systems is the bit, which is actually an acronym that stands for BInary digit. It can hold only 2 values or states: 0 or 1, true
More informationEncoding Systems: Combining Bits to form Bytes
Encoding Systems: Combining Bits to form Bytes Alphanumeric characters are represented in computer storage by combining strings of bits to form unique bit configuration for each character, also called
More informationData Representation in Computers
Chapter 3 Data Representation in Computers After studying this chapter the student will be able to: *Learn about binary, octal, decimal and hexadecimal number systems *Learn conversions between two different
More informationComputer Science 281 Binary and Hexadecimal Review
Computer Science 281 Binary and Hexadecimal Review 1 The Binary Number System Computers store everything, both instructions and data, by using many, many transistors, each of which can be in one of two
More informationUnit 2: Number Systems, Codes and Logic Functions
Unit 2: Number Systems, Codes and Logic Functions Introduction A digital computer manipulates discrete elements of data and that these elements are represented in the binary forms. Operands used for calculations
More informationTheory of Logic Circuits. Laboratory manual. Exercise 6
Zakład Mikroinformatyki i Teorii Automatów Cyfrowych Theory of Logic Circuits Laboratory manual Exercise 6 Selected arithmetic switching circuits 2008 Tomasz Podeszwa, Piotr Czekalski (edt.) 1. Number
More informationHere 4 is the least significant digit (LSD) and 2 is the most significant digit (MSD).
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 informationYear 9 CS Learning Cycle 4 Overview How is data represented in computer systems?
Year 9 CS Learning Cycle 4 Overview Learning Cycle Overview: Line of enquiry one: What is binary? Week 1 A kilobyte is 1000 bytes. I can count to more than 1000 on my fingers. There is only one way to
More informationIntroduction Number Systems and Conversion
UNIT 1 Introduction Number Systems and Conversion Objectives 1. Introduction The first part of this unit introduces the material to be studied later. In addition to getting an overview of the material
More informationData Storage 3.1. Foundations of Computer Science Cengage Learning
3 Data Storage 3.1 Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: List five different data types used in a computer. Describe how
More informationCMPS 10 Winter Homework Assignment 5
CMPS 10 Winter 2011 Homework Assignment 5 Problems: Chapter 4 (p.184): 1abc, 3abcd, 4ab, 5abc, 6, 7, 9abcd, 15abcd, 17, 18, 19, 20 1. Given our discussion of positional numbering systems in Section 4.2.1,
More informationEM108 Software Development for Engineers Section 5 Storing Information
EM108 5 Storing Information page 1 of 11 EM108 Software Development for Engineers Section 5 Storing Information 5.1 Motivation: Various information types o Various types of numbers o Text o Images, Audios,
More informationDigital System Design Prof. D Roychoudhry Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur
Digital System Design Prof. D Roychoudhry Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture  04 Digital Logic II May, I before starting the today s lecture
More informationAssembly Language for IntelBased Computers, 4 th Edition. Chapter 1: Basic Concepts
Assembly Language for IntelBased Computers, 4 th Edition Kip R. Irvine Chapter 1: Basic Concepts Slides prepared by Kip R. Irvine Revision date: 07/21/2002 Chapter corrections (Web) Assembly language
More informationBits, bytes, and representation of information
Bits, bytes, and representation of information digital representation means that everything is represented by numbers only the usual sequence: something (sound, pictures, text, instructions,...) is converted
More informationBinary Numbers. X. Zhang Fordham Univ.
Binary Numbers X. Zhang Fordham Univ. 1 Numeral System! A way for expressing numbers, using symbols in a consistent manner.!! "11" can be interpreted differently:!! in the binary symbol: three!! in the
More informationLECTURE 2: Number Systems
LECTURE : Number Systems CIS Fall 7 Instructor: Dr. Song Xing Department of Information Systems California State University, Los Angeles Learning Objectives Review Boolean algebra. Describe numbering systems
More informationMT1 Number Systems. In general, the number a 3 a 2 a 1 a 0 in a base b number system represents the following number:
MT1 Number Systems MT1.1 Introduction A number system is a well defined structured way of representing or expressing numbers as a combination of the elements of a finite set of mathematical symbols (i.e.,
More informationChapter 4. Binary Data Representation and Binary Arithmetic
Christian Jacob Chapter 4 Binary Data Representation and Binary Arithmetic 4.1 Binary Data Representation 4.2 Important Number Systems for Computers 4.2.1 Number System Basics 4.2.2 Useful Number Systems
More informationBinary Numbers. Binary Octal Hexadecimal
Binary Numbers Binary Octal Hexadecimal Binary Numbers COUNTING SYSTEMS UNLIMITED... Since you have been using the 10 different digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 all your life, you may wonder how
More information1 Basic Computing Concepts (4) Data Representations
1 Basic Computing Concepts (4) Data Representations The Binary System The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. The
More informationNumber Representation and Arithmetic in Various Numeral Systems
1 Number Representation and Arithmetic in Various Numeral Systems Computer Organization and Assembly Language Programming 203.8002 Adapted by Yousef Shajrawi, licensed by Huong Nguyen under the Creative
More informationالدكتور المھندس عادل مانع داخل
الدكتور المھندس عادل مانع داخل / میسان جامعة / كلیة الھندسة قسم الھندسة الكھرباي یة Chapter 1: Digital Systems Discrete Data Examples: 26 letters of the alphabet (A, B etc) 10 decimal digits (0, 1, 2 etc)
More informationBy the end of the lecture, you should be able to:
Extra Lecture: Number Systems Objectives  To understand: Base of number systems: decimal, binary, octal and hexadecimal Textual information stored as ASCII Binary addition/subtraction, multiplication
More informationA First Book of C++ Chapter 2 Data Types, Declarations, and Displays
A First Book of C++ Chapter 2 Data Types, Declarations, and Displays Objectives In this chapter, you will learn about: Data Types Arithmetic Operators Variables and Declarations Common Programming Errors
More informationNumber Systems and Data Representation CS221
Number Systems and Data Representation CS221 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, core,
More informationCDA 3200 Digital Systems. Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012
CDA 3200 Digital Systems Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012 Outline Data Representation Binary Codes Why 6311 and Excess3? Data Representation (1/2) Each numbering
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers. Factors 2. Multiples 3. Prime and Composite Numbers 4. Modular Arithmetic 5. Boolean Algebra 6. Modulo 2 Matrix Arithmetic 7. Number Systems
More informationComputer Systems Architecture
Computer Systems Architecture http://cs.nott.ac.uk/ txa/g51csa/ Thorsten Altenkirch School of Computer Science and IT University of Nottingham Lecture 01: Bits, bytes and numbers Bits Bit = Binary Digit
More informationRelative Data Redundancy
Image Compression Relative Data Redundancy Let b and b denote the number of bits in two representations of the same information, the relative data redundancy R is R = 11/C C is called the compression
More informationCHAPTER TWO. 2.1 Unsigned Binary Counting. Numbering Systems
CHAPTER TWO Numbering Systems Chapter one discussed how computers remember numbers using transistors, tiny devices that act like switches with only two positions, on or off. A single transistor, therefore,
More informationCS 16: Assembly Language Programming for the IBM PC and Compatibles
CS 16: Assembly Language Programming for the IBM PC and Compatibles First, a little about you Your name Have you ever worked with/used/played with assembly language? If so, talk about it Why are you taking
More informationBase Conversion written by Cathy Saxton
Base Conversion written by Cathy Saxton 1. Base 10 In base 10, the digits, from right to left, specify the 1 s, 10 s, 100 s, 1000 s, etc. These are powers of 10 (10 x ): 10 0 = 1, 10 1 = 10, 10 2 = 100,
More informationCommon Number Systems Number Systems
5/29/204 Common Number Systems Number Systems System Base Symbols Used by humans? Used in computers? Decimal 0 0,, 9 Yes No Binary 2 0, No Yes Octal 8 0,, 7 No No Hexadecimal 6 0,, 9, A, B, F No No Number
More informationEE 3170 Microcontroller Applications
EE 37 Microcontroller Applications Lecture 3 : Digital Computer Fundamentals  Number Representation (.) Based on slides for ECE37 by Profs. Sloan, Davis, Kieckhafer, Tan, and Cischke Number Representation
More informationNUMBER REPRESENTATIONS IN THE COMPUTER for COSC 120
NUMBER REPRESENTATIONS IN THE COMPUTER for COSC 120 First, a reminder of how we represent base ten numbers. Base ten uses ten (decimal) digits: 0, 1, 2,3, 4, 5, 6, 7, 8, 9. In base ten, 10 means ten. Numbers
More informationNumber Systems and. Data Representation
Number Systems and Data Representation 1 Lecture Outline Number Systems Binary, Octal, Hexadecimal Representation of characters using codes Representation of Numbers Integer, Floating Point, Binary Coded
More informationCSC 1103: Digital Logic. Lecture Six: Data Representation
CSC 1103: Digital Logic Lecture Six: Data Representation Martin Ngobye mngobye@must.ac.ug Mbarara University of Science and Technology MAN (MUST) CSC 1103 1 / 32 Outline 1 Digital Computers 2 Number Systems
More informationLecture 7: Image coding and compression
Lecture 7: Image coding and compression Robin Strand Centre for Image Analysis Swedish University of Agricultural Sciences Uppsala University Today Information and Data Redundancy Image Quality Coding
More informationCyber Security Workshop Encryption Reference Manual
Cyber Security Workshop Encryption Reference Manual May 2015 Basic Concepts in Encoding and Encryption Binary Encoding Examples Encryption Cipher Examples 1 P a g e Encoding Concepts Binary Encoding Basics
More informationThe Power of Binary 0, 1, 10, 11, 100, 101, 110,
The Power of Binary 0, 1, 10, 11, 100, 101, 110, 111... What is Binary? a binary number is a number expressed in the binary numeral system, or base2 numeral system, which represents numeric values using
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 informationDecimal Numbers: Base 10 Integer Numbers & Arithmetic
Decimal Numbers: Base 10 Integer Numbers & Arithmetic Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 )+(1x10 0 ) Ward 1 Ward 2 Numbers: positional notation Number
More informationPart 1: Logic Design. Tutorial
CPIT2 : Computer Organization and Architecture Course Lectures by Prof. Mohamed Khamis Part : Logic Design Tutorial by Teaching Assistant. Khalid Alharbi Department of Information Technology Faculty of
More informationTHE BINARY NUMBER SYSTEM
THE BINARY NUMBER SYSTEM Dr. Robert P. Webber, Longwood University Our civilization uses the base 10 or decimal place value system. Each digit in a number represents a power of 10. For example, 365.42
More informationGates, Circuits, and Boolean Algebra
Gates, Circuits, and Boolean Algebra Computers and Electricity A gate is a device that performs a basic operation on electrical signals Gates are combined into circuits to perform more complicated tasks
More informationBits, Bytes, and Representation of Information
Bits, Bytes, and Representation of Information Digital representation means that everything is represented by numbers only The usual sequence: something (sound, pictures, text, instructions,...) is converted
More informationComputer is a binary digital system. Data. Unsigned Integers (cont.) Unsigned Integers. Binary (base two) system: Has two states: 0 and 1
Computer Programming Programming Language Is telling the computer how to do something Wikipedia Definition: Applies specific programming languages to solve specific computational problems with solutions
More informationSwitching Circuits & Logic Design
Switching Circuits & Logic Design JieHong Roland Jiang 江介宏 Department of Electrical Engineering National Taiwan University Fall 2013 1 1 Number Systems and Conversion Babylonian number system (3100 B.C.)
More informationBinary. ! You are probably familiar with decimal
Arithmetic operations in assembly language Prof. Gustavo Alonso Computer Science Department ETH Zürich alonso@inf.ethz.ch http://www.inf.ethz.ch/department/is/iks/ Binary! You are probably familiar with
More informationUNIT 2 : NUMBER SYSTEMS
UNIT 2 : NUMBER SYSTEMS page 2.0 Introduction 1 2.1 Decimal Numbers 2 2.2 The Binary System 3 2.3 The Hexadecimal System 5 2.4 Number Base Conversion 6 2.4.1 Decimal To Binary 6 2.4.2 Decimal to Hex 7
More informationDigital Logic. The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer.
Digital Logic 1 Data Representations 1.1 The Binary System The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. The system we
More informationORG ; ZERO. Introduction To Computing
Dec 0 Hex 0 Bin 00000000 ORG ; ZERO Introduction To Computing OBJECTIVES this chapter enables the student to: Convert any number from base 2, base 10, or base 16 to any of the other two bases. Add and
More informationLecture 2. Binary and Hexadecimal Numbers
Lecture 2 Binary and Hexadecimal Numbers Purpose: Review binary and hexadecimal number representations Convert directly from one base to another base Review addition and subtraction in binary representations
More informationBits and Bytes. Computer Literacy Lecture 4 29/09/2008
Bits and Bytes Computer Literacy Lecture 4 29/09/2008 Lecture Overview Lecture Topics How computers encode information How to quantify information and memory How to represent and communicate binary data
More informationAPPENDIX B. Routers route based on the network number. The router that delivers the data packet to the correct destination host uses the host ID.
APPENDIX B IP Subnetting IP Addressing Routers route based on the network number. The router that delivers the data packet to the correct destination host uses the host ID. IP Classes An IP address is
More informationNumber Systems I. CIS0082 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October
Number Systems I CIS0082 Logic and Foundations of Mathematics David Goodwin david.goodwin@perisic.com 11:00, Tuesday 18 th October 2011 Outline 1 Number systems Numbers Natural numbers Integers Rational
More informationDigital Circuits. Frequently Asked Questions
Digital Circuits Frequently Asked Questions Module 1: Digital & Analog Signals 1. What is a signal? Signals carry information and are defined as any physical quantity that varies with time, space, or any
More informationDigital Logic Circuits
Digital Logic Circuits Digital describes any system based on discontinuous data or events. Typically digital is computer data or electronic sampling of an analog signal. Computers are digital machines
More informationSigned Binary Arithmetic
Signed Binary Arithmetic In the real world of mathematics, computers must represent both positive and negative binary numbers. For example, even when dealing with positive arguments, mathematical operations
More informationBinary Numbers. Binary Numbers. Wolfgang Schreiner Research Institute for Symbolic Computation (RISC) Johannes Kepler University, Linz, Austria
Binary Numbers Wolfgang Schreiner Research Institute for Symbolic Computation (RISC) Johannes Kepler University, Linz, Austria Wolfgang.Schreiner@risc.unilinz.ac.at http://www.risc.unilinz.ac.at/people/schreine
More informationThe string of digits 101101 in the binary number system represents the quantity
Data Representation Section 3.1 Data Types Registers contain either data or control information Control information is a bit or group of bits used to specify the sequence of command signals needed for
More informationencoding compression encryption
encoding compression encryption ASCII utf8 utf16 zip mpeg jpeg AES RSA diffiehellman Expressing characters... ASCII and Unicode, conventions of how characters are expressed in bits. ASCII (7 bits) 
More informationBinary Representation
Binary Representation The basis of all digital data is binary representation. Binary  means two 1, 0 True, False Hot, Cold On, Off We must tbe able to handle more than just values for real world problems
More informationBinary Representation. Number Systems. Positional Notation
Binary Representation The basis of all digital data is binary representation. Binary  means two 1, 0 True, False Hot, Cold On, Off We must be able to handle more than just values for real world problems
More informationLab 1: Information Representation I  Number Systems
Unit 1: Computer Systems, pages 1 of 7  Department of Computer and Mathematical Sciences CS 1408 Intro to Computer Science with Visual Basic 1 Lab 1: Information Representation I  Number Systems Objectives:
More informationLab 1: Information Representation I  Number Systems
Unit 1: Computer Systems, pages 1 of 7  Department of Computer and Mathematical Sciences CS 1410 Intro to Computer Science with C++ 1 Lab 1: Information Representation I  Number Systems Objectives:
More informationBinary Representation. Number Systems. Base 10, Base 2, Base 16. Positional Notation. Conversion of Any Base to Decimal.
Binary Representation The basis of all digital data is binary representation. Binary  means two 1, 0 True, False Hot, Cold On, Off We must be able to handle more than just values for real world problems
More informationNumber Systems and Base Conversions
Number Systems and Base Conversions As you know, the number system that we commonly use is the decimal or base 10 number system. That system has 10 digits, 0 through 9. While it's very convenient for
More informationOct: 50 8 = 6 (r = 2) 6 8 = 0 (r = 6) Writing the remainders in reverse order we get: (50) 10 = (62) 8
ECE Department Summer LECTURE #5: Number Systems EEL : Digital Logic and Computer Systems Based on lecture notes by Dr. Eric M. Schwartz Decimal Number System: Our standard number system is base, also
More informationCSI 333 Lecture 1 Number Systems
CSI 333 Lecture 1 Number Systems 1 1 / 23 Basics of Number Systems Ref: Appendix C of Deitel & Deitel. Weighted Positional Notation: 192 = 2 10 0 + 9 10 1 + 1 10 2 General: Digit sequence : d n 1 d n 2...
More informationNUMBERING SYSTEMS C HAPTER 1.0 INTRODUCTION 1.1 A REVIEW OF THE DECIMAL SYSTEM 1.2 BINARY NUMBERING SYSTEM
12 Digital Principles Switching Theory C HAPTER 1 NUMBERING SYSTEMS 1.0 INTRODUCTION 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,
More informationChapter 3: Number Systems
Slide 1/40 Learning Objectives In this chapter you will learn about: Nonpositional number system Positional number system Decimal number system Binary number system Octal number system Hexadecimal number
More informationDiscrete Structures. Rajmohan Rajaraman Eric Ropiak Chris Burrows Ravi Sundaram
Discrete Structures Harriet Fell Javed A. Aslam Rajmohan Rajaraman Eric Ropiak Chris Burrows Ravi Sundaram Discrete Structures Version 2.1 Harriet Fell Javed A. Aslam Rajmohan Rajaraman Eric Ropiak Chris
More informationBinary Numbers. Binary Numbers. Wolfgang Schreiner Research Institute for Symbolic Computation (RISC) Johannes Kepler University, Linz, Austria
Binary Numbers Wolfgang Schreiner Research Institute for Symbolic Computation (RISC) Johannes Kepler University, Linz, Austria Wolfgang.Schreiner@risc.unilinz.ac.at http://www.risc.unilinz.ac.at/people/schreine
More informationChapter 4: Computer Codes
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 36 Slide 2/30 Data
More informationBits, Data Types, and Operations. University of Texas at Austin CS310H  Computer Organization Spring 2010 Don Fussell
Bits, Data Types, and Operations University of Texas at Austin CS3H  Computer Organization Spring 2 Don Fussell How do we represent data in a computer? At the lowest level, a computer is an electronic
More informationNumber Representation
Number Representation Number System :: The Basics We are accustomed to using the socalled decimal number system Ten digits ::,,,3,4,5,6,7,8,9 Every digit position has a weight which is a power of Base
More informationSolution for Homework 2
Solution for Homework 2 Problem 1 a. What is the minimum number of bits that are required to uniquely represent the characters of English alphabet? (Consider upper case characters alone) The number of
More informationRadix Number Systems. Number Systems. Number Systems 4/26/2010. basic idea of a radix number system how do we count:
Number Systems binary, octal, and hexadecimal numbers why used conversions, including to/from decimal negative binary numbers floating point numbers character codes basic idea of a radix number system
More informationIntroduction ToNumber Systems
Introduction ToNumber Systems Collected by: Zainab Alkadhem Page 1 of 25 Digital systems have such a prominent role in everyday life that we refer to the present technological period as the digital age.
More informationInteger Numbers. The Number Bases of Integers Textbook Chapter 3
Integer Numbers The Number Bases of Integers Textbook Chapter 3 Number Systems Unary, or marks: /////// = 7 /////// + ////// = ///////////// Grouping lead to Roman Numerals: VII + V = VVII = XII Better:
More informationEE 308 Spring Binary, Hex and Decimal Numbers (4bit representation) Binary. Hex. Decimal A B C D E F
EE 8 Spring Binary, Hex and Decimal Numbers (bit representation) Binary Hex 8 9 A B C D E F Decimal 8 9 EE 8 Spring What does a number represent? Binary numbers are a code, and represent what the programmer
More informationNumber Systems. Decimal Number System. Number Systems Week 3
Number Systems When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only
More informationLecture.5. Number System:
Number System: Lecturer: Dr. Laith Abdullah Mohammed Lecture.5. The number system that we use in daytoday life is called Decimal Number System. It makes use of 10 fundamental digits i.e. 0, 1, 2, 3,
More information2 Number Systems. Source: Foundations of Computer Science Cengage Learning. Objectives After studying this chapter, the student should be able to:
2 Number Systems 2.1 Source: Foundations of Computer Science Cengage Learning Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish
More information