EE 3170 Microcontroller Applications


 Abigail Powell
 1 years ago
 Views:
Transcription
1 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 Integers in different radices (bases) decimal, binary, octal, hexadecimal Unsigned Binary Numbers Twos Complement Signed Binary Numbers Definition, Properties, Arithmetic The ASCII Character Code EE37/CC/Lecture#3 EE37/CC/Lecture#3 2 Preliminaries Three Systems of Number Representation Radix = the base of a number system Given radix k : one digit has one of k values need k symbols for values [ k] Common Radices: decimal: k =, symbols = [ 9] binary: k = 2, symbols = [,] octal: k = 8, symbols = [...7] hexadecimal: k = 6, symbols = [ 9, a, b, c, d, e, f ] Three systems of representing unsigned numbers, all of them positional, but each based on a different radix, or base: Decimal (radix): This is the standard representation that you re used to. Binary (radix2): This is the actual representation used in all digital systems at the hardware level. Hexadecimal, or hex, (radix6): This is closely related to binary, often used to represent values in digital systems using fewer digits than required by binary. The octal (radix8) representation is also common, but we won t use it in this course. EE37/CC/Lecture#3 3 EE37/CC/Lecture#3 4
2 Binary Numbers Binary to Decimal Exercise Binary (base 2) numbers are arranged like decimal numbers in positions. Each position stands for a power of 2. Example: 2 is x2 5 + x2 4 + x2 3 + x2 2 + x2 + x2 = = 53 Changing from binary to decimal just means adding the powers of 2 for which the position has a. 2 A. 239 B. 247 C. 25 D. 253 E. 255 is EE37/CC/Lecture#3 5 EE37/CC/Lecture#3 6 How Do We Change from Decimal to Binary? Divide the decimal number repeatedly by 2. Put the remainders from right to left. 53/2 = 26 R 26/2 = 3 R 3/2 = 6 R 6/2 = 3 R 3/2 = R /2 = R Decimal to Binary Exercise 99 is A. B. C. D. E. 53 = 2 EE37/CC/Lecture#3 7 EE37/CC/Lecture#3 8 2
3 How Many Bits Do We Need? The range of unsigned eightbit binary numbers is: The range of unsigned 6bit binary numbers is: The range of unsigned nbit binary numbers is: range = [, 2 n ] How Many Bits Do We Need? The number of binary digits (bits) we need depends on the size of the number we want to represent. 8 bits gives 256 numbers 6 bits gives 65.5k numbers 24 bits gives 6.7M numbers 32 bits gives 4.3 G numbers EE37/CC/Lecture#3 9 EE37/CC/Lecture#3 Observations Computer Prefixes Modern computers use multiples of 8 bits. Sometimes these have special names. 8 bits 6 bits 32 bits byte word Standard computer prefixes are based on powers of 2 rather than powers of and some are pronounced differently. Symbol K M G T Pronounced kay meg gig tera Power of bits long word P peta 5 We will mainly use 8 and 6 bits in EE37. E exa 6 Know at least the first four of these. EE37/CC/Lecture#3 EE37/CC/Lecture#3 2 3
4 Grouping Bits into Hex Long bit strings are hard to remember recognize work with Hence we group four bits together in a hexadecimal (base 6) digit or nibble. Hex Decimal Binary A B C 2 D 3 E 4 F 5 EE37/CC/Lecture#3 3 How Do We Change Binary to Hex? Starting at right, group bits by four. Change each group into its hex number. Put $ (Motorola s hex designator) in front. % is Motorola s binary designator. Decimal is default (no designator.) Note: Just pad on the left with enough s to get a multiple of four bits. Example: % D E 9 B $DE9B EE37/CC/Lecture#3 4 Binary to Hex Exercise % is A. $B586 B. $BD8E C. $E8DB How Do We Change Hex to Binary? Replace each hex digit by its 4bit binary equivalent. Put a % (Motorola s binary designator) in front. Example: $A476 A % EE37/CC/Lecture#3 5 EE37/CC/Lecture#3 6 4
5 Hex to Binary Exercise Summary: Conversion Between Radices $28A7 is A. % B. % C. % From: binary or hexadecimal To: decimal use the radix expansions Binary to or from Hex Each hex digit = exactly 4 binary bits. So, one (8bit) byte can hold 2 hex digits Simply collect bits into groups of 4 (starting at right): EE37/CC/Lecture#3 7 EE37/CC/Lecture#3 8 Boolean Values Unsigned Numbers Two states ON OFF +5 V V open closed clockwise counterclockwise all s any nonzero value EE37/CC/Lecture#3 9 Unsigned numbers Use all bits for magnitude Can be thought of as positive. b7 b6 b5 b4 b3 b2 b b Each bit represents 2 n Range is to 255 (2 8 ) Observations If the right bit is, the number is even. If the right n bits are, the number is divisible by 2 n If the left bit of an 8bit number is, the number is at least 28. EE37/CC/Lecture#3 2 5
6 How Can We Represent Signed Numbers? We need one bit for the sign. Use the leftmost bit. = +, =  Other bits are magnitude. Three possibilities shown with 4 bits. +5 =, 5 = signmagnitude +5 =, 5 = s complement +5 =, 5 = 2 s complement Observations? Twos Complement Signed Numbers Definition: negation = complement all bits then add. The mostsignificant bit is the signbit = for positive numbers = for negative numbers Range = [2 n, 2 n ] Uses the same arithmetic hardware as unsigned overflow bits are discarded Subtracting a number is equivalent to adding its twos complement negative number (pp.8) EE37/CC/Lecture#3 2 EE37/CC/Lecture# bit 2 s complement How Can We Find 2 s Complement Representations? 2 s complement is used in modern computers. Consider 3bit 2 s complement. Range is 4 to +3. Number b3 b2 b For positive numbers Write binary equivalent Add s at left as needed for total of n bits. Example: 8bit 2 s complement representation of = = in 2 s complement 4 EE37/CC/Lecture#3 23 EE37/CC/Lecture#3 24 6
7 How Can We Find 2 s Complement Representations? For negative numbers Write binary equivalent of positive number Add s at left as needed for n bits total. Complement each bit. ( ; ) Add. Example: 8bit 2 s complement rep. of = = in 2 s complement 7 = + = EE37/CC/Lecture# s Complement Exercise 23 in 6bit 2 s complement is A. B. C. D. EE37/CC/Lecture#3 26 Observations To find the magnitude of a negative 2 s complement number left bit = Complement each bit Add Example: + = or 7 2 s complement represents both positive and negative numbers. Observations We can negate a positive 2 s complement number with exactly the same procedure. Complement each bit. Add. Example: + = or 7 decimal EE37/CC/Lecture#3 27 EE37/CC/Lecture#3 28 7
8 Magnitude of 2 s Complement Number The magnitude of the 6bit 2 s complement number is A. B. 2 C. 3 D. 4 E. 22 Range of 2 s Complement Numbers Range of nbit 2 s complement numbers is 2 n to 2 n . Examples: 4bit to to +7 8bit to to +27 EE37/CC/Lecture#3 29 EE37/CC/Lecture#3 3 Range of 6bit 2 s Complement A. 64 to +63 B. 64 to +64 C. 32 to +32 D. 32 to +3 E. 3 to +32 How Do We Change 8bit 2 s Complement to More Bits? Sign Extension Copy the sign bit to the left. Examples: 8bit to 6bit 8bit to 32bit EE37/CC/Lecture#3 3 EE37/CC/Lecture#3 32 8
9 How Do We Encode Decimal Numbers? Binary Coded Decimal (BCD) is handy for decimal numbers. Each digit is encoded in 4bit binary. Why BCD? Convenient for certain I/O devices that work w/ decimal numbers Examples: 97 = BCD How Do We Know if Numbers Are Signed or Unsigned? You, the programmer, decide whether numbers are signed or unsigned. The computer doesn t know what a bit pattern means until you tell it. The bit pattern could be a character. 2 = BCD EE37/CC/Lecture#3 33 EE37/CC/Lecture#3 34 Character Representations Characters must be represented as binary numbers uppercase, lowercase, Numerals, Punctuation, control characters (nonprinting) How many Bits? 7 bits : 28 Characters = EBCDIC & ASCII 8 bits : 256 Characters = Extended ASCII 6 bits : 26 Characters = Unicode How Do We Represent Characters? ASCII (American Standard Code for Information Interchange) Standard (7bit) 27 characters Extended (8bit) 255 characters Example: M = $4D = % from table EE37/CC/Lecture#3 35 EE37/CC/Lecture#3 36 9
10 ASCII Character Code Control Characters: First 32 values [ 2 6 ] Numerals: number X = 3X 6 i.e. [ ] very easy to recognize and decode Upper Case = [4 6 5A 6 ] = [,,] Lower Case = [6 6 7A 6 ] = [,,] Punctuation is scattered through remaining patterns ASCII EE37/CC/Lecture#3 37 EE37/CC/Lecture#3 38 Summary ASCII Extended Converting numbers among decimal, binary and hex (EE27) Two s complement numbers (EE27) Ranges of signed and unsigned numbers How to represent characters EE37/CC/Lecture#3 39 EE37/CC/Lecture#3 4
By 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 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 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 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 information2.1 Binary Numbers. 2.3 Number System Conversion. From Binary to Decimal. From Decimal to Binary. Section 2 Binary Number System Page 1 of 8
Section Binary Number System Page 1 of 8.1 Binary Numbers The number system we use is a positional number system meaning that the position of each digit has an associated weight. The value of a given number
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 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 informationCOMP2121: Microprocessors and Interfacing
Interfacing Lecture 3: Number Systems (I) http://www.cse.unsw.edu.au/~cs2121 Lecturer: Hui Wu Session 2, 2005 Overview Positional notation Decimal, hexadecimal and binary One complement Two s complement
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 informationChap 3 Data Representation
Chap 3 Data Representation 311 Data Types How to representation and conversion between these data types? 311 Data Types : Number System Radix : Decimal : radix 10 Binary : radix 2 311 Data Types : 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 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 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 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 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 informationNumber Representation
Number Representation CS10001: Programming & Data Structures Pallab Dasgupta Professor, Dept. of Computer Sc. & Engg., Indian Institute of Technology Kharagpur Topics to be Discussed How are numeric data
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 informationReview 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 computer. Different
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 informationNumber 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 informationThe largest has a 0 in the sign position and 0's in all other positions:
10.2 Sign Magnitude Representation Sign Magnitude is straightforward method for representing both positive and negative integers. It uses the most significant digit of the digit string to indicate the
More informationLecture 2: Number System
Lecture 2: Number System Today s Topics Review binary and hexadecimal number representation Convert directly from one base to another base Review addition and subtraction in binary representation Determine
More informationCPE 323 Data Types and Number Representations
CPE 323 Data Types and Number Representations Aleksandar Milenkovic Numeral Systems: Decimal, binary, hexadecimal, and octal We ordinarily represent numbers using decimal numeral system that has 10 as
More informationDigital Arithmetic. Digital Arithmetic: Operations and Circuits Dr. Farahmand
Digital Arithmetic Digital Arithmetic: Operations and Circuits Dr. Farahmand Binary Arithmetic Digital circuits are frequently used for arithmetic operations Fundamental arithmetic operations on binary
More informationP A R T DIGITAL TECHNOLOGY
P A R T A DIGITAL TECHNOLOGY 1 CHAPTER NUMBERING SYSTEMS 1.0 INTRODUCTION This chapter discusses several important concepts including the binary, octal and hexadecimal numbering systems, binary data organization
More informationCHAPTER 2 Data Representation in Computer Systems
CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 47 2.2 Positional Numbering Systems 48 2.3 Converting Between Bases 48 2.3.1 Converting Unsigned Whole Numbers 49 2.3.2 Converting Fractions
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 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 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 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 informationData Representation. Representing Data
Data Representation COMP 1002/1402 Representing Data A computer s basic unit of information is: a bit (Binary digit) An addressable memory cell is a byte (8 bits) Capable of storing one character 10101010
More informationChapter No.5 DATA REPRESENTATION
Chapter No.5 DATA REPRESENTATION Q.5.01 Complete the following statements. i) Data is a collection of ii) Data becomes information when properly. iii) Octal equivalent of binary number 1100010 is iv) 2
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 informationData types. lecture 4
Data types lecture 4 Information in digital computers is represented using binary number system. The base, i.e. radix, of the binary system is 2. Other common number systems: octal (base 8), decimal (base
More informationEE 261 Introduction to Logic Circuits. Module #2 Number Systems
EE 261 Introduction to Logic Circuits Module #2 Number Systems Topics A. Number System Formation B. Base Conversions C. Binary Arithmetic D. Signed Numbers E. Signed Arithmetic F. Binary Codes Textbook
More informationEEE130 Digital Electronics I Lecture #2
EEE130 Digital Electronics I Lecture #2 Number Systems, Operations and Codes By Dr. Shahrel A. Suandi Topics to be discussed 21 Decimal Numbers 22 Binary Numbers 23 DecimaltoBinary Conversion 24
More informationLecture 1 Introduction, Numbers, and Number System Page 1 of 8
Lecture Introduction, Numbers and Number System Contents.. Number Systems (Appendix B)... 2. Example. Converting to Base 0... 2.2. Number Representation... 2.3. Number Conversion... 3. To convert a number
More informationCHAPTER 1 BINARY SYSTEM
STUDENT COPY DIGITAL & MICROPROCESSORS 3 CHAPTER 1 BINARY SYSTEM Base Conversion: A number a n, a n 1 a 2, a 1 a 0 a 1 a 2 a 3 expressed in a base r system has coefficient multiplied by powers of r. n
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 information1 / 40. Data Representation. January 9 14, 2013
1 / 40 Data Representation January 9 14, 2013 Quick logistical notes In class exercises Bring paper and pencil (or laptop) to each lecture! Goals: break up lectures, keep you engaged chance to work through
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 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 informationSystems I: Computer Organization and Architecture
Systems I: Computer Organization and Architecture Lecture 2: Number Systems and Arithmetic Number Systems  Base The number system that we use is base : 734 = + 7 + 3 + 4 = x + 7x + 3x + 4x = x 3 + 7x
More informationComputer Number Systems
Computer Number Systems Thorne, Edition 2 : Section 1.3, Appendix I (Irvine, Edition VI : Section 1.3) SYSC3006 1 Starting from What We Already Know Decimal Numbers Based Number Systems : 1. Base defines
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 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 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 informationD r = d p1 d p2.. d 1 d 0.d 1 d 2. D n. EECC341  Shaaban
Positional Number Systems A number system consists of an order set of symbols (digits) with relations defined for +,,*, / The radix (or base) of the number system is the total number of digits allowed
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 informationCodes and number systems
Coding Codes and number systems Assume that you want to communicate with your friend with a flashlight in a night, what will you do? Introduction to Computer YungYu Chuang light painting? What s the problem?
More informationNumber Representation
Number Representation COMP375 Computer Organization and darchitecture t How do we represent data in a computer? At the lowest level, a computer is an electronic machine. works by controlling the flow of
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 information2011, The McGrawHill Companies, Inc. Chapter 3
Chapter 3 3.1 Decimal System The radix or base of a number system determines the total number of different symbols or digits used by that system. The decimal system has a base of 10 with the digits 0 through
More informationBinary Numbers. Bob Brown Information Technology Department Southern Polytechnic State University
Binary Numbers Bob Brown Information Technology Department Southern Polytechnic State University Positional Number Systems The idea of number is a mathematical abstraction. To use numbers, we must represent
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 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 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 informationLevent EREN levent.eren@ieu.edu.tr A306 Office Phone:4889882 INTRODUCTION TO DIGITAL LOGIC
Levent EREN levent.eren@ieu.edu.tr A306 Office Phone:4889882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A n
More informationLecture 2: Number Representation
Lecture 2: Number Representation CSE 30: Computer Organization and Systems Programming Summer Session II 2011 Dr. Ali Irturk Dept. of Computer Science and Engineering University of California, San Diego
More information2. Number Systems  Positional Number Systems (1)  2. Number Systems  Binary Numbers  2. Number Systems  Positional Number Systems (2) 
Sistemas Digitais I LESI  2º ano Lesson 2  Number Systems Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática  Positional Number Systems (1)  We use daily a positional number system.
More informationNumber Systems Richard E. Haskell
NUMBER SYSTEMS D Number Systems Richard E. Haskell Data inside a computer are represented by binary digits or bits. The logical values of these binary digits are denoted by and, while the corresponding
More informationCSCC85 Spring 2006: Tutorial 0 Notes
CSCC85 Spring 2006: Tutorial 0 Notes Yani Ioannou January 11 th, 2006 There are 10 types of people in the world, those who understand binary, and those who don t. Contents 1 Number Representations 1 1.1
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 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 information1. Convert the following binary exponential expressions to their 'English'
Answers to Practice Problems Practice Problems  Integer Number System Conversions 1. Convert the decimal integer 427 10 into the following number systems: a. 110101011 2 c. 653 8 b. 120211 3 d. 1AB 16
More informationA B C
Data Representation Module 2 CS 272 Sam Houston State University Dr. Tim McGuire Copyright 2001 by Timothy J. McGuire, Ph.D. 1 Positional Number Systems Decimal (base 10) is an example e.g., 435 means
More informationUsing 0 s and 1 s to Represent Stuff
Using 0 s and 1 s to Represent Stuff First, how many things can we represent? In one bit, two things. In two bits, four things. In three bits,? How many things do we want to represent? For numbers, at
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 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 informationChapter 2 Numeric Representation.
Chapter 2 Numeric Representation. Most of the things we encounter in the world around us are analog; they don t just take on one of two values. How then can they be represented digitally? The key is that
More informationUseful Number Systems
Useful Number Systems Decimal Base = 10 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Binary Base = 2 Digit Set = {0, 1} Octal Base = 8 = 2 3 Digit Set = {0, 1, 2, 3, 4, 5, 6, 7} Hexadecimal Base = 16 = 2
More informationCHAPTER V NUMBER SYSTEMS AND ARITHMETIC
CHAPTER V1 CHAPTER V CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V2 NUMBER SYSTEMS RADIXR REPRESENTATION Decimal number expansion 73625 10 = ( 7 10 4 ) + ( 3 10 3 ) + ( 6 10 2 ) + ( 2 10 1 ) +(
More informationNumber Systems, Base Conversions, and Computer Data Representation
, Base Conversions, and Computer Data Representation Decimal and Binary Numbers When we write decimal (base 10) numbers, we use a positional notation system. Each digit is multiplied by an appropriate
More informationTwo s Complement Arithmetic
Two s Complement Arithmetic We now address the issue of representing integers as binary strings in a computer. There are four formats that have been used in the past; only one is of interest to us. The
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 informationNumeral Systems. The number twentyfive can be represented in many ways: Decimal system (base 10): 25 Roman numerals:
Numeral Systems Which number is larger? 25 8 We need to distinguish between numbers and the symbols that represent them, called numerals. The number 25 is larger than 8, but the numeral 8 above is larger
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 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 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 information1 Number System (Lecture 1 and 2 supplement)
1 Number System (Lecture 1 and 2 supplement) By Dr. Taek Kwon Many different number systems perhaps from the prehistoric era have been developed and evolved. Among them, binary number system is one of
More informationChapter 1: Digital Systems and Binary Numbers
Chapter 1: Digital Systems and Binary Numbers Digital age and information age Digital computers general purposes many scientific, industrial and commercial applications Digital systems telephone switching
More informationDecimaltoBinary Conversion. Computer & Microprocessor Architecture HCA103. Repeated Divisionby2 Method. Repeated Multiplicationby2 Method
DecimaltoBinary Conversion Computer & Microprocessor Architecture HCA103 Computer Arithmetic Algorithm 1 Step 1: Break the number in two parts: Whole number and fraction part. Step 2: Repeated Divisionby2
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 informationNumber Systems! Why Bits (Binary Digits)?!
Number Systems Why Bits (Binary Digits)? Computers are built using digital circuits Inputs and outputs can have only two values True (high voltage) or false (low voltage) Represented as and Can represent
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 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 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 informationLSN 2 Number Systems. ECT 224 Digital Computer Fundamentals. Department of Engineering Technology
LSN 2 Number Systems Department of Engineering Technology LSN 2 Decimal Number System Decimal number system has 10 digits (09) Base 10 weighting system... 10 5 10 4 10 3 10 2 10 1 10 0. 101 102 103
More informationImperial College London Department of Computing
Imperial College London Department of Computing Architecture SELFSTUDY NOTES January 2016 Integers and Characters (1) SelfStudy Welcome to the Computer Architecture course. These notes cover basic topics
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 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 informationBinary Representation and Computer Arithmetic
Binary Representation and Computer Arithmetic The decimal system of counting and keeping track of items was first created by Hindu mathematicians in India in A.D. 4. Since it involved the use of fingers
More informationChapter 3 DATA REPRESENTATION. 3.1 Character Representation
Chapter 3 DATA REPRESENTATION Binary codes are used to represent both characters and numbers inside computers. Moreover, the binary codes used to represent numbers must be consistent with the arithmetic
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 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 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 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 informationTHE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DIGITAL LOGIC DESIGN DISCUSSION ECOM Eng. Huda M.
THE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DIGITAL LOGIC DESIGN DISCUSSION ECOM 2012 Eng. Huda M. Dawoud September, 2015 1.1 List the octal and hexadecimal numbers
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 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 information