Lecture 1 Introduction, Numbers, and Number System Page 1 of 8


 Anthony Bishop
 1 years ago
 Views:
Transcription
1 Lecture Introduction, Numbers and Number System Contents.. Number Systems (Appendix B) Example. Converting to Base Number Representation Number Conversion To convert a number N expressed in base 0 to base B Example.2 Converting Decimal Number to base Example.3 Converting Decimal Number to base Example.4 Converting Decimal Number to base Example.5 Converting Decimal Number to base Binarytohexadecimal (4 bits = hex digit) Binarytooctal (3 bits = octal digit) Hexadecimaltobinary Octaltobinary Example.6 Converting Number Signed Binary Number Two s Complement Numbers Example.7 Two s Complement Numbers Example.8 Two s Complement Numbers Find Decimal Value of Signed Binary Number Negating two s Complement Numbers Example.9 Negating in Two s Complement System Negating Octal and Hexadecimal Numbers... 6 a. Example.0 Negating Hexadecimal Numbers in Two s Complement System Addition in Two s Complement System Subtraction in Two s Complement System Examples on Two s Complements Example. Addition and Subtraction in Two s Complement Systems... 8 Lecture Introduction, Numbers, and Number System Page of 8
2 .. Number Systems (Appendix B) Representation of an integer number on base B is done by creating a set of coefficients a n a a 0 with weights specified by powers of the base B. The coefficients in base B are numbers that can take values 0 through B. A number N can be written in base B as N 2 0 a... a aa n n 2 0 a B... a B a B a B B n 2 0 Fractional numbers can be written by introducing negative powers of the base. A fractional number N can be written in base B as N a... a aa. a a a... a m m m n B n... 2 B 0B B 2B 3B... nb a B a B a a a a a a There are four common number systems: decimal, hexadecimal, octal, and binary.. Example. Converting to Base 0 Find the equivalent numbers in the decimal base system of the following numbers: (204.2)0 = (204.2)8 = * * *8 + 4*8 0 + * *82 = (A2F.)6 = * * *6 + 5*6 0 + *6  + * 62 = ( )2= * * * * * *2 2 + *2 + 0*2 0 + *2  +0*22 = Number Representation Decimal Binary Octal Hex A B C D E F Lecture Introduction, Numbers, and Number System Page 2 of 8
3 .3. Number Conversion. To convert a number N expressed in base 0 to base B Separate integer part of number from fractional part Divide integer part by B continuously and save the remainder at each step. Multiply fractional part by B continuously and save integer part at each step. N a aa a a a B a B a B a B a B B Example.2 Converting Decimal Number to base 8 Converting the following decimal numbers into base 8: (75.32) (75.32)0 ( )8 Remainder Fraction Result * * * * * 8 3. Example.3 Converting Decimal Number to base 8 Converting the following decimal number into base 8: ( ) ( )0 ( ) Remainder Fraction Result * * * * * * 8 4. Example.4 Converting Decimal Number to base 6 Converting the following decimal number into base 6: ( ) ( )0 (A4.A) Remainder Fraction Result * A 5. Example.5 Converting Decimal Number to base 2 Converting the following decimal number into base 6: (53.375) (53.375)0 (00.0)2 Remainder Fraction Result * * * Lecture Introduction, Numbers, and Number System Page 3 of 8
4 6. Binarytohexadecimal (4 bits = hex digit) Group binary digits into groups of four and assign each group a hex digit B E Binarytooctal (3 bits = octal digit) Hexadecimaltobinary C 2 8 E Octaltobinary Example.6 Converting Number (5CB.2F)6 = ( )2 (47.62)8 = ( )2 ( )2 = (DEA.A9)6 ( )2 = ( )8.4. Signed Binary Number For signed numbers, in the binary system, the sign of the number is denoted by the leftmost bit: 0 = positive = negative For a nbit number, the remaining n bits represent the magnitude. For signed binary system, there is a duplicate representation of 0 such as +0 ( ) and 0 ( ). As a result, there is one less combination of bits to represent signed numbers..5. Two s Complement Numbers All modern computers use the two s complement number system to represent negative numbers. s Complement of N: complement individual bits (0 and 0) 2 s Complement of N: complement individual bit and add to it. In the two s complement system, positive numbers are identical to binary numbers with the sign bit is 0. Lecture Introduction, Numbers, and Number System Page 4 of 8
5 Range of number in a system of n bits: Unsigned number: 0 N 2 n s complement: 2 n + N 2 n 2 s complement: 2 n N 2 n The 2 s complement of N is used to represent N. It can represent integers in the range between 2 n to 2 n , where n is the number of bits available for representing N (for unsigned numbers N, the range would be 0 to 2 n ).. Example.7 Two s Complement Numbers Find the two s complement of the following numbers in 8bit system: 0, 8, 4, +7, and 4. 8bit s Compl. + 2 s Compl Example.8 Two s Complement Numbers Find the equivalent decimal numbers of the following number (2 s complement) in 6bit system: 6bit s Compl. + Magnitude Numbers Find Decimal Value of Signed Binary Number Observe that the 2 s complement of a negative number is the corresponding positive number. For example, 50=02 and 2 s complement of 02 is 002 Procedure ) Find the 2 s complement of the number, i.e. its positive value 2) Convert the positive binary number to decimal 3) Add a negative sign to the decimal value Two s Complement Numbers in 6bit system Signed System s Complement 2 s Complement Lecture Introduction, Numbers, and Number System Page 5 of 8
6 Negating two s Complement Numbers To negate a number in the Two s Complement system: Invert all bits of the number Add.. Example.9 Negating in Two s Complement System Find the opposite numbers of the followings numbers (2 s complement) in 6bit system: 2 s Compl. s Compl. + 2 s Compl. Opposite Number Negating Octal and Hexadecimal Numbers Convert the octal or hex number to its binary equivalent with an appropriate number of bits (e.g. 8, 6, 32 ) Negate the binary equivalent Convert the two s complement number to its octal or hex equivalent Lecture Introduction, Numbers, and Number System Page 6 of 8
7 a. Example.0 Negating Hexadecimal Numbers in Two s Complement System Find the opposite number of the following hexadecimal numbers Binary Equivalent s Complement. + 2 s Complement Hexadecimal Equivalent A EF9 FEB A0CF F3 FFCA F0FA F06.7. Addition in Two s Complement System Any carryout from the signed bit is ignored (+2) 000 +( 2) ignore (+2) 000 +( 2) Ignore.8. Subtraction in Two s Complement System The easiest way of performing subtraction is to negate the subtrahend and add it to the minuend. First, find the 2 s complement of the subtrahend and then perform addition. 2 s Compl 2 s Compl (+2) ( 2) ignore 2 s Compl 2 s Compl (+2) ( 2) ignore Lecture Introduction, Numbers, and Number System Page 7 of 8
8 .9. Examples on Two s Complements. Example. Addition and Subtraction in Two s Complement Systems Perform arithmetic operations of these numbers in 8bit system: 2 s Compl (+6) (+2) s Compl 2 s Compl (+) ( ) Lecture Introduction, Numbers, and Number System Page 8 of 8
Computer 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 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 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 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 informationToday. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real Time Systems: Binary Arithmetic
Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1
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 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 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 informationLecture 11: Number Systems
Lecture 11: Number Systems Numeric Data Fixed point Integers (12, 345, 20567 etc) Real fractions (23.45, 23., 0.145 etc.) Floating point such as 23. 45 e 12 Basically an exponent representation Any number
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 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 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 informationCOMPSCI 210. Binary Fractions. Agenda & Reading
COMPSCI 21 Binary Fractions Agenda & Reading Topics: Fractions Binary Octal Hexadecimal Binary > Octal, Hex Octal > Binary, Hex Decimal > Octal, Hex Hex > Binary, Octal Animation: BinFrac.htm Example
More informationChapter Binary, Octal, Decimal, and Hexadecimal Calculations
Chapter 5 Binary, Octal, Decimal, and Hexadecimal Calculations This calculator is capable of performing the following operations involving different number systems. Number system conversion Arithmetic
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 informationChapter 6 Digital Arithmetic: Operations & Circuits
Chapter 6 Digital Arithmetic: Operations & Circuits Chapter 6 Objectives Selected areas covered in this chapter: Binary addition, subtraction, multiplication, division. Differences between binary addition
More information3. Convert a number from one number system to another
3. Convert a number from one number system to another Conversion between number bases: Hexa (16) Decimal (10) Binary (2) Octal (8) More Interest Way we need conversion? We need decimal system for real
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 informationNUMBER SYSTEMS. 1.1 Introduction
NUMBER SYSTEMS 1.1 Introduction There are several number systems which we normally use, such as decimal, binary, octal, hexadecimal, etc. Amongst them we are most familiar with the decimal number system.
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 informationCPEN 214  Digital Logic Design Binary Systems
CPEN 4  Digital Logic Design Binary Systems C. Gerousis Digital Design 3 rd Ed., Mano Prentice Hall Digital vs. Analog An analog system has continuous range of values A mercury thermometer Vinyl records
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 informationUnsigned Conversions from Decimal or to Decimal and other Number Systems
Page 1 of 5 Unsigned Conversions from Decimal or to Decimal and other Number Systems In all digital design, analysis, troubleshooting, and repair you will be working with binary numbers (or base 2). It
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 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 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 informationLecture 8: Binary Multiplication & Division
Lecture 8: Binary Multiplication & Division Today s topics: Addition/Subtraction Multiplication Division Reminder: get started early on assignment 3 1 2 s Complement Signed Numbers two = 0 ten 0001 two
More informationCOMBINATIONAL CIRCUITS
COMBINATIONAL CIRCUITS http://www.tutorialspoint.com/computer_logical_organization/combinational_circuits.htm Copyright tutorialspoint.com Combinational circuit is a circuit in which we combine the different
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 informationNumber Systems and Radix Conversion
Number Systems and Radix Conversion Sanjay Rajopadhye, Colorado State University 1 Introduction These notes for CS 270 describe polynomial number systems. The material is not in the textbook, but will
More informationTo convert an arbitrary power of 2 into its English equivalent, remember the rules of exponential arithmetic:
Binary Numbers In computer science we deal almost exclusively with binary numbers. it will be very helpful to memorize some binary constants and their decimal and English equivalents. By English equivalents
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 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 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 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 informationDecimal to Binary Conversion
Decimal to Binary Conversion A tool that makes the conversion of decimal values to binary values simple is the following table. The first row is created by counting right to left from one to eight, for
More informationNumber and codes in digital systems
Number and codes in digital systems Decimal Numbers You are familiar with the decimal number system because you use them everyday. But their weighted structure is not understood. In the decimal number
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 informationGoals. Unary Numbers. Decimal Numbers. 3,148 is. 1000 s 100 s 10 s 1 s. Number Bases 1/12/2009. COMP370 Intro to Computer Architecture 1
Number Bases //9 Goals Numbers Understand binary and hexadecimal numbers Be able to convert between number bases Understand binary fractions COMP37 Introduction to Computer Architecture Unary Numbers Decimal
More information4 Operations On Data
4 Operations On Data 4.1 Source: Foundations of Computer Science Cengage Learning Objectives After studying this chapter, students should be able to: List the three categories of operations performed on
More informationNumbering Systems. InThisAppendix...
G InThisAppendix... Introduction Binary Numbering System Hexadecimal Numbering System Octal Numbering System Binary Coded Decimal (BCD) Numbering System Real (Floating Point) Numbering System BCD/Binary/Decimal/Hex/Octal
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 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 informationCS201: Architecture and Assembly Language
CS201: Architecture and Assembly Language Lecture Three Brendan Burns CS201: Lecture Three p.1/27 Arithmetic for computers Previously we saw how we could represent unsigned numbers in binary and how binary
More informationELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE470/570: MicroprocessorBased System Design Fall 2014.
REVIEW OF NUMBER SYSTEMS Notes Unit 2 BINARY NUMBER SYSTEM In the decimal system, a decimal digit can take values from to 9. For the binary system, the counterpart of the decimal digit is the binary digit,
More informationChapter 7 Lab  Decimal, Binary, Octal, Hexadecimal Numbering Systems
Chapter 7 Lab  Decimal, Binary, Octal, Hexadecimal Numbering Systems This assignment is designed to familiarize you with different numbering systems, specifically: binary, octal, hexadecimal (and decimal)
More informationBinary Numbers The Computer Number System
Binary Numbers The Computer Number System Number systems are simply ways to count things. Ours is the base0 or radix0 system. Note that there is no symbol for 0 or for the base of any system. We count,2,3,4,5,6,7,8,9,
More informationPositional Numbering System
APPENDIX B Positional Numbering System A positional numbering system uses a set of symbols. The value that each symbol represents, however, depends on its face value and its place value, the value associated
More information2010/9/19. Binary number system. Binary numbers. Outline. Binary to decimal
2/9/9 Binary number system Computer (electronic) systems prefer binary numbers Binary number: represent a number in base2 Binary numbers 2 3 + 7 + 5 Some terminology Bit: a binary digit ( or ) Hexadecimal
More informationBinary Number System. 16. Binary Numbers. Base 10 digits: 0 1 2 3 4 5 6 7 8 9. Base 2 digits: 0 1
Binary Number System 1 Base 10 digits: 0 1 2 3 4 5 6 7 8 9 Base 2 digits: 0 1 Recall that in base 10, the digits of a number are just coefficients of powers of the base (10): 417 = 4 * 10 2 + 1 * 10 1
More informationCS101 Lecture 11: Number Systems and Binary Numbers. Aaron Stevens 14 February 2011
CS101 Lecture 11: Number Systems and Binary Numbers Aaron Stevens 14 February 2011 1 2 1 3!!! MATH WARNING!!! TODAY S LECTURE CONTAINS TRACE AMOUNTS OF ARITHMETIC AND ALGEBRA PLEASE BE ADVISED THAT CALCULTORS
More information198:211 Computer Architecture
198:211 Computer Architecture Topics: Lecture 8 (W5) Fall 2012 Data representation 2.1 and 2.2 of the book Floating point 2.4 of the book 1 Computer Architecture What do computers do? Manipulate stored
More informationNUMBER SYSTEMS TUTORIAL
NUMBER SYSTEMS TUTORIAL Courtesy of: thevbprogrammer.com Number Systems Concepts The study of number systems is useful to the student of computing due to the fact that number systems other than the familiar
More informationCOMP 250 Fall 2012 lecture 2 binary representations Sept. 11, 2012
Binary numbers The reason humans represent numbers using decimal (the ten digits from 0,1,... 9) is that we have ten fingers. There is no other reason than that. There is nothing special otherwise about
More informationDigital Design. Assoc. Prof. Dr. Berna Örs Yalçın
Digital Design Assoc. Prof. Dr. Berna Örs Yalçın Istanbul Technical University Faculty of Electrical and Electronics Engineering Office Number: 2318 Email: siddika.ors@itu.edu.tr Grading 1st Midterm 
More informationNumber Conversions Dr. Sarita Agarwal (Acharya Narendra Dev College,University of Delhi)
Conversions Dr. Sarita Agarwal (Acharya Narendra Dev College,University of Delhi) INTRODUCTION System A number system defines a set of values to represent quantity. We talk about the number of people
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 information= Chapter 1. The Binary Number System. 1.1 Why Binary?
Chapter The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base0 system. When you
More informationBinary Numbering Systems
Binary Numbering Systems April 1997, ver. 1 Application Note 83 Introduction Binary numbering systems are used in virtually all digital systems, including digital signal processing (DSP), networking, and
More informationCHAPTER 3 Numbers and Numeral Systems
CHAPTER 3 Numbers and Numeral Systems Numbers play an important role in almost all areas of mathematics, not least in calculus. Virtually all calculus books contain a thorough description of the natural,
More informationBinary, Hexadecimal, Octal, and BCD Numbers
23CH_PHCalter_TMSETE_949118 23/2/2007 1:37 PM Page 1 Binary, Hexadecimal, Octal, and BCD Numbers OBJECTIVES When you have completed this chapter, you should be able to: Convert between binary and decimal
More informationplc numbers  13.1 Encoded values; BCD and ASCII Error detection; parity, gray code and checksums
plc numbers  3. Topics: Number bases; binary, octal, decimal, hexadecimal Binary calculations; s compliments, addition, subtraction and Boolean operations Encoded values; BCD and ASCII Error detection;
More informationSistemas Digitais I LESI  2º ano
Sistemas Digitais I LESI  2º ano Lesson 6  Combinational Design Practices Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática UNIVERSIDADE DO MINHO ESCOLA DE ENGENHARIA  PLDs (1)  The
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 informationMATH0910 Review Concepts (Haugen)
Unit 1 Whole Numbers and Fractions MATH0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,
More informationDecimal, Hexadecimal and Binary Numbers Writing an assembly language program
Decimal, Hexadecimal and Binary Numbers Writing an assembly language program o Disassembly of MC9S12 op codes o Use flow charts to lay out structure of program o Use common flow structures ifthen ifthenelse
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 informationRecall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points.
2 MODULE 4. DECIMALS 4a Decimal Arithmetic Adding Decimals Recall the process used for adding decimal numbers. Adding Decimals. To add decimal numbers, proceed as follows: 1. Place the numbers to be added
More information1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal:
Exercises 1  number representations Questions 1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal: (a) 3012 (b)  435 2. For each of
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 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 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 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 informationDigital Logic Design. Introduction
Digital Logic Design Introduction A digital computer stores data in terms of digits (numbers) and proceeds in discrete steps from one state to the next. The states of a digital computer typically involve
More informationThis 3digit ASCII string could also be calculated as n = (Data[2]0x30) +10*((Data[1]0x30)+10*(Data[0]0x30));
Introduction to Embedded Microcomputer Systems Lecture 5.1 2.9. Conversions ASCII to binary n = 100*(Data[0]0x30) + 10*(Data[1]0x30) + (Data[2]0x30); This 3digit ASCII string could also be calculated
More information6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10
Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base system. When you
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 informationParamedic Program PreAdmission Mathematics Test Study Guide
Paramedic Program PreAdmission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page
More informationEverything you wanted to know about using Hexadecimal and Octal Numbers in Visual Basic 6
Everything you wanted to know about using Hexadecimal and Octal Numbers in Visual Basic 6 Number Systems No course on programming would be complete without a discussion of the Hexadecimal (Hex) number
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 informationNUMBER SYSTEMS. William Stallings
NUMBER SYSTEMS William Stallings The Decimal System... The Binary System...3 Converting between Binary and Decimal...3 Integers...4 Fractions...5 Hexadecimal Notation...6 This document available at WilliamStallings.com/StudentSupport.html
More informationBinary, Octal, Decimal, and Hexadecimal Calculations
Chapter 5 Binary, Octal, Decimal, and Hexadecimal Calculations This calculator is capable of performing the following operations involving different number systems. Number system conversion Arithmetic
More informationBinary math. Resources and methods for learning about these subjects (list a few here, in preparation for your research):
Binary math This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationHOMEWORK # 2 SOLUTIO
HOMEWORK # 2 SOLUTIO Problem 1 (2 points) a. There are 313 characters in the Tamil language. If every character is to be encoded into a unique bit pattern, what is the minimum number of bits required to
More informationCS321. Introduction to Numerical Methods
CS3 Introduction to Numerical Methods Lecture Number Representations and Errors Professor Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 405060633 August 7, 05 Number in
More informationBorland C++ Compiler: Operators
Introduction Borland C++ Compiler: Operators An operator is a symbol that specifies which operation to perform in a statement or expression. An operand is one of the inputs of an operator. For example,
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 informationADDITION. Children should extend the carrying method to numbers with at least four digits.
Y5 AND Y6 ADDITION Children should extend the carrying method to numbers with at least four digits. 587 3587 + 475 + 675 1062 4262 1 1 1 1 1 Using similar methods, children will: add several numbers with
More informationBINARY CODED DECIMAL: B.C.D.
BINARY CODED DECIMAL: B.C.D. ANOTHER METHOD TO REPRESENT DECIMAL NUMBERS USEFUL BECAUSE MANY DIGITAL DEVICES PROCESS + DISPLAY NUMBERS IN TENS IN BCD EACH NUMBER IS DEFINED BY A BINARY CODE OF 4 BITS.
More informationFixedPoint Arithmetic
FixedPoint Arithmetic FixedPoint Notation A Kbit fixedpoint number can be interpreted as either: an integer (i.e., 20645) a fractional number (i.e., 0.75) 2 1 Integer FixedPoint Representation Nbit
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 informationBinary Division. Decimal Division. Hardware for Binary Division. Simple 16bit Divider Circuit
Decimal Division Remember 4th grade long division? 43 // quotient 12 521 // divisor dividend 480 4136 5 // remainder Shift divisor left (multiply by 10) until MSB lines up with dividend s Repeat until
More informationThis Unit: Floating Point Arithmetic. CIS 371 Computer Organization and Design. Readings. Floating Point (FP) Numbers
This Unit: Floating Point Arithmetic CIS 371 Computer Organization and Design Unit 7: Floating Point App App App System software Mem CPU I/O Formats Precision and range IEEE 754 standard Operations Addition
More informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  DECIMALS AND WHOLE NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
More informationNumber Systems. Introduction / Number Systems
Number Systems Introduction / Number Systems Data Representation Data representation can be Digital or Analog In Analog representation values are represented over a continuous range In Digital representation
More informationECE 0142 Computer Organization. Lecture 3 Floating Point Representations
ECE 0142 Computer Organization Lecture 3 Floating Point Representations 1 Floatingpoint arithmetic We often incur floatingpoint programming. Floating point greatly simplifies working with large (e.g.,
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 informationVerilog  Representation of Number Literals
Verilog  Representation of Number Literals... And here there be monsters! (Capt. Barbossa) Numbers are represented as: value ( indicates optional part) size The number of binary
More informationDIGITAL FUNDAMENTALS lesson 4 Number systems
The decimal number system In the decimal number system the base is 0. For example the number 4069 means 4x000 + 0x00 + 6x0 + 9x. The powers of 0 with the number 4069 in tabelvorm are: power 0 3 0 2 0 0
More information