The Mathematics Driving License for Computer Science CS10410


 Quentin Thomas
 2 years ago
 Views:
Transcription
1 The Mathematics Driving License for Computer Science CS10410 Approximating Numbers, Number Systems and 2 s Complement by Nitin Naik
2 Approximating Numbers There are two kinds of numbers: Exact Number and Approximate Number. Exact Numbers arise from counting. Approximate Numbers arise from measurement or calculation. We can never perform a completely accurate measurement with a ruler, tape measure or thermometer. There is always some inaccuracy involved.
3 Approximating Numbers.. Sometimes instead of giving exact numbers, it is preferable to give approximations. This is especially when if we want to be vague about the numbers we are reporting! Certain numbers simply cannot be written exactly in decimal form. Many fractions and all irrational numbers fall into this category. For example the fraction 1/3 is approximately but not exactly equal to and the irrational number 3 is approximately but not exactly equal to 1.73.
4 Examples
5 Significant Digits or Figures All the digits in the number are significant digits (also known as significant figures) except if the digit is a zero that is used just to locate the decimal point then it is not significant. This means a digit which is 0 is significant if it is not a place holder. In an approximate number the leftmost digit is said to be the Most Significant Digit and the rightmost digit is the Least Significant Digit. Significant digits give an indication of the accuracy of a number.
6 Significant Digits or Figures.. Example1: The approximate number is It has 4 significant digits. The digit 5 is the Most Significant Digit (MSD). The digit 9 is the Least Significant Digit (LSD).
7 Significant Digits or Figures..
8 Accuracy and Precision Accuracy The accuracy of an approximate number is given by the number of significant digits in it. Precision The precision of an approximate number is given by the position of the rightmost significant digit (decimal position of the last significant digit).
9 Example Comparing the two numbers and Accuracy Here is more accurate because it has four significant digits, where only has two. Precision The two numbers have the same precision, as the last significant digit is in the thousandths position for both.
10 Rounding Numbers When rounding number to a certain place value then all digits to the right of that place are dropped.
11 Rounding Down If the first dropped digit in number is 0, 1, 2, 3, or 4 then the least significant digit kept is not changed. This is called rounding down.
12 Rounding Up If the first dropped digit in number is 5, 6, 7, 8 or 9 then the least significant digit kept is increased by 1. This is called rounding up.
13 Rounding Examples Example1: The number rounded to four significant digits is The number rounded to three significant digits is 70.5 The number rounded to two significant digits is 71
14 Rounding Examples.. Example2:Some examples of rounding to 2 decimal places (the dropped digits are shown in red):
15 Rounding Examples.. Example3:Some examples of rounding to 3 significant figures (the dropped digits are shown in red):
16 Operations with Approximate Numbers When adding or subtracting approximate numbers, the result should have the precision of the least precise number. Example1: When adding 2.3, and 12.67, our final answer should be correct to one decimal place = (the symbol for "is approximately equal to")
17 Operations with Approximate Numbers.. When multiplying or dividing approximate numbers, the result should have the accuracy of the least accurate number. Example2: When multiplying and 2.37, our final answer should have three significant digits =
18 Operations with Approximate Numbers.. When finding the square root of a number, the result has the same accuracy as the number. Example3: should be written correct to 4 significant digits: (same accuracy)
19 Number System It is the set of characters and mathematical rules that are used to represent a number.
20 Decimal Number System The Decimal number system consists of ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 and afterwards the numbers are formed by grouping these digits together and known as Base10 system.
21 Decimal Number System..
22 Binary Number System The Binary number system is similar to the decimal system except binary system contains only two digits 0 and 1 and called Base2 system.
23 Octal Number System The Octal number system consists of eight digits 0, 1, 2, 3, 4, 5, 6, and 7 and called Base8 system. Octal was used extensively in early mainframe computer systems, but has become less popular in favor of binary and hexadecimal today.
24 Hexadecimal Number System The Hexadecimal number system uses 16 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F and thus called Base16 system. Hexadecimal numbers are easy to convert to the computer's internal binary code and are more compact than binary numbers.
25 Hexadecimal Number System.. Decimal Values of Hex Alphabets
26 Number System Conversions Actually we commonly understand only Decimal number system so the number written in other three number systems must be converted to know the actual decimal value of that number. Number system conversions are also required for many computer applications and operations. Here we will study the most important number system conversions.
27 Binary to Decimal Conversion For this conversion remember these values: 2 0 =1 2 0 =1/1=1 2 1 =2 21 =1/2= =4 22 =1/4= =8 23 =1/8= = =1/16= = =1/32= = =1/64= = =1/128= = =1/256= = =1/512= = =1/1024=
28 Binary to Decimal Conversion (Integer Part)
29 Binary to Decimal Conversion (Integer Part)..
30 Binary to Decimal Conversion (Real Part)
31 Octal to Decimal Conversion For this conversion remember these values:
32 Octal to Decimal Conversion..
33 Hexadecimal to Decimal Conversion For this conversion remember these values:
34 Hexadecimal to Decimal Conversion..
35 BinarytoOctal or OctaltoBinary Three binary digits are equivalent to one octal digit, as shown in the table below:
36 BinarytoOctal To convert from binary to octal, divide the binary number into groups of 3 digits starting on the right of the binary number. If the leftmost group has less than 3 bits, put in the necessary number of leading zeroes on the left. For each group of three bits, write the corresponding single octal digit.
37 BinarytoOctal..
38 BinarytoOctal..
39 OctaltoBinary To convert from octal to binary, write the corresponding group of three binary digits for each octal digit.
40 OctaltoBinary..
41 BinarytoHexadecimal or HexadecimaltoBinary Four binary digits are equivalent to one hexadecimal digit, as shown in the given table.
42 BinarytoHexadecimal To convert from binary to hexadecimal, divide the binary number into groups of 4 digits starting on the right of the binary number. If the leftmost group has less than 4 bits, put in the necessary number of leading zeroes on the left. For each group of four bits, write the corresponding single hex digit.
43 BinarytoHexadecimal..
44 BinarytoHexadecimal..
45 HexadecimaltoBinary To convert from hexadecimal to binary, write the corresponding group of four binary digits for each hex digit.
46 HexadecimaltoBinary..
47 Two's Complement Notation Property Two's complement number representation is used for signed numbers on most modern computers. Two's complement representation allows the use of binary arithmetic operations on signed integers, yielding the correct 2's complement results.
48 Two's Complement Notation.. Positive Numbers Positive 2's complement numbers are represented as the simple binary. Negative Numbers Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero. Sign Bit The most significant bit is called the sign bit. Operations This notation allows a computer to add and subtract numbers using the same operations (thus we do not need to implement adders and subtractors).
49 One's Complement In one's complement, positive numbers are represented as usual in regular binary. However, negative numbers are represented differently. To negate a number, replace all zeros with ones, and ones with zeros  flip the bits. Example: 12 = and 12 = (1 s Complement) As in signed magnitude, the leftmost bit indicates the sign (1 is negative, 0 is positive). To compute the value of a negative number, flip the bits and translate as before.
50 Two's Complement Example: 12 = (1 s Complement) = (2 s Complement)
51 References Numbers.pdf htm Systems%20Tutorial.pdf chnotes/program/2s_comp.htm /Readings/studentbinary#one
52 Thank You
Base 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationDivide: Paper & Pencil. Computer Architecture ALU Design : Division and Floating Point. Divide algorithm. DIVIDE HARDWARE Version 1
Divide: Paper & Pencil Computer Architecture ALU Design : Division and Floating Point 1001 Quotient Divisor 1000 1001010 Dividend 1000 10 101 1010 1000 10 (or Modulo result) See how big a number can be
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 informationA Short Guide to Significant Figures
A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures  read the full text of this guide to gain a complete understanding of what these rules really
More informationNow that we have a handle on the integers, we will turn our attention to other types of numbers.
1.2 Rational Numbers Now that we have a handle on the integers, we will turn our attention to other types of numbers. We start with the following definitions. Definition: Rational Number any number that
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 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 informationFractional Numbers. Fractional Number Notations. Fixedpoint Notation. Fixedpoint Notation
2 Fractional Numbers Fractional Number Notations 2010  Claudio Fornaro Ver. 1.4 Fractional numbers have the form: xxxxxxxxx.yyyyyyyyy where the x es constitute the integer part of the value and the y
More informationCOMPASS Numerical Skills/PreAlgebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13
COMPASS Numerical Skills/PreAlgebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre
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 informationFigure 1. A typical Laboratory Thermometer graduated in C.
SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES
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 informationAddition Methods. Methods Jottings Expanded Compact Examples 8 + 7 = 15
Addition Methods Methods Jottings Expanded Compact Examples 8 + 7 = 15 48 + 36 = 84 or: Write the numbers in columns. Adding the tens first: 47 + 76 110 13 123 Adding the units first: 47 + 76 13 110 123
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 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 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 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 informationSubnetting Examples. There are three types of subnetting examples I will show in this document:
Subnetting Examples There are three types of subnetting examples I will show in this document: 1) Subnetting when given a required number of networks 2) Subnetting when given a required number of clients
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 informationWe could also take square roots of certain decimals nicely. For example, 0.36=0.6 or 0.09=0.3. However, we will limit ourselves to integers for now.
7.3 Evaluation of Roots Previously we used the square root to help us approximate irrational numbers. Now we will expand beyond just square roots and talk about cube roots as well. For both we will be
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
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 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 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 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 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 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 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 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 informationCHAPTER 5 Roundoff errors
CHAPTER 5 Roundoff errors In the two previous chapters we have seen how numbers can be represented in the binary numeral system and how this is the basis for representing numbers in computers. Since any
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 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 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 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 informationThe student will be able to... The teacher will... SKILLS/CONCEPTS K
MATHEMATCS Subject Area: Component V: MATHEMATCS WHOLE NUMBER SENSE ndiana Academic Standard 1: Number Sense and Computation Understanding the number system is the basis of mathematics. Students develop
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 informationClassless Subnetting Explained
Classless Subnetting Explained When given an IP Address, Major Network Mask, and a Subnet Mask, how can you determine other information such as: The subnet address of this subnet The broadcast address
More information2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division
Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called
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 informationAccuplacer Arithmetic Study Guide
Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole
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 information1.3 Order of Operations
1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit
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 informationIntroduction to Fractions
Introduction to Fractions Fractions represent parts of a whole. The top part of a fraction is called the numerator, while the bottom part of a fraction is called the denominator. The denominator states
More information2.3 IPv4 Address Subnetting Part 2
.3 IPv4 Address Subnetting Part Objective Upon completion of this activity, you will be able to determine subnet information for a given IP address and subnetwork mask. When given an IP address, network
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 informationMathematics Success Grade 8
T92 Mathematics Success Grade 8 [OBJECTIVE] The student will create rational approximations of irrational numbers in order to compare and order them on a number line. [PREREQUISITE SKILLS] rational numbers,
More informationTI83 Plus Graphing Calculator Keystroke Guide
TI83 Plus Graphing Calculator Keystroke Guide In your textbook you will notice that on some pages a keyshaped icon appears next to a brief description of a feature on your graphing calculator. In this
More informationChapter 1. Binary, octal and hexadecimal numbers
Chapter 1. Binary, octal and hexadecimal numbers This material is covered in the books: Nelson Magor Cooke et al, Basic mathematics for electronics (7th edition), Glencoe, Lake Forest, Ill., 1992. [Hamilton
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 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 informationA Step towards an Easy Interconversion of Various Number Systems
A towards an Easy Interconversion of Various Number Systems Shahid Latif, Rahat Ullah, Hamid Jan Department of Computer Science and Information Technology Sarhad University of Science and Information Technology
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 information