Computer Number Systems Supplement
|
|
- Winfred Shields
- 6 years ago
- Views:
Transcription
1 Computer Number Systems Supplement Dr. Ken Hoganson, All Rights Reserved. SUPPLEMENT CONTENTS S.1 Decimal System: Powers-of-the-Base 2 S.2 Converting to Binary: Division/Remainder Algorithm. 3 S.3 Binary Addition. 4 S.4 Bits, Bytes, and Words. 5 S.5 Hexadecimal Number System.. 6 S.6 Negative Numbers 8
2 Computer Number Systems, Dr. Ken Hoganson, 2 S.1 Decimal System: Powers-of-the-Base The decimal number system is based on powers of the base 10. The place value of each digit is a power of ten. We are so comfortable with this system, that we don t even think about the underlying mechanism. For instance, the number 1259 uses digits in place values that are based on powers of the base (base 10): the 9 is in the 10 0 the 5 is in the 10 1 the 2 is in the 10 2 the 1 is in the 10 3 column - 1s column column - 10s column column - 100s column column s column 1259 is 9 X 1 = X 10 = X 100 = X 1000 = The computer s hardware logic is implemented with transistors, which can work like switches, turning electricity on or off. If we consider on to be a 1, and off to be 0, then internal computer logic can be represented using the Binary number system. The Binary number system uses the same mechanism as the decimal system outlined above, but the base is different - base 2 (binary) rather than base 10 (decimal). The place values for binary are based on powers of the base 2: So, the binary number can be converted to decimal so we can understand it, by using the powers-of-the-base mechanism: = 1 X 1 = 1 1 X 2 = 2 0 X 4 = 0 0 X 8 = 0 1 X 16 = 16 1 X 32 = 32 0 X 64 = 0 1 X 128 = 128 v SUM = 179 in decimal
3 Computer Number Systems, Dr. Ken Hoganson, 3 S.2 Division/Remainder Algorithm: Converting to Binary Section C.1 explained how the decimal system works, and how the binary system uses the same mechanism. In the process, a way to convert a binary number to a decimal number was discovered, by using the powers-of-the-base system. To convert in the other direction, from decimal to binary, requires a different method called the division/remainder method. The idea is to repeatedly divide the decimal number to be converted, by the base to be converted into (base 2). The remainders that result are the binary digits. Example: convert 155 to binary: Start from the bottom and work up. Stop 2)1 Q = 0, R = 1 2)2 Q = 1, R = 0 2)4 Q = 2, R = 0 2)9 Q = 4, R = 1 2)19 Q = 9, R = 1 2)38 Q = 19, R = 0 2)77 Q = 38, R = 1 Start: 2 )155 Q = 77, R = 1 Answer is Be careful to read the digits in the correct order. Check the answer with the powers-of-the-base system: 1 X 1 = 1 1 X 2 = 2 1 X 8 = 8 1 X 16 = 16 1 X 128 =
4 Computer Number Systems, Dr. Ken Hoganson, 4 S.3: Addition in Binary Just as in decimal, binary numbers can be added together. Because the base is different, the carry over to the next column is different. In decimal, when a column adds up to more than 9, a carry is added to the column to the left (the next higher place value). Since the base is 2 in binary with digits of 0 and 1, when a sum evaluates to more than 1, a carry must be added to the column to the left. Examples:
5 Computer Number Systems, Dr. Ken Hoganson, 5 S.4: Bits, Bytes, and Words Bits are organized into groups inside the computer system. The most common grouping is to place eight bits in a byte. A byte just looks like a string of eight zeros and ones: The range of possible binary values that a byte can hold is from to There are 256 possible combinations of zeros and ones arranged in any order in a byte. The number of possible combinations is based on a power of the base: 2 #of bits = the number of combinations Examples: Number of bits Number of combinations = 2 combinations (0 and 1) = 4 combinations, (00, 01, 10, 11) = = 1024 A byte can hold a small number, or a single character. Characters are all the letters of the alphabet in upper and lower case, punctuation symbols, the digits 0-9, and can include other special symbols. Bytes can be grouped together to form words. A word is simply one or more bytes, but is has a meaning in terms of the computer s power. A computer with a word size of a single byte, can work with and manipulate data eight bits at a time (a rough approximation). A sixteen-bit computer (word size of two bytes) is more powerful, because it can access and manipulate 16 bits at a time rather than 8. Typical word sizes for our common personal computers are 32-bit (4 bytes) and 64-bit (8 bytes). Computer systems include large quantities of bytes billions and trillions or bytes are becoming common. In dealing with these large numbers, a shorthand way to refer to large numbers of bytes has developed. Shorthand Term Roughly Power of 2 Actual K Kilobyte Thousand M or Meg Megabyte Million ,048,576 G or Gig Gigabtye Billion ,073,741,824 T Terabyte Trillion ,099,511,627,776
6 Computer Number Systems, Dr. Ken Hoganson, 6 S.5: Hexadecimal Number System Another number system used in computing is the hexadecimal system. Hexadecimal is base-16 number system, that is, just as decimal has a base of 10 (10 digits, 0-9), and binary is base 2 (2 digits, 0-1), hexadecimal is base-16 (16 digits, 0-15). But representing the values from is problematic a single numeral is needed to represent those values. The first six letters of the alphabet are used for those integers: A B C D E F Note that just as decimal includes digits for 0-9, and the 10 is two digits, with the 1 in the tens column, hexadecimal includes digits for 0-15, and sixteen is represented with a 1 in the sixteen s column. In hexadecimal, 10 is worth sixteen in decimal. The same place value mechanism used in decimal and binary applies to hexadecimal as well, place values are based on powers of the base, in this case, base sixteen. For example, 1B52 in hexadecimal can be converted to our more familiar decimal system: the 2 is in the 16 0 column - 1s column the 5 is in the 16 1 column - 16s column the B (11) is in the 16 2 column - 256s column the 1 is in the 16 3 column s column 1B52 16 is 2 X 1 = X 16 = X 256 = X 4096 = Subscripts are often used to indicate the base of the number, which is not always apparent just from looking at the digits. Hexadecimal turns out to be a useful number system for working with binary digital computers because of the relationship between base-16 and base-2. Sixteen is a convenient power of the base-2: 2 4 = 16. So four binary (base-2) digits that span values from (15) cover the same set of value as one hexadecimal digit (0-15). Thus, a group of four bits can be conveniently represented with a single hexadecimal digit as follows:
7 Computer Number Systems, Dr. Ken Hoganson, 7 Base-2, Binary Base-16, Hexadecimal A 1011 B 1100 C 1101 D 1110 E 1111 F So if a group of four binary digits can be represented with a single hexadecimal digit, then an 8- bit byte can be represented with two hexadecimal digits: Binary Hexadecimal CB F7 Note that it is far more convenient to talk about digital binary values in hexadecimal than it is in binary. For instance, a sixteen bit binary value: can be easily shared or recorded as C925. Converting from binary to hexadecimal (hex), and hex to binary is easily down without a formal conversion process, simply by grouping bits into groups of four bits, and translating that binary value to its equivalent hex digit. At first the student may need to use decimal as an intermediary: D F Converting multi-digit values: Binary Hex , ,1 B1 Hex Binary A8 10, F 3,
8 Computer Number Systems, Dr. Ken Hoganson, 8 Section S.6: Negative Numbers So far we have worked with unsigned binary values, but number systems need to be able to represent both positive and negative numbers. For the purposes of this discussion, we will limit ourselves to values with 8 binary bits. In eight bits, a range of values can be represented. There are 256 possible combinations of 0s and 1s with eight bits, ranging from up to An examination of the range of values follows: Binary Hex Decimal FC FD FE FF 255 There are 256 possible combinations allowing values from 0 to 255. The number of combinations is also based on Powers-of-the-Base: 2 8 = 256. To represent negative numbers (in eight bits) some of the available values must be dedicated to represent negative numbers, and some to positive value.
9 Computer Number Systems, Dr. Ken Hoganson, 9 Sign-Magnitude The most obvious way to represent negative numbers is to use one of the digits to represent a sign bit, which indicates whether the number is to be positive or negative. The convention is to use the left-most bit for the sign bit, with zero meaning a positive number and 1 meaning a negative number. The available combinations of 0s and 1s now have a different meaning: Binary Hex Decimal S E F negative zero? FC FD FE FF -127 Two problems with sign-magnitude representation are apparent from the above table of values: 1. There are two representations for zero, both a positive zero and a negative zero. Not only is this incorrect, but the two representations for zero waste a combination that could otherwise be used to represent some other value. 2. Another problem with sign-magnitude representation is revealed only when attempting basic mathematics. For instance adding a positive and negative number should work correctly: = -12! The problem with working with positive and negative numbers can be fixed for sign-magnitude. Addition circuits can be designed to work correctly for adding numbers of each combination of signs of values: Four different addition circuits can be designed inside the CPU to handle each case, but this requires four times the circuitry and transistors to implement, clearly not efficient. And special cases need to be created for the other operations, not just addition. And each case must also correctly recognize the two representations for zero.
10 Computer Number Systems, Dr. Ken Hoganson, 10 Two s Complement A better approach is a method called Two s-complement. It is more complicated and nonintuitive, and only the unsolvable problems of the sign-magnitude representation drive the use of two s-complement. But two s-complement does indeed work correctly and avoids the need for separate circuits to implement math with combinations of positive and negative numbers. In Two s Complement, A single bit is used to represent the sign of the number, and the left-most bit is still used for the sign. But the meaning of the combinations of bits is different than signmagnitude for the negative numbers. The negative numbers count down from -128 in the progression of bit combinations: Binary Hex Decimal S E F FC FD FE FF -1 It is now difficult to read a negative number, as the meaning of the bits are reversed (complemented). Note that there is now only one representation for zero, and the extra combination allows an extra value to be represented: So the combinations with the zero as the sign bit range from 0 up to 127, and the combinations with the one as the sign bit range from down to -1. Fortunately, there is a simple way to translate or understand the meanings of the negative values, and its how this representation got its name. To convert a positive value to its negative representation in two s complement, a two-step process is used: Start with the binary positive representation: Complement (reverse) all the bits (one s complement) Add one.
11 Computer Number Systems, Dr. Ken Hoganson, 11 Example: find the two s complement representation of -3: A positive 3 in 8-bits is: Complementing the bits: Add one = -3 This is the same value for negative 3 shown in the previous table of values. The same two s-complement steps can also be used to translate or convert a negative value: A negative 3 in 8-bits is: Complementing the bits: Add one = +3 So a negative two s complement value can be read by finding its positive value equivalent for the magnitude of the number, and remembering that it s the negative of that value. Two s-complement and Math: Two s-complement does indeed solve the problem with working with combinations of signs: = = = +2! Notice that the carry from the addition of ones to the next place value carrys over beyond the eight bits, and inside the computer, this result is noted but the bit is discarded [Somewhat amusingly described as thrown into the bit bucket, though there is no actual bit-bucket inside the machine]. Another example: = = = -12!
12 Computer Number Systems, Dr. Ken Hoganson, 12 Supplement Exercises: Work out the following problems on paper (show your work). Convert from binary to decimal: Work the following problems, converting decimal to binary (show all work) Work the following programs, representing the following decimal numbers in two s complement binary in eight bits
Module 1: Information Representation I -- Number Systems
Unit 1: Computer Systems, pages 1 of 7 - Department of Computer and Mathematical Sciences CS 1305 Intro to Computer Technology 1 Module 1: Information Representation I -- Number Systems Objectives: Learn
More informationCS & IT Conversions. Magnitude 10,000 1,
CS & IT Conversions There are several number systems that you will use when working with computers. These include decimal, binary, octal, and hexadecimal. Knowing how to convert between these number systems
More informationThus needs to be a consistent method of representing negative numbers in binary computer arithmetic operations.
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 informationDec Hex Bin ORG ; ZERO. Introduction To Computing
Dec Hex Bin 0 0 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 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 informationNumber representations
Number representations Number bases Three number bases are of interest: Binary, Octal and Hexadecimal. We look briefly at conversions among them and between each of them and decimal. Binary Base-two, or
More informationNumber Systems. Decimal numbers. Binary numbers. Chapter 1 <1> 8's column. 1000's column. 2's column. 4's column
1's column 10's column 100's column 1000's column 1's column 2's column 4's column 8's column Number Systems Decimal numbers 5374 10 = Binary numbers 1101 2 = Chapter 1 1's column 10's column 100's
More informationNumber Systems Using and Converting Between Decimal, Binary, Octal and Hexadecimal Number Systems
Number Systems Using and Converting Between Decimal, Binary, Octal and Hexadecimal Number Systems In everyday life, we humans most often count using decimal or base-10 numbers. In computer science, it
More informationMemory Addressing, Binary, and Hexadecimal Review
C++ By A EXAMPLE Memory Addressing, Binary, and Hexadecimal Review You do not have to understand the concepts in this appendix to become well-versed in C++. You can master C++, however, only if you spend
More informationThe type of all data used in a C++ program must be specified
The type of all data used in a C++ program must be specified A data type is a description of the data being represented That is, a set of possible values and a set of operations on those values There are
More informationNumbers and Representations
Çetin Kaya Koç http://koclab.cs.ucsb.edu/teaching/cs192 koc@cs.ucsb.edu Çetin Kaya Koç http://koclab.cs.ucsb.edu Fall 2016 1 / 38 Outline Computational Thinking Representations of integers Binary and decimal
More informationCHW 261: Logic Design
CHW 261: Logic Design Instructors: Prof. Hala Zayed Dr. Ahmed Shalaby http://www.bu.edu.eg/staff/halazayed14 http://bu.edu.eg/staff/ahmedshalaby14# Slide 1 Slide 2 Slide 3 Digital Fundamentals CHAPTER
More informationUsing sticks to count was a great idea for its time. And using symbols instead of real sticks was much better.
2- Numbering Systems Tutorial 2-1 What is it? There are many ways to represent the same numeric value. Long ago, humans used sticks to count, and later learned how to draw pictures of sticks in the ground
More informationNumber Systems. Dr. Tarek A. Tutunji Philadelphia University, Jordan
Number Systems Dr. Tarek A. Tutunji Philadelphia University, Jordan Number Systems Programmable controllers use binary numbers in one form or another to represent various codes and quantities. Every number
More informationLecture (01) Digital Systems and Binary Numbers By: Dr. Ahmed ElShafee
١ Lecture (01) Digital Systems and Binary Numbers By: Dr. Ahmed ElShafee Digital systems Digital systems are used in communication, business transactions, traffic control, spacecraft guidance, medical
More informationChapter 2: Number Systems
Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This two-valued number system is called binary. As presented earlier, there are many
More informationNumeral Systems. -Numeral System -Positional systems -Decimal -Binary -Octal. Subjects:
Numeral Systems -Numeral System -Positional systems -Decimal -Binary -Octal Subjects: Introduction A numeral system (or system of numeration) is a writing system for expressing numbers, that is a mathematical
More informationComputer Organization
Computer Organization Register Transfer Logic Number System Department of Computer Science Missouri University of Science & Technology hurson@mst.edu 1 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5,
More informationCC411: Introduction To Microprocessors
CC411: Introduction To Microprocessors OBJECTIVES this chapter enables the student to: Use number { base 2, base 10, or base 16 }. Add and subtract binary/hex numbers. Represent any binary number in 2
More informationLecture (01) Introduction Number Systems and Conversion (1)
Lecture (01) Introduction Number Systems and Conversion (1) By: Dr. Ahmed ElShafee ١ Digital systems Digital systems are used in communication, business transactions, traffic control, spacecraft guidance,
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers Mano & Ciletti Chapter 1 By Suleyman TOSUN Ankara University Outline Digital Systems Binary Numbers Number-Base Conversions Octal and Hexadecimal Numbers Complements
More informationA complement number system is used to represent positive and negative integers. A complement number system is based on a fixed length representation
Complement Number Systems A complement number system is used to represent positive and negative integers A complement number system is based on a fixed length representation of numbers Pretend that integers
More informationSigned umbers. Sign/Magnitude otation
Signed umbers So far we have discussed unsigned number representations. In particular, we have looked at the binary number system and shorthand methods in representing binary codes. With m binary digits,
More informationObjectives. Connecting with Computer Science 2
Objectives Learn why numbering systems are important to understand Refresh your knowledge of powers of numbers Learn how numbering systems are used to count Understand the significance of positional value
More informationThe x86 Microprocessors. Introduction. The 80x86 Microprocessors. 1.1 Assembly Language
The x86 Microprocessors Introduction 1.1 Assembly Language Numbering and Coding Systems Human beings use the decimal system (base 10) Decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Computer systems use the
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd Chapter 2 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Decimal Numbers The position of each digit in a weighted
More informationDLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR
UNIT I Digital Systems: Binary Numbers, Octal, Hexa Decimal and other base numbers, Number base conversions, complements, signed binary numbers, Floating point number representation, binary codes, error
More informationReview of Data Representation & Binary Operations Dhananjai M. Rao CSA Department Miami University
Review of Data Representation & Binary Operations Dhananjai M. Rao () CSA Department Miami University 1. Introduction In digital computers all data including numbers, characters, and strings are ultimately
More informationBinary, Hexadecimal and Octal number system
Binary, Hexadecimal and Octal number system Binary, hexadecimal, and octal refer to different number systems. The one that we typically use is called decimal. These number systems refer to the number of
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers Prof. Wangrok Oh Dept. of Information Communications Eng. Chungnam National University Prof. Wangrok Oh(CNU) 1 / 51 Overview 1 Course Summary 2 Binary Numbers 3 Number-Base
More information1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM
1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1.1 Introduction Given that digital logic and memory devices are based on two electrical states (on and off), it is natural to use a number
More informationObjective 1.02 Understand Numbering Systems
Objective.0 Understand Numbering Systems C O M P U T E R P R O G R A M M I N G I Number Systems Number systems we will talk about: Decimal (Base 0 ) Binary (Base ) Hexadecimal (Base 6 ) Decimal The number
More informationMoodle WILLINGDON COLLEGE SANGLI. ELECTRONICS (B. Sc.-I) Introduction to Number System
Moodle 1 WILLINGDON COLLEGE SANGLI ELECTRONICS (B. Sc.-I) Introduction to Number System E L E C T R O N I C S Introduction to Number System and Codes Moodle developed By Dr. S. R. Kumbhar Department of
More informationNumber Systems MA1S1. Tristan McLoughlin. November 27, 2013
Number Systems MA1S1 Tristan McLoughlin November 27, 2013 http://en.wikipedia.org/wiki/binary numeral system http://accu.org/index.php/articles/1558 http://www.binaryconvert.com http://en.wikipedia.org/wiki/ascii
More informationLecture (02) Operations on numbering systems
Lecture (02) Operations on numbering systems By: Dr. Ahmed ElShafee ١ Dr. Ahmed ElShafee, ACU : Spring 2018, CSE202 Logic Design I Complements of a number Complements are used in digital computers to simplify
More informationT02 Tutorial Slides for Week 2
T02 Tutorial Slides for Week 2 ENEL 353: Digital Circuits Fall 2017 Term Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary 19 September, 2017
More informationSlide Set 1. for ENEL 339 Fall 2014 Lecture Section 02. Steve Norman, PhD, PEng
Slide Set 1 for ENEL 339 Fall 2014 Lecture Section 02 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2014 ENEL 353 F14 Section
More informationExcerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997
Excerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997 APPENDIX A.1 Number systems and codes Since ten-fingered humans are addicted to the decimal system, and since computers
More informationAppendix. Numbering Systems. In This Appendix...
Numbering Systems ppendix In This ppendix... Introduction... inary Numbering System... exadecimal Numbering System... Octal Numbering System... inary oded ecimal () Numbering System... 5 Real (Floating
More informationCHAPTER 2 Number Systems
CHAPTER 2 Number Systems Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish between non-positional and positional number systems.
More informationBINARY SYSTEM. Binary system is used in digital systems because it is:
CHAPTER 2 CHAPTER CONTENTS 2.1 Binary System 2.2 Binary Arithmetic Operation 2.3 Signed & Unsigned Numbers 2.4 Arithmetic Operations of Signed Numbers 2.5 Hexadecimal Number System 2.6 Octal Number System
More informationNumber System. Introduction. Decimal Numbers
Number System Introduction Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26
More informationNUMBER SYSTEMS AND CODES
C H A P T E R 69 Learning Objectives Number Systems The Decimal Number System Binary Number System Binary to Decimal Conversion Binary Fractions Double-Dadd Method Decimal to Binary Conversion Shifting
More informationAppendix. Numbering Systems. In this Appendix
Numbering Systems ppendix n this ppendix ntroduction... inary Numbering System... exadecimal Numbering System... Octal Numbering System... inary oded ecimal () Numbering System... 5 Real (Floating Point)
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 informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers & Number Systems
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers & Number Systems Introduction Numbers and Their Properties Multiples and Factors The Division Algorithm Prime and Composite Numbers Prime Factors
More informationNumber Systems. Both numbers are positive
Number Systems Range of Numbers and Overflow When arithmetic operation such as Addition, Subtraction, Multiplication and Division are performed on numbers the results generated may exceed the range of
More informationNUMERIC SYSTEMS USED IN NETWORKING
NUMERIC SYSTEMS USED IN NETWORKING Decimal - Binary - Hexadecimal Table ASCII Code 128 64 32 16 8 4 2 1 The Letter A 0 1 0 0 0 0 0 1 Data Units Base 10 Numbering System Base 2 Numbering System Decimal
More informationBinary Codes. Dr. Mudathir A. Fagiri
Binary Codes Dr. Mudathir A. Fagiri Binary System The following are some of the technical terms used in binary system: Bit: It is the smallest unit of information used in a computer system. It can either
More informationChapter 1 Review of Number Systems
1.1 Introduction Chapter 1 Review of Number Systems Before the inception of digital computers, the only number system that was in common use is the decimal number system which has a total of 10 digits
More information1.3 Systems of numeration: To represent quantities in the different systems of numeration, specific symbols are used, which are also called ciphers.
Chapter One 1.1 Introduction: Numbers are used to express quantities. There are many numerations systems used in the field of digital electronics, one of the most important being the binary system of numeration
More informationTHE LOGIC OF COMPOUND STATEMENTS
CHAPTER 2 THE LOGIC OF COMPOUND STATEMENTS Copyright Cengage Learning. All rights reserved. SECTION 2.5 Application: Number Systems and Circuits for Addition Copyright Cengage Learning. All rights reserved.
More informationChapter 2 Exercises and Answers
Chapter 2 Exercises and nswers nswers are in blue. For Exercises -5, match the following numbers with their definition.. Number. Natural number C. Integer number D. Negative number E. Rational number unit
More informationLevel ISA3: Information Representation
Level ISA3: Information Representation 1 Information as electrical current At the lowest level, each storage unit in a computer s memory is equipped to contain either a high or low voltage signal Each
More informationReal Numbers finite subset real numbers floating point numbers Scientific Notation fixed point numbers
Real Numbers We have been studying integer arithmetic up to this point. We have discovered that a standard computer can represent a finite subset of the infinite set of integers. The range is determined
More informationMs Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES. 1.1 Introduction
Ms Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES Structure 2.1 Introduction 2.2 Objectives 2.3 Binary Numbers 2.3.1 Binary-to-Decimal conversion 2.3.2 Decimal-to-Binary Conversion 2.4 Octal Numbers
More informationBits, Words, and Integers
Computer Science 52 Bits, Words, and Integers Spring Semester, 2017 In this document, we look at how bits are organized into meaningful data. In particular, we will see the details of how integers are
More informationThe type of all data used in a C (or C++) program must be specified
The type of all data used in a C (or C++) program must be specified A data type is a description of the data being represented That is, a set of possible values and a set of operations on those values
More informationDiscussion. Why do we use Base 10?
MEASURING DATA Data (the plural of datum) are anything in a form suitable for use with a computer. Whatever a computer receives as an input is data. Data are raw facts without any clear meaning. Computers
More informationData Representation 1
1 Data Representation Outline Binary Numbers Adding Binary Numbers Negative Integers Other Operations with Binary Numbers Floating Point Numbers Character Representation Image Representation Sound Representation
More informationNumber Systems Prof. Indranil Sen Gupta Dept. of Computer Science & Engg. Indian Institute of Technology Kharagpur Number Representation
Number Systems Prof. Indranil Sen Gupta Dept. of Computer Science & Engg. Indian Institute of Technology Kharagpur 1 Number Representation 2 1 Topics to be Discussed How are numeric data items actually
More informationTopic Notes: Bits and Bytes and Numbers
Computer Science 220 Assembly Language & Comp Architecture Siena College Fall 2010 Topic Notes: Bits and Bytes and Numbers Binary Basics At least some of this will be review, but we will go over it for
More informationDigital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes
Digital Fundamentals CHAPTER 2 Number Systems, Operations, and Codes Decimal Numbers The decimal number system has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 The decimal numbering system has a base of
More informationMastering Binary Math
Cisco certification candidates, from the CCNA to the CCIE, must master binary math. This includes basic conversions, such as binary-to-decimal and decimal-to-binary, as well as more advanced scenarios
More informationSlide Set 1. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary
Slide Set 1 for ENEL 353 Fall 2017 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2017 SN s ENEL 353 Fall 2017 Slide Set 1 slide
More informationDIGITAL SYSTEM DESIGN
DIGITAL SYSTEM DESIGN UNIT I: Introduction to Number Systems and Boolean Algebra Digital and Analog Basic Concepts, Some history of Digital Systems-Introduction to number systems, Binary numbers, Number
More informationOctal and Hexadecimal Integers
Octal and Hexadecimal Integers CS 350: Computer Organization & Assembler Language Programming A. Why? Octal and hexadecimal numbers are useful for abbreviating long bitstrings. Some operations on octal
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 information1010 2?= ?= CS 64 Lecture 2 Data Representation. Decimal Numbers: Base 10. Reading: FLD Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
CS 64 Lecture 2 Data Representation Reading: FLD 1.2-1.4 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 ) + (1x10 0 ) 1010 10?= 1010 2?= 1
More informationdata within a computer system are stored in one of 2 physical states (hence the use of binary digits)
Binary Digits (bits) data within a computer system are stored in one of 2 physical states (hence the use of binary digits) 0V and 5V charge / NO charge on a transistor gate ferrite core magnetised clockwise
More informationTeaching KS3 Computing. Session 3 Theory: More on binary and representing text Practical: Introducing IF
Teaching KS3 Computing Session 3 Theory: More on binary and representing text Practical: Introducing IF Today s session 5:00 6:00 Representing text as numbers characters and the computer 6.00 7.00 Programming
More informationFinal Labs and Tutors
ICT106 Fundamentals of Computer Systems - Topic 2 REPRESENTATION AND STORAGE OF INFORMATION Reading: Linux Assembly Programming Language, Ch 2.4-2.9 and 3.6-3.8 Final Labs and Tutors Venue and time South
More informationCHAPTER 2 (b) : AND CODES
DKT 122 / 3 DIGITAL SYSTEMS 1 CHAPTER 2 (b) : NUMBER SYSTEMS OPERATION AND CODES m.rizal@unimap.edu.my sitizarina@unimap.edu.my DECIMAL VALUE OF SIGNED NUMBERS SIGN-MAGNITUDE: Decimal values of +ve & -ve
More informationREPRESENTING INFORMATION:
REPRESENTING INFORMATION: BINARY, HEX, ASCII CORRESPONDING READING: WELL, NONE IN YOUR TEXT. SO LISTEN CAREFULLY IN LECTURE (BECAUSE IT WILL BE ON THE EXAM(S))! CMSC 150: Fall 2015 Controlling Information
More informationData Representation. DRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.
Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic ( volts) and one for logic (3.3
More informationComputer Sc. & IT. Digital Logic. Computer Sciencee & Information Technology. 20 Rank under AIR 100. Postal Correspondence
GATE Postal Correspondence Computer Sc. & IT 1 Digital Logic Computer Sciencee & Information Technology (CS) 20 Rank under AIR 100 Postal Correspondence Examination Oriented Theory, Practice Set Key concepts,
More 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 base-0 system. When you
More informationPositional notation Ch Conversions between Decimal and Binary. /continued. Binary to Decimal
Positional notation Ch.. /continued Conversions between Decimal and Binary Binary to Decimal - use the definition of a number in a positional number system with base - evaluate the definition formula using
More informationBSC & BIT Numbering Systems. ITU Lecture 3b
BSC & BIT -1 2017-18 Numbering Systems ITU 07102 Lecture 3b Introduction We use a number to present a quantity (value) of any thing that can be quantified. Quantities are measured, monitored, recorded,
More informationConversion Between Number Bases
Conversion Between Number Bases MATH 100 Survey of Mathematical Ideas J. Robert Buchanan Department of Mathematics Summer 2018 General Number Bases Bases other than 10 are sometimes used in numeration
More informationCMPE223/CMSE222 Digital Logic Design. Positional representation
CMPE223/CMSE222 Digital Logic Design Number Representation and Arithmetic Circuits: Number Representation and Unsigned Addition Positional representation First consider integers Begin with positive only
More informationThe. Binary. Number System
The Binary Number System Why is Binary important? Everything on a computer (or other digital device) is represented by Binary Numbers One to Five in various systems 1 2 3 4 5 I II III IV V 1 10 11 100
More informationWhat Is It? Instruction Register Address Register Data Register
What Is It? Consider the following set of 32 binary digits, written in blocks of four so that the example is not impossible to read. 0010 0110 0100 1100 1101 1001 1011 1111 How do we interpret this sequence
More informationChapter 3: Number Systems and Codes. Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc.
Chapter 3: Number Systems and Codes Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc., 5 th edition Decimal System The radix or base of a number system determines
More informationMC1601 Computer Organization
MC1601 Computer Organization Unit 1 : Digital Fundamentals Lesson1 : Number Systems and Conversions (KSB) (MCA) (2009-12/ODD) (2009-10/1 A&B) Coverage - Lesson1 Shows how various data types found in digital
More informationReal Numbers finite subset real numbers floating point numbers Scientific Notation fixed point numbers
Real Numbers We have been studying integer arithmetic up to this point. We have discovered that a standard computer can represent a finite subset of the infinite set of integers. The range is determined
More informationNumber Systems. Readings: , Problem: Implement simple pocket calculator Need: Display, adders & subtractors, inputs
Number Systems Readings: 3-3.3.3, 3.3.5 Problem: Implement simple pocket calculator Need: Display, adders & subtractors, inputs Display: Seven segment displays Inputs: Switches Missing: Way to implement
More informationTopic Notes: Bits and Bytes and Numbers
Computer Science 220 Assembly Language & Comp Architecture Siena College Fall 2011 Topic Notes: Bits and Bytes and Numbers Binary Basics At least some of this will be review for most of you, but we start
More informationWorld Inside a Computer is Binary
C Programming 1 Representation of int data World Inside a Computer is Binary C Programming 2 Decimal Number System Basic symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Radix-10 positional number system. The radix
More informationNumber systems and binary
CS101 Fundamentals of Computer and Information Sciences LIU 1 of 8 Number systems and binary Here are some informal notes on number systems and binary numbers. See also sections 3.1 3.2 of the textbook.
More informationChapter 2. Data Representation in Computer Systems
Chapter 2 Data Representation in Computer Systems Chapter 2 Objectives Understand the fundamentals of numerical data representation and manipulation in digital computers. Master the skill of converting
More informationumber Systems bit nibble byte word binary decimal
umber Systems 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. To perform useful operations on these
More informationComputer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2
Computer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2 Instructor: Rob Bergen Applied Computer Science University of Winnipeg Announcements Website is up
More informationDRAM uses a single capacitor to store and a transistor to select. SRAM typically uses 6 transistors.
Data Representation Data Representation Goal: Store numbers, characters, sets, database records in the computer. What we got: Circuit that stores 2 voltages, one for logic 0 (0 volts) and one for logic
More information1.1. INTRODUCTION 1.2. NUMBER SYSTEMS
Chapter 1. 1.1. INTRODUCTION Digital computers have brought about the information age that we live in today. Computers are important tools because they can locate and process enormous amounts of information
More informationVariables and Data Representation
You will recall that a computer program is a set of instructions that tell a computer how to transform a given set of input into a specific output. Any program, procedural, event driven or object oriented
More informationDigital Logic Lecture 2 Number Systems
Digital Logic Lecture 2 Number Systems By Ghada Al-Mashaqbeh The Hashemite University Computer Engineering Department Outline Introduction. Basic definitions. Number systems types. Conversion between different
More informationLOGIC DESIGN. Dr. Mahmoud Abo_elfetouh
LOGIC DESIGN Dr. Mahmoud Abo_elfetouh Course objectives This course provides you with a basic understanding of what digital devices are, how they operate, and how they can be designed to perform useful
More informationDIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM
COURSE / CODE DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) NUMBER SYSTEM A considerable subset of digital systems deals with arithmetic operations. To understand the
More informationLogic, Words, and Integers
Computer Science 52 Logic, Words, and Integers 1 Words and Data The basic unit of information in a computer is the bit; it is simply a quantity that takes one of two values, 0 or 1. A sequence of k bits
More information