Oct: 50 8 = 6 (r = 2) 6 8 = 0 (r = 6) Writing the remainders in reverse order we get: (50) 10 = (62) 8


 Elwin Hodge
 1 years ago
 Views:
Transcription
1 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 called radix This means we have possible digits: {,,,, 4, 5, 6,,, 9} We use a positional notation to show value Example: 9.46 = Number Systems in General: In positional notation for a rational number system of radix R >, a number N can be represented as the sum of its digits d i : N = m i= k d i R i, where k = # of digits right of the decimal m = # of digits left of the decimal  Any radix greater than can be used, but the most common are: Binary => Base, Octal => Base, Hexadecimal => Base 6 IncrementingCounting: Decimal Binary Octal Hexadecimal A B 4 C 5 D 4 6 E 5 F 6 Converting Other Number Systems to Decimal: Use the equation: N = Examples: (.) = (.4) (.4) 6 = m i= k = 6 d i R i = (.5) = (5.5) = (9.5) Page of
2 ECE Department Summer Converting Decimal to Other Number Systems: Divide the decimal number by the radix repeatedly Save the remainder after each division Continue dividing the new quotient until it is equal to Write the remainders in reverse order (the last remainder is first) Example: Convert (5) to Binary, Octal, and Hexadecimal Bin: 5 = 5 (r = ) 6 = (r = ) 5 = (r = ) = (r = ) = 6 (r = ) = (r = ) Writing the remainders in reverse order we get: (5) = () Oct: 5 = 6 (r = ) 6 = (r = 6) Writing the remainders in reverse order we get: (5) = (6) Hex: 5 6 = (r = ) 6 = (r = ) Writing the remainders in reverse order we get: (5) = () 6 Converting Decimal Fractions Multiply repeatedly by the desired radix. Remove the integer and write them in order after the decimal. Example: Convert (.5) to Binary, Octal, and Hex Bin:.5 =.65 (int = ).65 =.5 (int = ).5 =.5 (int = ).5 = (int = ) Writing the remainders in order we get: (.5) = (.) Oct:.5 = 6.5 (int = 6).5 = 4. (int = 4) Writing the remainders in order we get: (.5) = (.64) Hex:.5 6 =. (int = D) Writing the remainders in order we get: (.5) = (.D) 6 Page of
3 ECE Department Summer How many bits will it take? Compare the decimal number to n Find the smallest n that yields a result ( n ) greater than the decimal number Example: How many bits will () take? 6 = 64 = Therefore, () requires bits. Converting Between Binary, Octal, and Hexadecimal: There is a direct correlation between Binary bits and Octal or Hex numbers Binary => Base => Base Octal => Base => Base => A group of bits Hex => Base 6 => Base 4 => A group of 4 bits (Also, see IncrementingCounting table above.) Converting Octal or Hex to Binary: Write the or 4 bits corresponding to Octal or Hex numbers Example: Convert (4.6) to Binary Octal: 4. 6 {}{}{}.{}{} Therefore, (4.) = (.) Example: Convert (C.9A) 6 to Binary Hex: C. 9 A {}{}.{}{} Therefore, (C.9A) 6 = (.) Converting from Binary to Octal or Hex: Group the binary number by or 4 bits Write the corresponding Octal or Hex numbers Note: For numbers to the left of the decimal, start grouping with the LSb. For numbers to the right of the decimal, start grouping with the MSb. Note: If the bits do not group evenly, assume zeroes where they do not affect the original number s value. (Additional zeroes are bolded below.) Example: Convert (.) to Octal and Hex Octal: Groups of => {}{}{}{}.{}{} Therefore, (.) = (56.6) Hex: Groups of 5 => {}{}{}.{}{} 5 6. D Therefore, () = (56.D) 6 Page of
4 ECE Department Summer Page 4 of Converting from Octal to Hex or Hex to Octal It is easiest to convert to binary as an intermediate step. Note: It is also easier to convert Dec => Hex => Bin than Dec => Bin directly. Binary Arithmetic: Addition Like decimal, but carry over at rather than. Example: Add to. Subtraction Like decimal, but borrowing gives rather than. Example: Subtract from. Multiplication Like decimal, but easier since you only multiply by. Example: Multiply by. Tip: To double (multiply by ) a binary number, shift the bits to the left. Division Like decimal, but easy to get confused. Example: Divide by.. (or R = ) Tip: To halve (divide by ) a binary number, shift the bits to the right.
5 ECE Department Summer Arithmetic with Octal and Hexadecimal: Addition and Subtraction in Oct and Hex can be done in a similar manner Examples: Hex Oct Add: D C A 9 B.5. A. F Subtract: C D C 9 F A B 5.5. A. B For multiplication or division, it is best to convert to decimal Negative Numbers in Binary: So far, we have only looked at positive, or unsigned, binary numbers There are several ways to represent negative numbers Signed Magnitude The MSb is denotes the sign ( for positive, for negative) of the number The remaining bits give the magnitude of the number Example: () = (4) () = (4) What is the range of an bit unsigned binary number? => to 55 What is the range of a signedmagnitude binary number? =>  to It is cumbersome to try to do arithmetic with signed magnitude. s Complement Positive Number (N) MSb is a Remaining bits give the magnitude of the number Negative Number (N^) N^ = ( n ) N, where n is the number of bits This is the same as to flipping all s to s and s to s Example: What is the s complement of? Answer: Note: () = (5), () = (5) What is the range of an bit s complement number? =>  to Note: s complement has numbers that represent. Page 5 of
6 ECE Department Summer s Complement Positive Number (N) MSb is a Remaining bits give the magnitude of the number Negative Number (N*) N* = n N This is the same as flipping s to s and s to s, then adding Example: What is the s complement of? Answer: = Note: () = (5), () = (5) What is the range of an bit s complement number? =>  to Note: Negative numbers start with and positive numbers with. s Complement Arithmetic:  s complement is the most widely used representation of negative numbers Why? Addition, Subtraction, and Multiplication can all be done in s complement Example: Add (5) and () as 4 bit numbers in s Complement => () Dealing with 4 bit numbers so drop the 5 th bit. Example: Subtract () from (5) as 4 bit numbers in s Complement => () Borrow from the left even if there is no number there. Overflow occurs when: Adding two positive numbers results in a negative number Example: = Wrong! Adding two negative numbers results in a positive number Example: = => Wrong! Subtracting a negative from a positive results in a negative number Example: = Wrong! Subtracting a positive from a negative results in a positive number Example: = Wrong! Page 6 of
7 ECE Department Summer Binary Coded Decimal (BCD): Binary coded decimal is a way of representing decimal numbers in binary Each decimal number uses 4 bits (similar to hexadecimal) Decimal BCD Example: Convert (49) to BCD 4 9 {} {} {} {} Answer: (49) = ( ) BCD Example: Convert ( ) BCD to Decimal {} {} {} {} 6 Answer: ( ) BCD = (6) ASCII: American Standard Code for Information Interchange Uses bit binary to represent numbers, letters, and symbols See page in Roth book. Example: Write Joel in ASCII. J o e l ASCII: Page of
Useful 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 informationRadix Number Systems. Number Systems. Number Systems 4/26/2010. basic idea of a radix number system how do we count:
Number Systems binary, octal, and hexadecimal numbers why used conversions, including to/from decimal negative binary numbers floating point numbers character codes basic idea of a radix number system
More informationBy the end of the lecture, you should be able to:
Extra Lecture: Number Systems Objectives  To understand: Base of number systems: decimal, binary, octal and hexadecimal Textual information stored as ASCII Binary addition/subtraction, multiplication
More informationDigital Fundamentals
Digital Fundamentals with PLD Programming Floyd Chapter 2 29 Pearson Education Decimal Numbers The position of each digit in a weighted number system is assigned a weight based on the base or radix of
More informationLogic Design. Dr. Yosry A. Azzam
Logic Design Dr. Yosry A. Azzam Binary systems Chapter 1 Agenda Binary Systems : Binary Numbers, Binary Codes, Binary Logic ASCII Code (American Standard Code for Information Interchange) Boolean Algebra
More informationData Representation Binary Numbers
Data Representation Binary Numbers Integer Conversion Between Decimal and Binary Bases Task accomplished by Repeated division of decimal number by 2 (integer part of decimal number) Repeated multiplication
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 informationHere 4 is the least significant digit (LSD) and 2 is the most significant digit (MSD).
Number System Introduction Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26
More informationInteger Numbers. The Number Bases of Integers Textbook Chapter 3
Integer Numbers The Number Bases of Integers Textbook Chapter 3 Number Systems Unary, or marks: /////// = 7 /////// + ////// = ///////////// Grouping lead to Roman Numerals: VII + V = VVII = XII Better:
More informationCHAPTER V NUMBER SYSTEMS AND ARITHMETIC
CHAPTER V1 CHAPTER V CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V2 NUMBER SYSTEMS RADIXR REPRESENTATION Decimal number expansion 73625 10 = ( 7 10 4 ) + ( 3 10 3 ) + ( 6 10 2 ) + ( 2 10 1 ) +(
More informationUnderstanding Binary Numbers. Different Number Systems. Conversion: Bin Hex. Conversion MAP. Binary (0, 1) Hexadecimal 0 9, A(10), B(11),, F(15) :
Understanding Binary Numbers Computers operate on binary values (0 and 1) Easy to represent binary values electrically Voltages and currents. Can be implemented using circuits Create the building blocks
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 informationSwitching Circuits & Logic Design
Switching Circuits & Logic Design JieHong Roland Jiang 江介宏 Department of Electrical Engineering National Taiwan University Fall 2013 1 1 Number Systems and Conversion Babylonian number system (3100 B.C.)
More information2.1 Binary Numbers. 2.3 Number System Conversion. From Binary to Decimal. From Decimal to Binary. Section 2 Binary Number System Page 1 of 8
Section Binary Number System Page 1 of 8.1 Binary Numbers The number system we use is a positional number system meaning that the position of each digit has an associated weight. The value of a given number
More informationMT1 Number Systems. In general, the number a 3 a 2 a 1 a 0 in a base b number system represents the following number:
MT1 Number Systems MT1.1 Introduction A number system is a well defined structured way of representing or expressing numbers as a combination of the elements of a finite set of mathematical symbols (i.e.,
More 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 informationالدكتور المھندس عادل مانع داخل
الدكتور المھندس عادل مانع داخل / میسان جامعة / كلیة الھندسة قسم الھندسة الكھرباي یة Chapter 1: Digital Systems Discrete Data Examples: 26 letters of the alphabet (A, B etc) 10 decimal digits (0, 1, 2 etc)
More informationData Representation in Computers
Chapter 3 Data Representation in Computers After studying this chapter the student will be able to: *Learn about binary, octal, decimal and hexadecimal number systems *Learn conversions between two different
More 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 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 informationNumber Systems Richard E. Haskell
NUMBER SYSTEMS D Number Systems Richard E. Haskell Data inside a computer are represented by binary digits or bits. The logical values of these binary digits are denoted by and, while the corresponding
More information1 Basic Computing Concepts (4) Data Representations
1 Basic Computing Concepts (4) Data Representations The Binary System The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. The
More informationInteger and Real Numbers Representation in Microprocessor Techniques
Brno University of Technology Integer and Real Numbers Representation in Microprocessor Techniques Microprocessor Techniques and Embedded Systems Lecture 1 Dr. Tomas Fryza 30Sep2011 Contents Numerical
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 informationNUMBERING SYSTEMS C HAPTER 1.0 INTRODUCTION 1.1 A REVIEW OF THE DECIMAL SYSTEM 1.2 BINARY NUMBERING SYSTEM
12 Digital Principles Switching Theory C HAPTER 1 NUMBERING SYSTEMS 1.0 INTRODUCTION Inside today s computers, data is represented as 1 s and 0 s. These 1 s and 0 s might be stored magnetically on a disk,
More 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 informationNumber Systems and. Data Representation
Number Systems and Data Representation 1 Lecture Outline Number Systems Binary, Octal, Hexadecimal Representation of characters using codes Representation of Numbers Integer, Floating Point, Binary Coded
More 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 Representation and Arithmetic in Various Numeral Systems
1 Number Representation and Arithmetic in Various Numeral Systems Computer Organization and Assembly Language Programming 203.8002 Adapted by Yousef Shajrawi, licensed by Huong Nguyen under the Creative
More informationReview of Number Systems The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a computer. Different
More informationChap 3 Data Representation
Chap 3 Data Representation 311 Data Types How to representation and conversion between these data types? 311 Data Types : Number System Radix : Decimal : radix 10 Binary : radix 2 311 Data Types : Number
More 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 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 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 information1. Number Representation
CSEE 3827: Fundamentals of Computer Systems, Spring 2011 1. Number Representation Prof. Martha Kim (martha@cs.columbia.edu) Web: http://www.cs.columbia.edu/~martha/courses/3827/sp11/ Contents (H&H 1.31.4,
More informationCOMP2121: Microprocessors and Interfacing
Interfacing Lecture 3: Number Systems (I) http://www.cse.unsw.edu.au/~cs2121 Lecturer: Hui Wu Session 2, 2005 Overview Positional notation Decimal, hexadecimal and binary One complement Two s complement
More information1 Number System (Lecture 1 and 2 supplement)
1 Number System (Lecture 1 and 2 supplement) By Dr. Taek Kwon Many different number systems perhaps from the prehistoric era have been developed and evolved. Among them, binary number system is one of
More informationReview of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement
Review of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement Topic 1: Binary, Octal, and Hexadecimal Numbers The number system we generally use in our everyday lives is a decimal
More 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 informationTHE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DIGITAL LOGIC DESIGN DISCUSSION ECOM Eng. Huda M.
THE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DIGITAL LOGIC DESIGN DISCUSSION ECOM 2012 Eng. Huda M. Dawoud September, 2015 1.1 List the octal and hexadecimal numbers
More 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 2 Numeric Representation.
Chapter 2 Numeric Representation. Most of the things we encounter in the world around us are analog; they don t just take on one of two values. How then can they be represented digitally? The key is that
More informationLecture 1 Introduction, Numbers, and Number System Page 1 of 8
Lecture Introduction, Numbers and Number System Contents.. Number Systems (Appendix B)... 2. Example. Converting to Base 0... 2.2. Number Representation... 2.3. Number Conversion... 3. To convert a number
More 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 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 informationChapter I: Digital System and Binary Numbers
Chapter I: Digital System and Binary Numbers 11Digital Systems Digital systems are used in:  Communication  Business transaction  Traffic Control  Medical treatment  Internet The signals in digital
More informationNumber Representation
Number Representation Number System :: The Basics We are accustomed to using the socalled decimal number system Ten digits ::,,,3,4,5,6,7,8,9 Every digit position has a weight which is a power of Base
More informationNumber System Decimal, Binary, OtlH Octal, Hex Conversion (one to another)
Number system Number System Outline Decimal, Binary, OtlH Octal, Hex Conversion (one to another) Decimal to Binary, Octal, Hex & Vice Versa Binary to HEX & vice versa Other representation Signed, Unsigned,
More informationCommon Number Systems Number Systems
5/29/204 Common Number Systems Number Systems System Base Symbols Used by humans? Used in computers? Decimal 0 0,, 9 Yes No Binary 2 0, No Yes Octal 8 0,, 7 No No Hexadecimal 6 0,, 9, A, B, F No No Number
More informationEncoding Systems: Combining Bits to form Bytes
Encoding Systems: Combining Bits to form Bytes Alphanumeric characters are represented in computer storage by combining strings of bits to form unique bit configuration for each character, also called
More informationNumber Systems & Encoding
Number Systems & Encoding Lecturer: Sri Parameswaran Author: Hui Annie Guo Modified: Sri Parameswaran Week2 1 Lecture overview Basics of computing with digital systems Binary numbers Floating point numbers
More informationBinary Representation. Number Systems. Positional Notation
Binary Representation The basis of all digital data is binary representation. Binary  means two 1, 0 True, False Hot, Cold On, Off We must be able to handle more than just values for real world problems
More informationCSCC85 Spring 2006: Tutorial 0 Notes
CSCC85 Spring 2006: Tutorial 0 Notes Yani Ioannou January 11 th, 2006 There are 10 types of people in the world, those who understand binary, and those who don t. Contents 1 Number Representations 1 1.1
More 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 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 information2. Number Systems  Positional Number Systems (1)  2. Number Systems  Binary Numbers  2. Number Systems  Positional Number Systems (2) 
Sistemas Digitais I LESI  2º ano Lesson 2  Number Systems Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática  Positional Number Systems (1)  We use daily a positional number system.
More informationCHAPTER THREE. 3.1 Binary Addition. Binary Math and Signed Representations
CHAPTER THREE Binary Math and Signed Representations Representing numbers with bits is one thing. Doing something with them is an entirely different matter. This chapter discusses some of the basic mathematical
More informationLecture 1: Digital Systems and Binary Numbers
Lecture 1: Digital Systems and Binary Numbers Matthew Shuman September 30th, 2009 1 Digital Systems 11 in Text 1.1 Analog Systems Analog systems are continuous. Look at the analog clock in figure 1. The
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 informationEE 3170 Microcontroller Applications
EE 37 Microcontroller Applications Lecture 3 : Digital Computer Fundamentals  Number Representation (.) Based on slides for ECE37 by Profs. Sloan, Davis, Kieckhafer, Tan, and Cischke Number Representation
More informationNumber Systems and Base Conversions
Number Systems and Base Conversions As you know, the number system that we commonly use is the decimal or base 10 number system. That system has 10 digits, 0 through 9. While it's very convenient for
More informationNumber Systems and Number Representation
Number Systems and Number Representation 1 For Your Amusement Question: Why do computer programmers confuse Christmas and Halloween? Answer: Because 25 Dec = 31 Oct  http://www.electronicsweekly.com
More informationBinary Representation and Computer Arithmetic
Binary Representation and Computer Arithmetic The decimal system of counting and keeping track of items was first created by Hindu mathematicians in India in A.D. 4. Since it involved the use of fingers
More informationLecture 1: Digital Systems and Number Systems
Lecture 1: Digital Systems and Number Systems Matthew Shuman April 3rd, 2013 The Digital Abstraction 1.3 in Text Analog Systems Analog systems are continuous. Look at the analog clock in figure 1. The
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 informationTECH. Arithmetic & Logic Unit. CH09 Computer Arithmetic. Number Systems. ALU Inputs and Outputs. Binary Number System
CH09 Computer Arithmetic CPU combines of ALU and Control Unit, this chapter discusses ALU The Arithmetic and Logic Unit (ALU) Number Systems Integer Representation Integer Arithmetic FloatingPoint Representation
More informationCPE 323 Data Types and Number Representations
CPE 323 Data Types and Number Representations Aleksandar Milenkovic Numeral Systems: Decimal, binary, hexadecimal, and octal We ordinarily represent numbers using decimal numeral system that has 10 as
More informationBinary Numbers Again. Binary Arithmetic, Subtraction. Binary, Decimal addition
Binary Numbers Again Recall than N binary digits (N bits) can represent unsigned integers from 0 to 2 N 1. 4 bits = 0 to 15 8 bits = 0 to 255 16 bits = 0 to 65535 Besides simply representation, we would
More informationData types. lecture 4
Data types lecture 4 Information in digital computers is represented using binary number system. The base, i.e. radix, of the binary system is 2. Other common number systems: octal (base 8), decimal (base
More informationA B C
Data Representation Module 2 CS 272 Sam Houston State University Dr. Tim McGuire Copyright 2001 by Timothy J. McGuire, Ph.D. 1 Positional Number Systems Decimal (base 10) is an example e.g., 435 means
More informationCSC 1103: Digital Logic. Lecture Six: Data Representation
CSC 1103: Digital Logic Lecture Six: Data Representation Martin Ngobye mngobye@must.ac.ug Mbarara University of Science and Technology MAN (MUST) CSC 1103 1 / 32 Outline 1 Digital Computers 2 Number Systems
More 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 informationIntroduction Number Systems and Conversion
UNIT 1 Introduction Number Systems and Conversion Objectives 1. Introduction The first part of this unit introduces the material to be studied later. In addition to getting an overview of the material
More 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 informationCHAPTER 3 Number System and Codes
CHAPTER 3 Number System and Codes 3.1 Introduction On hearing the word number, we immediately think of familiar decimal number system with its 10 digits; 0,1, 2,3,4,5,6, 7, 8 and 9. these numbers are called
More information1. True or False? A natural number is the number 0 or any number obtained by adding 1 to a natural number.
CS Illuminated, 5 th ed. Chapter 2 Review Quiz 1. True or False? A natural number is the number 0 or any number obtained by adding 1 to a natural number. 2. True or False? The category of numbers called
More information1. Convert the following binary exponential expressions to their 'English'
Answers to Practice Problems Practice Problems  Integer Number System Conversions 1. Convert the decimal integer 427 10 into the following number systems: a. 110101011 2 c. 653 8 b. 120211 3 d. 1AB 16
More 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 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 informationEEE130 Digital Electronics I Lecture #2
EEE130 Digital Electronics I Lecture #2 Number Systems, Operations and Codes By Dr. Shahrel A. Suandi Topics to be discussed 21 Decimal Numbers 22 Binary Numbers 23 DecimaltoBinary Conversion 24
More informationAssembly Language for IntelBased Computers, 4 th Edition. Chapter 1: Basic Concepts
Assembly Language for IntelBased Computers, 4 th Edition Kip R. Irvine Chapter 1: Basic Concepts Slides prepared by Kip R. Irvine Revision date: 07/21/2002 Chapter corrections (Web) Assembly language
More 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 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 informationCSCI 230 Class Notes Binary Number Representations and Arithmetic
CSCI 230 Class otes Binary umber Representations and Arithmetic Mihran Tuceryan with some modifications by Snehasis Mukhopadhyay Jan 22, 1999 1 Decimal otation What does it mean when we write 495? How
More informationChapter 2: Number Systems
Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This twovalued number system is called binary. As presented earlier, there are many
More informationPresented By: Ms. Poonam Anand
Presented By: Ms. Poonam Anand Know the different types of numbers Describe positional notation Convert numbers in other bases to base 10 Convert base 10 numbers into numbers of other bases Describe the
More informationComputer Architecture CPIT 210 LAB 1 Manual. Prepared By: Mohammed Ghazi Al Obeidallah.
Computer Architecture CPIT 210 LAB 1 Manual Prepared By: Mohammed Ghazi Al Obeidallah malabaidallah@kau.edu.sa LAB 1 Outline: 1. Students should understand basic concepts of Decimal system, Binary system,
More informationLab 1: Information Representation I  Number Systems
Unit 1: Computer Systems, pages 1 of 7  Department of Computer and Mathematical Sciences CS 1408 Intro to Computer Science with Visual Basic 1 Lab 1: Information Representation I  Number Systems Objectives:
More informationLab 1: Information Representation I  Number Systems
Unit 1: Computer Systems, pages 1 of 7  Department of Computer and Mathematical Sciences CS 1410 Intro to Computer Science with C++ 1 Lab 1: Information Representation I  Number Systems Objectives:
More informationBinary, 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 information23 1 The Binary Number System
664 Chapter 23 Binary, Hexadecimal, Octal, and BCD Numbers 23 The Binary Number System Binary Numbers A binary number is a sequence of the digits 0 and, such as 000 The number shown has no fractional part
More informationEE 308 Spring Binary, Hex and Decimal Numbers (4bit representation) Binary. Hex. Decimal A B C D E F
EE 8 Spring Binary, Hex and Decimal Numbers (bit representation) Binary Hex 8 9 A B C D E F Decimal 8 9 EE 8 Spring What does a number represent? Binary numbers are a code, and represent what the programmer
More informationChapter II Binary Data Representation
Chapter II Binary Data Representation The atomic unit of data in computer systems is the bit, which is actually an acronym that stands for BInary digit. It can hold only 2 values or states: 0 or 1, true
More informationNumber Representation
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 informationTheory of Logic Circuits. Laboratory manual. Exercise 6
Zakład Mikroinformatyki i Teorii Automatów Cyfrowych Theory of Logic Circuits Laboratory manual Exercise 6 Selected arithmetic switching circuits 2008 Tomasz Podeszwa, Piotr Czekalski (edt.) 1. Number
More 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 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 informationNumber System. Some important number systems are as follows. Decimal number system Binary number system Octal number system Hexadecimal number system
Number System When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand positional number system where there are only
More informationIntroduction to Telecommunications and Computer Engineering Unit 2: Number Systems and Logic
Introduction to Telecommunications and Computer Engineering Unit 2: Number Systems and Logic Syedur Rahman Lecturer, CSE Department North South University syedur.rahman@wolfson.oon.org Acknowledgements
More informationNumber Systems and Data Representation CS221
Number Systems and Data Representation CS221 Inside today s computers, data is represented as 1 s and 0 s. These 1 s and 0 s might be stored magnetically on a disk, or as a state in a transistor, core,
More information