Encoding Systems: Combining Bits to form Bytes

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Encoding Systems: Combining Bits to form Bytes"

Transcription

1 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 byte Characters are translated into bytes according to an encoding system (EBCDIC, ASCII) Parity checking ensures that data transmission is complete and accurate Numbering System

2 Numbering Systems and Computers The two primary numbering systems used in conjunction with computer are binary and decimal Decimal is translated into binary on input and binary is translated into decimal on output The hexadecimal numbering system is used in reading and reviewing binary output in the form of a memory dump Numbering System 2

3 Numbering Systems (cont.) Name Base Digits Hexadecimal >.. 9 and A.. F Decimal.. 9 Octal Binary 2, Numbering System 3

4 Numbering Systems(cont.) Converting Decimal to Binary Number Remainder (37) =() 2 Numbering System 4

5 Numbering Systems (cont.) Converting Binary to Decimal () 2 =X2 + X2 +X2 2 + x2 3 + x2 4 +x2 5 = = ( 37) Numbering System 5

6 Numbering Systems(cont.) Converting Decimal to Octal Number Remainder (37) =(45) 8 Numbering System 6

7 Numbering Systems(cont.) Converting Binary to Octal ( 37) = (45) 8 = () 2 Notice the special relation between binary and octal, if we take every three bits we will find that: () 2 = x2 +x2 +x2 2 = (5) 8 () 2 = x2 +x2 +x2 2 = (4) 8 Numbering System 7

8 Numbering Systems (cont.) Converting Decimal to Hexadecimal Number ( 37) = (25) 6 Remainder Numbering System 8

9 6 3 Numbering Systems (cont.) Converting Decimal to Hexadecimal Number Remainder 6 5 (F) (3) = (F) 6 Numbering System 9

10 Numbering Systems(cont.) Converting Binary to Hexadecimal ( 37) = (25) 6 = () 2 Notice the special relation between binary and Hexadecimal, if we take every four bits we will find that: () 2 = x2 +x2 +x2 2 + x2 = (5) 6 () 2 = x2 +x2 +x2 2 + x2 = (2) 6 Numbering System

11 Computer Representation of Information Basic unit of information is the Bit or Binary digit. With a single bit, we can represent two distinct values and. With two bits, we can represent four distinct values:,,, and. In general, with m bits, we can represent 2m distinct values. A byte is a grouping of 8 bits. A word is a grouping of either 6, 32, or 64 bits, depending on the computer system. A word is typically 32 bits on most systems, a half word is 6 bits, and a double word is 64 bits. Numbering System

12 Representation of Characters Characters are typically represented by single byte. The ASCII standard (American Standard Code for Information Interchange) defines unique binary codes for English letters, digits, and special symbols. The ASCII standard defines only 28 characters, with decimal codes to 27. A single byte can represent up to 256 characters. The remaining 28 characters, coded 28 to 255, can be used for a second language. For example, the ASCII standard can be extended for Arabic letters. Some languages, such as Chinese, Japanese, and Korean, have more than 256 characters. Characters can be encoded using 2 bytes, rather than a single byte. Numbering System 2

13 Representation of Characters Binary Decimal Character Representation Code space 32! A 65 B 66 Z 9 [ 9 a 97 b 98 Numbering System 3

14 Representation of Integers Unsigned Integers Represented using a fixed number of bits or bytes With m bits, we can have 2 m distinct values:,, 2,, 2 m. Using byte to represent an integer, m = 8, 2 8 distinct values:,, 2,, 2 8 = 255. Using 2 bytes to represent an integer, m = 6, 2 6 distinct values:,, 2,, 2 6 = Using 4 bytes to represent an integer, m = 32, 2 32 distinct values:,, 2,, 2 32 = Signed Integers Unsigned representation of integers does not allow negative numbers. We need to divide the 2 m distinct values into positive and negative values. Two methods are used to represent signed integers: Sign-Magnitude Representation Two s Complement Representation Numbering System 4

15 Sign-Magnitude Representation Signed integers can be represented as a sign and a magnitude. Using m bits to represent a signed integer: the most significant bit is used to represent the sign. sign = is positive. sign = is negative. The least significant m bits are used to represent the magnitude. With m bits for the magnitude, the range of the magnitude is from to 2 m. For an m-bit signed integer in sign-magnitude representation, the range of values is from 2 m to + 2 m. When m = 8, the range of values is from 27 to +27. Examples using 8-bit sign-magnitude representation (m = 8) +29 = 2 29 = 2 + = 2 = 2 There are two different representations of (+ and ). Addition of a positive and a negative number must be treated as a subtraction problem. The sign and the magnitude of both operands must be checked to obtain the correct result Numbering System 5

16 Two s Complement Representation Sign-magnitude representation is natural for humans, but not for computers. A better representation for computers is the 2 s complement representation. 2 s complement of an m-bit number N = (Bitwise complement of N) + Bitwise complement of N is called the s complement of N. Examples of 8-bit numbers and their 2 s complement representation: + = 2 = 2 s complement of 2 = 2 + = = 2 29 = 2 s complement of 2 = 2 + = = 2 s complement of 2 = 2 + = 2 For an m-bit signed integer in 2 s complement notation, the range of integer values is from 2 m to 2 m. When m = 8, the range is from 28 to 27. When m = 6, the range is from to When m = 32, the range is from to Numbering System 6

17 Comparison Table for 8-bit Number Representations 8-bit Binary Decimal equivalent when Representation Unsigned Sign-Mag 2 s Comp When 8-bit binary representation is interpreted as unsigned: Decimal equivalent is counted from = 2 to 255 = 2 When interpreted as sign-magnitude: Positive values are counted from + = 2 to +27 = 2 Negative values are counted from 27 = 2 to = 2 When interpreted as 2 s complement: Positive values are counted from = 2 = to +27 = 2 Negative values are counted from 28 = 2 to = 2 Numbering System 7

18 Binary Addition a b c carry sum Examples: carry carry sum +2 sum carry carry sum 8 sum + 27 Numbering System 8

19 Binary Addition The addition of 3 bits a + b + c produces a sum bit and a carry bit. Signed Integers are represented in 2 s complement notation. Addition of integers in 2 s complement notation results in a signed integer. Although a carry out is produced in the 2nd and 4th computations, it is ignored. Numbering System 9

Number Representation

Number 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 information

2011, The McGraw-Hill Companies, Inc. Chapter 3

2011, The McGraw-Hill 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 information

LSN 2 Number Systems. ECT 224 Digital Computer Fundamentals. Department of Engineering Technology

LSN 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 (0-9) Base 10 weighting system... 10 5 10 4 10 3 10 2 10 1 10 0. 10-1 10-2 10-3

More information

CDA 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 CDA 3200 Digital Systems Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012 Outline Data Representation Binary Codes Why 6-3-1-1 and Excess-3? Data Representation (1/2) Each numbering

More information

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

Oct: 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 information

The string of digits 101101 in the binary number system represents the quantity

The 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 information

Chapter 4: Computer Codes

Chapter 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 information

EE 261 Introduction to Logic Circuits. Module #2 Number Systems

EE 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 information

Binary Representation. Number Systems. Base 10, Base 2, Base 16. Positional Notation. Conversion of Any Base to Decimal.

Binary 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 information

Solution for Homework 2

Solution 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 information

Computer Science 281 Binary and Hexadecimal Review

Computer Science 281 Binary and Hexadecimal Review Computer Science 281 Binary and Hexadecimal Review 1 The Binary Number System Computers store everything, both instructions and data, by using many, many transistors, each of which can be in one of two

More information

Data Representation. Data Representation, Storage, and Retrieval. Data Representation. Data Representation. Data Representation. Data Representation

Data 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 information

Today. Binary addition Representing negative numbers. Andrew H. Fagg: Embedded Real- Time Systems: Binary Arithmetic

Today. 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 information

Signed Binary Arithmetic

Signed 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 information

plc numbers - 13.1 Encoded values; BCD and ASCII Error detection; parity, gray code and checksums

plc 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 information

Binary Representation

Binary Representation Binary Representation The basis of all digital data is binary representation. Binary - means two 1, 0 True, False Hot, Cold On, Off We must tbe able to handle more than just values for real world problems

More information

Number and codes in digital systems

Number 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 information

CSI 333 Lecture 1 Number Systems

CSI 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 information

Useful Number Systems

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 information

Number Systems I. CIS008-2 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October

Number Systems I. CIS008-2 Logic and Foundations of Mathematics. David Goodwin. 11:00, Tuesday 18 th October Number Systems I CIS008-2 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 information

HOMEWORK # 2 SOLUTIO

HOMEWORK # 2 SOLUTIO HOMEWORK # 2 SOLUTIO Problem 1 (2 points) a. There are 313 characters in the Tamil language. If every character is to be encoded into a unique bit pattern, what is the minimum number of bits required to

More information

Activity 1: Bits and Bytes

Activity 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 information

Section 1.4 Place Value Systems of Numeration in Other Bases

Section 1.4 Place Value Systems of Numeration in Other Bases Section.4 Place Value Systems of Numeration in Other Bases Other Bases The Hindu-Arabic system that is used in most of the world today is a positional value system with a base of ten. The simplest reason

More information

Decimal Numbers: Base 10 Integer Numbers & Arithmetic

Decimal 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 information

Numeral Systems. The number twenty-five can be represented in many ways: Decimal system (base 10): 25 Roman numerals:

Numeral Systems. The number twenty-five 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 information

Binary Numbers. Binary Octal Hexadecimal

Binary 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 information

Base Conversion written by Cathy Saxton

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 information

Digital 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 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 information

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-470/570: Microprocessor-Based System Design Fall 2014.

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-470/570: Microprocessor-Based 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 information

Lecture 2. Binary and Hexadecimal Numbers

Lecture 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 information

198:211 Computer Architecture

198:211 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 information

Systems I: Computer Organization and Architecture

Systems 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 information

Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC

Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC Levent EREN levent.eren@ieu.edu.tr A-306 Office Phone:488-9882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A n

More information

2 Number Systems 2.1. Foundations of Computer Science Cengage Learning

2 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 information

Chapter Binary, Octal, Decimal, and Hexadecimal Calculations

Chapter 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 information

To convert an arbitrary power of 2 into its English equivalent, remember the rules of exponential arithmetic:

To 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 information

The Essentials of Computer Organization and Architecture. Linda Null and Julia Lobur Jones and Bartlett Publishers, 2003

The Essentials of Computer Organization and Architecture. Linda Null and Julia Lobur Jones and Bartlett Publishers, 2003 The Essentials of Computer Organization and Architecture Linda Null and Julia Lobur Jones and Bartlett Publishers, 2003 Chapter 2 Instructor's Manual Chapter Objectives Chapter 2, Data Representation,

More information

Chapter 1: Digital Systems and Binary Numbers

Chapter 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 information

2 Number Systems. Source: Foundations of Computer Science Cengage Learning. Objectives After studying this chapter, the student should be able to:

2 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 information

Counting in base 10, 2 and 16

Counting in base 10, 2 and 16 Counting in base 10, 2 and 16 1. Binary Numbers A super-important fact: (Nearly all) Computers store all information in the form of binary numbers. Numbers, characters, images, music files --- all of these

More information

CPEN 214 - Digital Logic Design Binary Systems

CPEN 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 information

Number Systems, Base Conversions, and Computer Data Representation

Number 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 information

Unsigned Conversions from Decimal or to Decimal and other Number Systems

Unsigned 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 information

CS 16: Assembly Language Programming for the IBM PC and Compatibles

CS 16: Assembly Language Programming for the IBM PC and Compatibles CS 16: Assembly Language Programming for the IBM PC and Compatibles First, a little about you Your name Have you ever worked with/used/played with assembly language? If so, talk about it Why are you taking

More information

Numbering Systems. InThisAppendix...

Numbering 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 information

Binary Numbers. Bob Brown Information Technology Department Southern Polytechnic State University

Binary 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 information

CS101 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 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 information

The Answer to the 14 Most Frequently Asked Modbus Questions

The Answer to the 14 Most Frequently Asked Modbus Questions Modbus Frequently Asked Questions WP-34-REV0-0609-1/7 The Answer to the 14 Most Frequently Asked Modbus Questions Exactly what is Modbus? Modbus is an open serial communications protocol widely used in

More information

= Chapter 1. The Binary Number System. 1.1 Why Binary?

= 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 information

Today s topics. Digital Computers. More on binary. Binary Digits (Bits)

Today s topics. Digital Computers. More on binary. Binary Digits (Bits) Today s topics! Binary Numbers! Brookshear.-.! Slides from Prof. Marti Hearst of UC Berkeley SIMS! Upcoming! Networks Interactive Introduction to Graph Theory http://www.utm.edu/cgi-bin/caldwell/tutor/departments/math/graph/intro

More information

NUMBER SYSTEMS. 1.1 Introduction

NUMBER 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 information

Bachelors of Computer Application Programming Principle & Algorithm (BCA-S102T)

Bachelors of Computer Application Programming Principle & Algorithm (BCA-S102T) Unit- I Introduction to c Language: C is a general-purpose computer programming language developed between 1969 and 1973 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating

More information

Digital Design. Assoc. Prof. Dr. Berna Örs Yalçın

Digital Design. Assoc. Prof. Dr. Berna Örs Yalçın Digital Design Assoc. Prof. Dr. Berna Örs Yalçın Istanbul Technical University Faculty of Electrical and Electronics Engineering Office Number: 2318 E-mail: siddika.ors@itu.edu.tr Grading 1st Midterm -

More information

Positional Numbering System

Positional 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 information

Introduction to Programming

Introduction to Programming Introduction to Programming SS 2012 Adrian Kacso, Univ. Siegen adriana.dkacsoa@duni-siegena.de Tel.: 0271/740-3966, Office: H-B 8406 Stand: April 25, 2012 Betriebssysteme / verteilte Systeme Introduction

More information

The programming language C. sws1 1

The programming language C. sws1 1 The programming language C sws1 1 The programming language C invented by Dennis Ritchie in early 1970s who used it to write the first Hello World program C was used to write UNIX Standardised as K&C (Kernighan

More information

Pemrograman Dasar. Basic Elements Of Java

Pemrograman Dasar. Basic Elements Of Java Pemrograman Dasar Basic Elements Of Java Compiling and Running a Java Application 2 Portable Java Application 3 Java Platform Platform: hardware or software environment in which a program runs. Oracle

More information

Computers. Hardware. The Central Processing Unit (CPU) CMPT 125: Lecture 1: Understanding the Computer

Computers. Hardware. The Central Processing Unit (CPU) CMPT 125: Lecture 1: Understanding the Computer Computers CMPT 125: Lecture 1: Understanding the Computer Tamara Smyth, tamaras@cs.sfu.ca School of Computing Science, Simon Fraser University January 3, 2009 A computer performs 2 basic functions: 1.

More information

2010/9/19. Binary number system. Binary numbers. Outline. Binary to decimal

2010/9/19. 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 base-2 Binary numbers 2 3 + 7 + 5 Some terminology Bit: a binary digit ( or ) Hexadecimal

More information

Lecture 2: Number Representation

Lecture 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 information

Number Conversions Dr. Sarita Agarwal (Acharya Narendra Dev College,University of Delhi)

Number 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 information

Digital codes. Resources and methods for learning about these subjects (list a few here, in preparation for your research):

Digital codes. Resources and methods for learning about these subjects (list a few here, in preparation for your research): Digital codes 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 information

DNA Data and Program Representation. Alexandre David 1.2.05 adavid@cs.aau.dk

DNA Data and Program Representation. Alexandre David 1.2.05 adavid@cs.aau.dk DNA Data and Program Representation Alexandre David 1.2.05 adavid@cs.aau.dk Introduction Very important to understand how data is represented. operations limits precision Digital logic built on 2-valued

More information

THE BINARY NUMBER SYSTEM

THE 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 information

Lecture 4 Representing Data on the Computer. Ramani Duraiswami AMSC/CMSC 662 Fall 2009

Lecture 4 Representing Data on the Computer. Ramani Duraiswami AMSC/CMSC 662 Fall 2009 Lecture 4 Representing Data on the Computer Ramani Duraiswami AMSC/CMSC 662 Fall 2009 x = ±(1+f) 2 e 0 f < 1 f = (integer < 2 52 )/ 2 52-1022 e 1023 e = integer Effects of floating point Effects of floating

More information

First Bytes Programming Lab 2

First Bytes Programming Lab 2 First Bytes Programming Lab 2 This lab is available online at www.cs.utexas.edu/users/scottm/firstbytes. Introduction: In this lab you will investigate the properties of colors and how they are displayed

More information

Memory is implemented as an array of electronic switches

Memory is implemented as an array of electronic switches Memory Structure Memory is implemented as an array of electronic switches Each switch can be in one of two states 0 or 1, on or off, true or false, purple or gold, sitting or standing BInary digits (bits)

More information

3. Convert a number from one number system to another

3. 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 information

Binary. ! You are probably familiar with decimal

Binary. ! You are probably familiar with decimal Arithmetic operations in assembly language Prof. Gustavo Alonso Computer Science Department ETH Zürich alonso@inf.ethz.ch http://www.inf.ethz.ch/department/is/iks/ Binary! You are probably familiar with

More information

Lecture 03 Bits, Bytes and Data Types

Lecture 03 Bits, Bytes and Data Types Lecture 03 Bits, Bytes and Data Types In this lecture Computer Languages Assembly Language The compiler Operating system Data and program instructions Bits, Bytes and Data Types ASCII table Data Types

More information

Chapter 2. Binary Values and Number Systems

Chapter 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 information

1. Give the 16 bit signed (twos complement) representation of the following decimal numbers, and convert to hexadecimal:

1. 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 information

Review 1/2. CS61C Characters and Floating Point. Lecture 8. February 12, Review 2/2 : 12 new instructions Arithmetic:

Review 1/2. CS61C Characters and Floating Point. Lecture 8. February 12, Review 2/2 : 12 new instructions Arithmetic: Review 1/2 CS61C Characters and Floating Point Lecture 8 February 12, 1999 Handling case when number is too big for representation (overflow) Representing negative numbers (2 s complement) Comparing signed

More information

Bits and Bytes. Computer Literacy Lecture 4 29/09/2008

Bits and Bytes. Computer Literacy Lecture 4 29/09/2008 Bits and Bytes Computer Literacy Lecture 4 29/09/2008 Lecture Overview Lecture Topics How computers encode information How to quantify information and memory How to represent and communicate binary data

More information

Encoding Text with a Small Alphabet

Encoding Text with a Small Alphabet Chapter 2 Encoding Text with a Small Alphabet Given the nature of the Internet, we can break the process of understanding how information is transmitted into two components. First, we have to figure out

More information

I PUC - Computer Science. Practical s Syllabus. Contents

I PUC - Computer Science. Practical s Syllabus. Contents I PUC - Computer Science Practical s Syllabus Contents Topics 1 Overview Of a Computer 1.1 Introduction 1.2 Functional Components of a computer (Working of each unit) 1.3 Evolution Of Computers 1.4 Generations

More information

COMP 250 Fall 2012 lecture 2 binary representations Sept. 11, 2012

COMP 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 information

Intel Hexadecimal Object File Format Specification Revision A, 1/6/88

Intel Hexadecimal Object File Format Specification Revision A, 1/6/88 Intel Hexadecimal Object File Format Specification Revision A, 1/6/88 DISCLAIMER Intel makes no representation or warranties with respect to the contents hereof and specifically disclaims any implied warranties

More information

Classful Subnetting Explained

Classful Subnetting Explained Classful ting Explained When given an IP Address and a Mask, how can you determine other information such as: The subnet address of this subnet The broadcast address of this subnet The range of Host Addresses

More information

Classless Subnetting Explained

Classless 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 information

Machine Architecture and Number Systems. Major Computer Components. Schematic Diagram of a Computer. The CPU. The Bus. Main Memory.

Machine Architecture and Number Systems. Major Computer Components. Schematic Diagram of a Computer. The CPU. The Bus. Main Memory. 1 Topics Machine Architecture and Number Systems Major Computer Components Bits, Bytes, and Words The Decimal Number System The Binary Number System Converting from Decimal to Binary Major Computer Components

More information

Chapter 3: Dataflow Modeling

Chapter 3: Dataflow Modeling Chapter 3: Dataflow Modeling Prof. Ming-Bo Lin Department of Electronic Engineering National Taiwan University of Science and Technology Digital System Designs and Practices Using Verilog HDL and FPGAs

More information

CPU Organization and Assembly Language

CPU Organization and Assembly Language COS 140 Foundations of Computer Science School of Computing and Information Science University of Maine October 2, 2015 Outline 1 2 3 4 5 6 7 8 Homework and announcements Reading: Chapter 12 Homework:

More information

BINARY CODED DECIMAL: B.C.D.

BINARY 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 information

Number of bits needed to address hosts 8

Number of bits needed to address hosts 8 Advanced Subnetting Example 1: Your ISP has assigned you a Class C network address of 198.47.212.0. You have 3 networks in your company with the largest containing 134 hosts. You need to figure out if

More information

Data Storage 3.1. Foundations of Computer Science Cengage Learning

Data 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 information

NUMBER SYSTEMS. William Stallings

NUMBER 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 information

Goals. 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

Goals. 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 information

Binary Numbers The Computer Number System

Binary Numbers The Computer Number System Binary Numbers The Computer Number System Number systems are simply ways to count things. Ours is the base-0 or radix-0 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 information

Decimal, Hexadecimal and Binary Numbers Writing an assembly language program

Decimal, Hexadecimal and Binary Numbers Writing an assembly language program Decimal, Hexadecimal and Binary Numbers Writing an assembly language program o Disassembly of MC9S12 op codes o Use flow charts to lay out structure of program o Use common flow structures if-then if-then-else

More information

Digital Logic Design. Introduction

Digital Logic Design. Introduction Digital Logic Design Introduction A digital computer stores data in terms of digits (numbers) and proceeds in discrete steps from one state to the next. The states of a digital computer typically involve

More information

The New IoT Standard: Any App for Any Device Using Any Data Format. Mike Weiner Product Manager, Omega DevCloud KORE Telematics

The New IoT Standard: Any App for Any Device Using Any Data Format. Mike Weiner Product Manager, Omega DevCloud KORE Telematics The New IoT Standard: Any App for Any Device Using Any Data Format Mike Weiner Product Manager, Omega DevCloud KORE Telematics About KORE The world s largest M2M/IoT services provider 12 Carriers Enterprise

More information

Data Storage. Chapter 3. Objectives. 3-1 Data Types. Data Inside the Computer. After studying this chapter, students should be able to:

Data Storage. Chapter 3. Objectives. 3-1 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 information

Japanese Character Printers EPL2 Programming Manual Addendum

Japanese Character Printers EPL2 Programming Manual Addendum Japanese Character Printers EPL2 Programming Manual Addendum This addendum contains information unique to Zebra Technologies Japanese character bar code printers. The Japanese configuration printers support

More information

Binary math. Resources and methods for learning about these subjects (list a few here, in preparation for your research):

Binary 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 information

Decimal to Binary Conversion

Decimal 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 information

Binary, Hexadecimal, Octal, and BCD Numbers

Binary, 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 information

Technical Support Bulletin Nr.18 Modbus Tips

Technical Support Bulletin Nr.18 Modbus Tips Technical Support Bulletin Nr.18 Modbus Tips Contents! Definitions! Implemented commands! Examples of commands or frames! Calculating the logical area! Reading a signed variable! Example of commands supported

More information

The use of binary codes to represent characters

The use of binary codes to represent characters The use of binary codes to represent characters Teacher s Notes Lesson Plan x Length 60 mins Specification Link 2.1.4/hi Character Learning objective (a) Explain the use of binary codes to represent characters

More information

Computer Systems. Computer Systems COMP1208. Objectives of the Module. Course Assessment. Reading List. What will you need

Computer Systems. Computer Systems COMP1208. Objectives of the Module. Course Assessment. Reading List. What will you need Computer Systems Computer Systems Lecturer: Ruth Coffey Room KE-4-027, email: ruth.coffey@dit.ie Today s Lecture >> Module Overview Objectives of Module Course Assessment Reading List Introduction to Computer

More information