# Activity 1: Bits and Bytes

Save this PDF as:

Size: px
Start display at page:

Download "Activity 1: Bits and Bytes"

## Transcription

1 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 switches. These transistors are either on or off. A circuit is either open or closed. Something that only has two states is called binary. The binary number system, which only has two digits (0 and 1), was adopted for use on computers. The computer must have a system of representing all the keys on the keyboard and everything on the screen using only 0 and 1. To represent numbers and letters, the ASCII code was developed where 8 bits were grouped together to represent a single number or letter. There are only two possible values for each digit: 0 and 1. It is a base 2 number system, because there are only 2 possible digits. Each 0 or 1 is called a bit (binary digit). A byte contains 8 bits. A kilobyte (KB) contains 2 10 bytes (1,024 approximately one thousand). A megabyte (MB) contains 2 20 bytes (1,048,576 approximately one million). A gigabyte (GB) contains 2 30 bytes (1,073,741,824 approximately one billion). A terabyte (TB) contains 2 40 bytes (approximately a thousand billion bytes). Decimal Number System This is our most familiar number system and it uses ten digits: 0 to 9. It is a base 10 numbers system, because there are 10 different digits.

2 Converting from Binary to Decimal Example 1 Convert binary to decimal. 1. Write down the binary number. 2. Write the powers of base 2 below the binary number. 3. Multiply each of the binary digits by the corresponding power. 4. Sum the products x x 64 0 x 32 1 x 16 0 x 8 1 x 4 0 x 2 1 x =149. Therefore, binary = 149 decimal. 1. Convert binary to decimal.

3 Converting from Decimal to Binary Example 2 Convert 151 decimal to binary. 1. Write down a list of the powers of base Look for the largest binary number that will go into the decimal number. 3. Subtract. 4. Place a one below the digit. 5. Repeat the steps 2 and 3 using the remainder. 2 7 = = = = = = = = Therefore, 151 decimal = binary. 1. Convert 200 decimal to binary.

4 American Standard for Information Interchange Code (ASCII) On both Windows and Unix systems, the 128 most commonly-used characters are each represented by a sequence of 7 bits known as the character's ASCII code. They are traditionally stored as bytes (8 bits), e.g., the 7-bit ASCII code plus a leading zero The characters include letters, digits, punctuation marks, and nonprintable control characters such as the backspace, tab, carriage return, etc. The following is sample of ASCII code: Letter Binary Decimal A B C Notice that there is a pattern to the way that ASCII codes have been assigned. There are unique codes for every digit, number, and special character. Example 3 Enter the word CAT into your word processor. The following string of binary digits will be stored in the computer memory If you enter the word cat instead of CAT the following string of binary digits will be stored This is because there are different ASCII codes for lowercase and uppercase letters. Unicode Unicode is another digital coding scheme. Java uses Unicode, in which all the characters are represented by 16 bits (2 bytes). This means that it can represent more than 65,000 unique characters. ASCII works well with English; however, it is not large enough to support Asian and other languages that use a different alphabet. Unicode has the ability to provide representation for every letter of an alphabet in all different languages (Latin, Japanese etc.).

5 ICS3U (Java): Introduction to Computer Science, Grade 11, University Preparation Hexadecimal Number System There are 16 digits in the hexadecimal system: A (10) B (11) C (12) D (13) E (14) and F (15). This is a base 16 number system, because there are 16 different digits. Hexadecimal is often shortened to just hex. Converting Hex to Binary Example 4 Converting hex to binary is very easy. 1. Write down the hex digits. 2. Under each digit, write the equivalent four digit binary number. 3. To find the four digit binary number, use the same method that we used to convert from decimal to binary, but consider A=10, B=11, C=12, D=13, E=14, F=15. 0 = = = = = = = = = = 1001 A = 10 = 1010 B = 11 = 1011 C = 12 = 1100 D = 13 = 1101 E = 14 = 1110 F = 15 = 1111 Convert F8 hex to binary. F So, F8 hex = binary. 1. Convert D5 hex to binary.

6 Converting Binary to Hex 1. Break the binary number up into groups of four digits. Add zeros to the left if necessary. 2. Assign a hex value to each group of four binary digits. 3. The method to assign the number is the same as converting from binary to decimal, but use A for 10, B for 11, C for 12, D for 13, E for 14, F for 15. Or use the chart above. Example 5 Convert binary to hex B 8 So, the answer is B8. 1. Convert binary to hex. Example 6 Convert FA8 hex to decimal. Converting Hex to Decimal 1. Write down the hex number. 2. Below the number, write down the powers of base Multiply the each hex digit by the value of the corresponding power. 4. Sum the products. F A x x 16 8 x 1 15 x x X 1 = = Therefore, FA8 hex = 4008 decimal. 1. Convert 432 hexadecimal to decimal.

7 Converting Decimal to Hex Example 7 1. Divide the decimal number by 16. Treat the division as an integer division. 2. Write down the remainder (in hexadecimal). 3. Divide the result again by 16. Treat the division as an integer division. 4. Repeat steps 2 and 3 until result is The hex value is the digit sequence of the remainders from the last to first. Convert 590 decimal to hexadecimal. 590/16 = 36 remainder = 14 (Note 14 decimal = E hex) 36/16 = 2 remainder 4 2/16 = 0 remainder 2 Answer: 590 decimal = 24E hex. When are Hex Numbers Used? One use of hex numbers is colour codes. Two hex digits can represent 8 bits or 1 byte. Eight bits are used to represent a decimal value of up to 255. Colours are represented by 3 values that range from 0 to 255. Therefore it takes 6 hex digits to represent a RGB colour. Example 8 Color Hex Value RGB Value Red FF , 0, 0

### 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

### 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

### Lecture.5. Number System:

Number System: Lecturer: Dr. Laith Abdullah Mohammed Lecture.5. The number system that we use in day-to-day life is called Decimal Number System. It makes use of 10 fundamental digits i.e. 0, 1, 2, 3,

More information

### Lab 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 information

### Lab 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 information

### 1 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 information

### 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

### Number systems Fall, 2007

Number Systems What does 1234 mean? Before taking one step into computing, you need to understand the simplest mathematical idea, number systems. You will need to be comfortable with both binary (base

More information

### The Hexadecimal Number System and Memory Addressing

APPENDIX C The Hexadecimal Number System and Memory Addressing U nderstanding the number system and the coding system that computers use to store data and communicate with each other is fundamental to

More information

### 1.3 Data Representation

8628-28 r4 vs.fm Page 9 Thursday, January 2, 2 2:4 PM.3 Data Representation 9 appears at Level 3, uses short mnemonics such as ADD, SUB, and MOV, which are easily translated to the ISA level. Assembly

More information

### ORG ; ZERO. Introduction To Computing

Dec 0 Hex 0 Bin 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 information

### Lesson 14..Binary, Hex, and Octal

Lesson 14..Binary, Hex, and Octal 14-1 We will examine four different number systems here, decimal, binary, hexadecimal (hex), and octal. In your study of these number systems it is very important to note

More information

### Part 1 Theory Fundamentals

Part 1 Theory Fundamentals 2 Chapter 1 Information Representation Learning objectives By the end of this chapter you should be able to: show understanding of the basis of different number systems show

More information

### Number 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

### 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

### 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

### CSC 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 information

### Data 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 information

### Encoding 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 information

### 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

### Data Representation Methods in the Computer system

3 Data Representation Methods in the Computer system In this unit you will learn, ² computer data representation, ² Decimal, Binary, Octal and Hexadecimal number systems, ² most and least significant positional

More information

### Data Representation. Why Study Data Representation?

Why Study Data Representation? Computers process and store information in binary format For many aspects of programming and networking, the details of data representation must be understood C Programming

More information

### 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

### Binary Numbers. X. Zhang Fordham Univ.

Binary Numbers X. Zhang Fordham Univ. 1 Numeral System! A way for expressing numbers, using symbols in a consistent manner.!! "11" can be interpreted differently:!! in the binary symbol: three!! in the

More information

### 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

### Computer Systems Architecture

Computer Systems Architecture http://cs.nott.ac.uk/ txa/g51csa/ Thorsten Altenkirch School of Computer Science and IT University of Nottingham Lecture 01: Bits, bytes and numbers Bits Bit = Binary Digit

More information

### 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

### Computer Number Systems

Computer Number Systems Thorne, Edition 2 : Section 1.3, Appendix I (Irvine, Edition VI : Section 1.3) SYSC3006 1 Starting from What We Already Know Decimal Numbers Based Number Systems : 1. Base defines

More information

### Number Representation

Number Representation Number System :: The Basics We are accustomed to using the so-called 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 information

### Data Representation. Topic 1. Contents. Prerequisite knowledge Before studying this topic you should be able to:

1 Topic 1 Data Representation Contents 1.1 Introduction...................................... 3 1.2 Numbers....................................... 3 1.2.1 The binary number system.........................

More information

### Chapter 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 information

### Number 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 information

### 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

### The largest has a 0 in the sign position and 0's in all other positions:

10.2 Sign Magnitude Representation Sign Magnitude is straight-forward method for representing both positive and negative integers. It uses the most significant digit of the digit string to indicate the

More information

### 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

### Bits, Bytes, and Codes

Bits, Bytes, and Codes Telecommunications 1 Peter Mathys Black and White Image Suppose we want to draw a B&W image on a computer screen. We first subdivide the screen into small rectangles or squares called

More information

### Number 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 information

### Binary 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 information

### Computing Studies. Data Representation. Computer Architecture. Buckhaven High School. Version 1. Software Design and Development

Computing Studies Software Design and Development Data Representation & Computer Architecture & Buckhaven High School Version 1 Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 7 Page 11 Page 12 Page 13

More information

### UNIT 2 : NUMBER SYSTEMS

UNIT 2 : NUMBER SYSTEMS page 2.0 Introduction 1 2.1 Decimal Numbers 2 2.2 The Binary System 3 2.3 The Hexadecimal System 5 2.4 Number Base Conversion 6 2.4.1 Decimal To Binary 6 2.4.2 Decimal to Hex 7

More information

### 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

### 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

### Chapter No.5 DATA REPRESENTATION

Chapter No.5 DATA REPRESENTATION Q.5.01 Complete the following statements. i) Data is a collection of ii) Data becomes information when properly. iii) Octal equivalent of binary number 1100010 is iv) 2

More information

### Year 9 CS Learning Cycle 4 Overview How is data represented in computer systems?

Year 9 CS Learning Cycle 4 Overview Learning Cycle Overview: Line of enquiry one: What is binary? Week 1 A kilobyte is 1000 bytes. I can count to more than 1000 on my fingers. There is only one way to

More information

### Logic 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 information

### CHAPTER 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 information

### A 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 information

### COMP2121: 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 information

### 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

### Chapter 2: Basics on computers and digital information coding. A.A. 2012-2013 Information Technology and Arts Organizations

Chapter 2: Basics on computers and digital information coding Information Technology and Arts Organizations 1 Syllabus (1/3) 1. Introduction on Information Technologies (IT) and Cultural Heritage (CH)

More information

### 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

### Number 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 information

### Information Science 1

Information Science 1 - Representa*on of Data in Memory- Week 03 College of Information Science and Engineering Ritsumeikan University Topics covered l Basic terms and concepts of The Structure of a Computer

More information

Review 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 information

### A First Book of C++ Chapter 2 Data Types, Declarations, and Displays

A First Book of C++ Chapter 2 Data Types, Declarations, and Displays Objectives In this chapter, you will learn about: Data Types Arithmetic Operators Variables and Declarations Common Programming Errors

More information

### Cyber Security Workshop Encryption Reference Manual

Cyber Security Workshop Encryption Reference Manual May 2015 Basic Concepts in Encoding and Encryption Binary Encoding Examples Encryption Cipher Examples 1 P a g e Encoding Concepts Binary Encoding Basics

More information

### 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

### EE 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 information

### Bits, Data Types, and Operations. University of Texas at Austin CS310H - Computer Organization Spring 2010 Don Fussell

Bits, Data Types, and Operations University of Texas at Austin CS3H - Computer Organization Spring 2 Don Fussell How do we represent data in a computer? At the lowest level, a computer is an electronic

More information

### Understanding 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 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 Lecture - 04 Digital Logic II May, I before starting the today s lecture

More information

### Definitions in Informatics Susen Rabold

Definitions in Informatics 2009-10-01 Susen Rabold Question after question AND (hopefully) answers Informatics Literacy Bit? Html? Xml? CSS? Bytes? Computers encode information What is information? Wikipedia:

More information

### Computer Science Terminology II

Computer Science 1000 Terminology II Storage a computer has two primary tasks store data operate on data a processor's primary job is to operate on data math operations move operations note that processors

More information

### 6 3 4 9 = 6 10 + 3 10 + 4 10 + 9 10

Lesson The Binary Number System. Why Binary? The number system that you are familiar with, that you use every day, is the decimal number system, also commonly referred to as the base- system. When you

More information

### الدكتور 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 information

### Digital 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 information

### 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

### IMPORTANT TERMS PROBLEMS PROBLEMS 47 SECTIONS 2-1 AND 2-2

PROBLEMS 47 IMPORTANT TERMS hexadecimal number system straight binary coding binary-coded-decimal (BCD) code PROBLEMS SECTIONS 2-1 AND 2-2 Gray code byte nibble word word size alphanumeric code American

More information

### Assembly Language for Intel-Based Computers, 4 th Edition. Chapter 1: Basic Concepts

Assembly Language for Intel-Based 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 information

### 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

### Number 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 information

### Number 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 information

### EE 308 Spring Binary, Hex and Decimal Numbers (4-bit 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 information

### Bits, bytes, and representation of information

Bits, bytes, and representation of information digital representation means that everything is represented by numbers only the usual sequence: something (sound, pictures, text, instructions,...) is converted

More information

### Chapter 02 discovering computers The components of system unit. Dr. Zeinab El Gazayerly

Chapter 02 discovering computers The components of system unit Dr. Zeinab El Gazayerly Differentiate among various styles of system units on desktop computers, notebook computers, and mobile devices Identify

More information

### Chapter 4. Binary Data Representation and Binary Arithmetic

Christian Jacob Chapter 4 Binary Data Representation and Binary Arithmetic 4.1 Binary Data Representation 4.2 Important Number Systems for Computers 4.2.1 Number System Basics 4.2.2 Useful Number Systems

More information

### After studying this lesson, you will gain a clear understanding on, Binary, Octal, Decimal and hexadecimal number systems

After studying this lesson, you will gain a clear understanding on, various number systems Binary, Octal, Decimal and hexadecimal number systems conversions among number systems units used in measuring

More information

### Assembly Language for Intel-Based Computers, 4 th Edition. Chapter 1: Basic Concepts. Chapter Overview. Welcome to Assembly Language

Assembly Language for Intel-Based Computers, 4 th Edition Kip R. Irvine Chapter 1: Basic Concepts Slides prepared by Kip R. Irvine Revision date: 10/27/2002 Chapter corrections (Web) Printing a slide show

More information

### Radix 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 information

### Digital 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 information

### Chapter 6. Inside the System Unit. What You Will Learn... Computers Are Your Future. What You Will Learn... Describing Hardware Performance

What You Will Learn... Computers Are Your Future Chapter 6 Understand how computers represent data Understand the measurements used to describe data transfer rates and data storage capacity List the components

More information

### 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

### 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

### Bits, Bytes, and Representation of Information

Bits, Bytes, and Representation of Information Digital representation means that everything is represented by numbers only The usual sequence: something (sound, pictures, text, instructions,...) is converted

More information

### By 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 information

### 23 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 information

### 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

### Computers Are Your Future Eleventh Edition

Computers Are Your Future Eleventh Edition Chapter 2: Inside the System Unit Copyright 2011 Pearson Education, Inc. Publishing as Prentice Hall 1 All rights reserved. No part of this publication may be

More information

### ASCII Code. Numerous codes were invented, including Émile Baudot's code (known as Baudot

ASCII Code Data coding Morse code was the first code used for long-distance communication. Samuel F.B. Morse invented it in 1844. This code is made up of dots and dashes (a sort of binary code). It was

More information

### 1. 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 information

### Unit 2: Number Systems, Codes and Logic Functions

Unit 2: Number Systems, Codes and Logic Functions Introduction A digital computer manipulates discrete elements of data and that these elements are represented in the binary forms. Operands used for calculations

More information

### 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

### EM108 Software Development for Engineers Section 5 Storing Information

EM108 5 Storing Information page 1 of 11 EM108 Software Development for Engineers Section 5 Storing Information 5.1 Motivation: Various information types o Various types of numbers o Text o Images, Audios,

More information

### 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

### Introduction ToNumber Systems

Introduction ToNumber Systems Collected by: Zainab Alkadhem Page 1 of 25 Digital systems have such a prominent role in everyday life that we refer to the present technological period as the digital age.

More information

### CHAPTER TWO. 2.1 Unsigned Binary Counting. Numbering Systems

CHAPTER TWO Numbering Systems Chapter one discussed how computers remember numbers using transistors, tiny devices that act like switches with only two positions, on or off. A single transistor, therefore,

More information

### Common 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 information

### Computer is a binary digital system. Data. Unsigned Integers (cont.) Unsigned Integers. Binary (base two) system: Has two states: 0 and 1

Computer Programming Programming Language Is telling the computer how to do something Wikipedia Definition: Applies specific programming languages to solve specific computational problems with solutions

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 information

### Everything you wanted to know about using Hexadecimal and Octal Numbers in Visual Basic 6

Everything you wanted to know about using Hexadecimal and Octal Numbers in Visual Basic 6 Number Systems No course on programming would be complete without a discussion of the Hexadecimal (Hex) number

More information