OCTAL, BINARY, AND HEXADECIMAL NUMBERS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "OCTAL, BINARY, AND HEXADECIMAL NUMBERS"

Transcription

1 OCTAL, BINARY, AND HEXADECIMAL NUMBERS A: REVIEW - DECIMAL or BASE 10 NUMBERS When we see a number like 2,578 we know the 2 counts for more than the 7, even though 7 is a larger number than 2. The reason the 2 counts for more than the 7 is because in our number system, the Hindu-Arabic numeral system, place value is more important than the size of the individual digit. When we talk about decimal numbers, we are not just talking about numbers that have a decimal point, like For now, any base 10 number will be referred to as a decimal number, and vice versa. In base 10, there are 10 different digits that can occupy a column. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If there are more than 9 items, we must represent that value using 2 or more digits. Back to the number: 2,578. The 8 is in the ones column, and 1 can be written as The 7 is in the tens column, and 10 can be written as The 5 is in the hundreds column, and 100 can be written as The 2 is in the thousands column, and 1000 can be written as Notice that the value of each column can be written as a power of 10. B: OCTAL or BASE 8 NUMBERS In octal there are only 8 different digits that can occupy a single column. They are 0, 1, 2, 3, 4, 5, 6, and 7. In base 10 there is no single digit to represent the number 10. In base 8 there is no single digit to represent the number 8 or 9. If there are more than 7 items, we must represent that value using 2 or more digits. Given the number: 33, The 2 is in the ones column, and 1 can be written as 8 0. The 6 is in the eights column, and 8 can be written as 8 1. The 4 is in the eight times eight, or 64s column, and 64 can be written as 8 2. The 3 is in the eight times eight times eight, or 512s column, and 512 can be written as 8 3. Converting an Octal Number into a Decimal Number Suppose I have the number above: 33, (Notice that there is a subscript after the number indicating that this is a base 8 number. In most cases, if there is no subscript you can assume the given number is base 10. Sometime a subscript of 10 is used to avoid confusion.) To convert the number 33, we look at what each digit represents. The 3 is the number of 512s we have: 3 * 512 = 1,536 The 4 is the number of 64s we have: 4 * 64 = 256 The 6 is the number of 8s we have: 6 * 8 = 48 The 2 is the number of 1s we have: 2 * 1 = 2 Adding up the far right column, we get: 1,842 So, 33, = 11,

2 Converting a Decimal Number into an Octal Number Given the number 307, how can that decimal number be converted into an octal number? The process is relatively straightforward. Look at the 4 digits from the previous octal number: 33, Going from left to right, the four columns represent the number of 512s, 64s, 8s, and 1s present. To begin the conversion of 307, we start by asking How many 512s are there in 307? There aren t any, so we will write down the digit zero, just as a place-holder. -> 0xxx Next, we ask How many 64s are there in 307? There are 4. The 4 in the 64s column accounted for 256. Subtract 256 from 307, to get 51 remaining. Next, we ask How many 8s are there in 51? There are 6. The 6 in the 8s column accounted for 48. Subtract from 48 from 51, to get 3 remaining. -> 04xx -> 046x There are three 1s left, so our final answer is: -> 0463 So, = C: BINARY or BASE 2 NUMBERS Binary numbers may look odd at first because they consist of zeroes and ones, and nothing else. Some typical binary numbers are: or or 10 or Given the number Let s identify the value of each of the ones. Going from right to left (or least significant to most significant): There is a 1 in the 1s column, and 1 can be written as 2 0. There is a 1 in the 2s column, and 2 can be written as 2 1. There is a 1 in the two times two, or 4s column, and 4 can be written as 2 2. There is a 0 in the two times two times two, or 8s column, and 8 can be written as 2 3. There is a 1 in the two times two times two times two, or 16s column, and 16 can be written as 2 4. Converting a Binary Number into a Decimal Number Suppose I have the number from above: To convert the number we look at what each binary digit represents and add up the total. There is a 1 in the 16s column: 1 * 16 = 16 There is a 0 in the 8s column: 0 * 8 = 0 There is a 1 in the 4s column: 1 * 4 = 4 There is a 1 in the 2s column: 1 * 2 = 2 There is a 1 in the 1s column: 1 * 1 = 1 Adding up the far right column, we get: 23 So, =

3 Converting a Decimal Number into a Binary Number The process of converting a decimal number into a binary number uses the same steps we saw previously when going from decimal to octal, with different numbers. Let s begin by identifying what each column represents in a binary number. Going from right to left, or smallest to largest, the columns are the 1s, 2s, 4s, 8s, 16s, 32s, 64s, 128s, 256s, 512s, and 1024s. (These numbers are simply the powers of 2, starting at zero.) To convert 487 into binary, we start by asking How many 1024s are there in 487? (Note: 1024 is the 11 th column, and 2 10 equals 1024.) There aren t any, so write down a zero as a place-holder. Next, we ask How many 512s are there in 487? There are 0. How many 256s are there in 487? There is 1. -> 0xxxxxxxxxx -> 00xxxxxxxxx -> 001xxxxxxxx Subtract 256 from 487 to get 231 remaining. How many 128s are there in 231? There is 1. -> 0011xxxxxxx Subtract 128 from 231 to get 103 remaining. How many 64s are there in 103? There is 1. -> 00111xxxxxx Subtract 64 from 103 to get 39 remaining. How many 32s are there in 39? There is 1. -> xxxxx Subtract 32 from 39 to get 7 remaining. How many 16s are there in 7? None. How many 8s are there in 7? None. How many 4s are there in 7? There is 1. -> xxxx -> xxx -> xx Subtract 4 from 7 to get 3 remaining. How many 2s are there in 3? There is 1. -> x Subtract 2 from 3 to get 1 remaining. Finally, there is 1 one left. -> So, =

4 D: HEXADECIMAL or BASE 16 NUMBERS Saving the strangest for last, hexadecimal numbers look very weird at first. With a little bit of work you will see that they behave like octal and binary numbers. In decimal there are 10 different digits that can occupy a column. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In octal there are only 8 different digits that can occupy a column. They are 0, 1, 2, 3, 4, 5, 6, and 7. In binary there are only 2 different digits that can occupy a column. They are 0 and 1. In hexadecimal there are 16 different digits that can occupy a column. We start with the 10 digits most familiar to us: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. But we need 6 more digits, so we will use letters, namely A, B, C, D, E, and F. Hold up one hand and count your fingers. In base 10, you have 5. In base 8, you also have 5. In base 2, you have 101! And in our new base 16, you still have 5. Now count the fingers on both of your hands. In decimal you have 10 fingers. In octal you have 12 fingers. In binary you have 1010 fingers. In base 16, you have A fingers. Basically, in base 16 we must be able to represent 10, 11, 12, 13, 14, and 15 items using a single digit. So we let AA 16 = 10, BB 16 = 11, CC 16 = 12, DD 16 = 13, EE 16 = 14, and FF 16 = 15. A couple of interesting hexadecimal numbers are DDDDDDDD 16 and BBBBBBBB 16 Given the number: The D (or 13) is in the 1s column, and 1 can be written as The A (or 10) is in the 16s column, and 16 can be written as The 3 is in the sixteen times sixteen, or 256s column, and 256 can be written as Converting a Hexadecimal Number into a Decimal Number Suppose I have the number from above: To convert the number we look at what each digit represents. The 3 is the number of 256s we have: 3 * 256 = 768 The A is the number of 16s we have: 10 * 16 = 160 The D is the number of 1s we have: 13 * 1 = 13 Adding up the far right column, we get: 941 So, =

5 Converting a Decimal Number into a Hexadecimal Number Like before, we look at each column, see what value it represents, and then determine how many whole times the column value goes into the number we have left. Let s convert the decimal number 747 into a hexadecimal number. The process is similar to what we did for octal and binary numbers, except that the columns represent different values. In base 16, the first four column values are: 16 0 = 1, 16 1 = 16, 16 2 = 256, and 16 3 = How many 4096s are there in 747? None. How many 256s are there in 747? There are 2. Subtract 2 times 256 from 747, to get 235 remaining. How many 16s are there in 235? There are 14. To represent 14 in one digit we use the number E. The E in the 16s column accounted for 224 = 14*16. Subtract from 224 from 235, to get 11 remaining. -> 0xxx -> 02xx -> 02Ex To represent 11 in one digit we use the number B. -> 02EB So, = Homework: (Do this on a separate piece of paper.) 1. Convert the following Octal Numbers into Decimal Numbers: a b c d. 1,362 8 e. 3, Convert the following Decimal Numbers into Octal Numbers: a. 29 b. 67 c. 130 d. 609 e Convert the following Binary Numbers into Decimal Numbers: a b c d e Convert the following Decimal Numbers into Binary Numbers: a. 7 b. 33 c. 140 d. 299 e Convert the following Hexadecimal Numbers into Decimal Numbers: a. 1BB 16 b. B2 16 c. ABC 16 d. 101F 16 e. 3AED Convert the following Decimal Numbers into Hexadecimal Numbers: a. 17 b. 50 c. 239 d e. 10,958

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. CHAPTER01 QUESTIONS MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Convert binary 010101 to octal. 1) A) 258 B) 58 C) 218 D) 158 2) Any number

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 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

6 The Hindu-Arabic System (800 BC)

6 The Hindu-Arabic System (800 BC) 6 The Hindu-Arabic System (800 BC) Today the most universally used system of numeration is the Hindu-Arabic system, also known as the decimal system or base ten system. The system was named for the Indian

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

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

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

The Subnet Training Guide

The Subnet Training Guide The Subnet Training Guide A Step By Step Guide on Understanding and Solving Subnetting Problems by Brendan Choi v25 easysubnetcom The Subnet Training Guide v25 easysubnetcom Chapter 1 Understanding IP

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

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

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

MEP Y9 Practice Book A

MEP Y9 Practice Book A 1 Base Arithmetic 1.1 Binary Numbers We normally work with numbers in base 10. In this section we consider numbers in base 2, often called binary numbers. In base 10 we use the digits 0, 1, 2, 3, 4, 5,

More information

CHAPTER 3 Numbers and Numeral Systems

CHAPTER 3 Numbers and Numeral Systems CHAPTER 3 Numbers and Numeral Systems Numbers play an important role in almost all areas of mathematics, not least in calculus. Virtually all calculus books contain a thorough description of the natural,

More 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

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

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

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

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

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

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

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

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

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

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

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

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

CS321. Introduction to Numerical Methods

CS321. Introduction to Numerical Methods CS3 Introduction to Numerical Methods Lecture Number Representations and Errors Professor Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 40506-0633 August 7, 05 Number in

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

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

Chapter 7 Lab - Decimal, Binary, Octal, Hexadecimal Numbering Systems

Chapter 7 Lab - Decimal, Binary, Octal, Hexadecimal Numbering Systems Chapter 7 Lab - Decimal, Binary, Octal, Hexadecimal Numbering Systems This assignment is designed to familiarize you with different numbering systems, specifically: binary, octal, hexadecimal (and decimal)

More 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

Number Systems and Radix Conversion

Number Systems and Radix Conversion Number Systems and Radix Conversion Sanjay Rajopadhye, Colorado State University 1 Introduction These notes for CS 270 describe polynomial number systems. The material is not in the textbook, but will

More information

I Have...Who Has... Multiplication Game

I Have...Who Has... Multiplication Game How to play the game: Distribute the cards randomly to your students. Some students may get more than one card. Select a student to begin by reading their card aloud. (example: 35. who has 4x4?) 35 4 x

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

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

Subnetting Examples. There are three types of subnetting examples I will show in this document:

Subnetting Examples. There are three types of subnetting examples I will show in this document: Subnetting Examples There are three types of subnetting examples I will show in this document: 1) Subnetting when given a required number of networks 2) Subnetting when given a required number of clients

More 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

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

Primes. Name Period Number Theory

Primes. Name Period Number Theory Primes Name Period A Prime Number is a whole number whose only factors are 1 and itself. To find all of the prime numbers between 1 and 100, complete the following exercise: 1. Cross out 1 by Shading in

More information

NUMBER SYSTEMS APPENDIX D. You will learn about the following in this appendix:

NUMBER SYSTEMS APPENDIX D. You will learn about the following in this appendix: APPENDIX D NUMBER SYSTEMS You will learn about the following in this appendix: The four important number systems in computing binary, octal, decimal, and hexadecimal. A number system converter program

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

Section 1.5 Arithmetic in Other Bases

Section 1.5 Arithmetic in Other Bases Section Arithmetic in Other Bases Arithmetic in Other Bases The operations of addition, subtraction, multiplication and division are defined for counting numbers independent of the system of numeration

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

IP Subnetting Colin Weaver, ITdojo

IP Subnetting Colin Weaver, ITdojo IP Subnetting Colin Weaver, ITdojo Note: This document assumes that subnet zero is NOT used. For a description of subnet-zero, go here (http://www.cisco.com/warp/public/105/40.html). Subnetting IP networks

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

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

Grade 6 Math Circles. Binary and Beyond

Grade 6 Math Circles. Binary and Beyond Faculty of Mathematics Waterloo, Ontario N2L 3G1 The Decimal System Grade 6 Math Circles October 15/16, 2013 Binary and Beyond The cool reality is that we learn to count in only one of many possible number

More information

Decimals and other fractions

Decimals and other fractions Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very

More information

Concepts in IP Addressing...

Concepts in IP Addressing... 3 Concepts in IP Addressing Terms You ll Need to Understand: Binary Hexadecimal Decimal Octet IP address Subnet Mask Subnet Host Increment Techniques You ll Need to Master: Identifying Address Class and

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

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

COMPSCI 210. Binary Fractions. Agenda & Reading

COMPSCI 210. Binary Fractions. Agenda & Reading COMPSCI 21 Binary Fractions Agenda & Reading Topics: Fractions Binary Octal Hexadecimal Binary -> Octal, Hex Octal -> Binary, Hex Decimal -> Octal, Hex Hex -> Binary, Octal Animation: BinFrac.htm Example

More 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 Hexadecimal Number System and Memory Addressing

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

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

Smart Meters Programme Schedule 2.6. (Insurance) (CSP North version)

Smart Meters Programme Schedule 2.6. (Insurance) (CSP North version) Smart Meters Programme Schedule 2.6 (Insurance) (CSP North version) Schedule 2.6 (Insurance) (CSP North version) Amendment History Version Date Status v.1 Signature Date Execution Copy 1. INSURANCE COVENANTS

More information

January 20, 2009 GEORGE W. WRIGHT VICE PRESIDENT, INFORMATION TECHNOLOGY OPERATIONS

January 20, 2009 GEORGE W. WRIGHT VICE PRESIDENT, INFORMATION TECHNOLOGY OPERATIONS January 20, 2009 GEORGE W. WRIGHT VICE PRESIDENT, INFORMATION TECHNOLOGY OPERATIONS SUBJECT: Audit Report Service Continuity at the Information Technology and (Report Number ) This report presents the

More information

Calculating IP VLSM Subnet Addresses

Calculating IP VLSM Subnet Addresses Calculating IP VLSM Subnet Addresses A. P. Robson adrian.robson@nepsweb.co.uk 29 October 2011 Contents 1 Introduction 1 2 Method 2 2.1 Gather Data............................. 2 2.2 Calculate Subnet Sizes........................

More information

Decimal Number (base 10) Binary Number (base 2)

Decimal Number (base 10) Binary Number (base 2) LECTURE 5. BINARY COUNTER Before starting with counters there is some vital information that needs to be understood. The most important is the fact that since the outputs of a digital chip can only be

More information

Chapter 19 Network Layer: Logical Addressing 19.1

Chapter 19 Network Layer: Logical Addressing 19.1 Chapter 19 Network Layer: Logical Addressing 19.1 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 19-1 IPv4 ADDRESSES An IPv4 address is a 32-bit address that

More information

NETWORK ADMINISTRATION

NETWORK ADMINISTRATION NETWORK ADMINISTRATION INTRODUCTION The PressureMAP software provides users who have access to an Ethernet network supporting TCP/IP with the ability to remotely log into the MAP System via a network connection,

More information

HERNANDEZ & ASSOCIATES, P.C.

HERNANDEZ & ASSOCIATES, P.C. Christine M. Hernández, Esq. HERNANDEZ & ASSOCIATES, P.C. Attorney for Respondent 1724 Vine Street Denver, Colorado 80206 Telephone: (303 623-1122 Facsimile: (303 893-6116 UNITED STATES DEPARTMENT OF JUSTICE

More information

UNDERSTANDING SMS: Practitioner s Basics

UNDERSTANDING SMS: Practitioner s Basics UNDERSTANDING SMS: Practitioner s Basics Michael Harrington, CFCE, EnCE It is estimated that in 2006, 72% of all mobile phone users world wide were active users of SMS or text messaging. In European countries

More information

Chapter 5. Binary, octal and hexadecimal numbers

Chapter 5. Binary, octal and hexadecimal numbers Chapter 5. Binary, octal and hexadecimal numbers A place to look for some of this material is the Wikipedia page http://en.wikipedia.org/wiki/binary_numeral_system#counting_in_binary Another place that

More information

Introduction to Computer & Information Systems

Introduction to Computer & Information Systems Introduction to Computer & Information Systems Binnur Kurt kurt@ce.itu.edu.tr Istanbul Technical University Computer Engineering Department Copyleft 2005 1 Version 0.1 About the Lecturer BSc İTÜ, Computer

More information

NEXT. Tools of the Participant Portal: Scientific Reports & Deliverables

NEXT. Tools of the Participant Portal: Scientific Reports & Deliverables NEXT Tools of the Participant Portal: Scientific Reports & Deliverables Scientific Reporting and Deliverables: Terminology Scientific Reporting: Standardised format & always due at the end of Reporting

More information

Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

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

= 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

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

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

LABORATORY. Exploring Number Systems OBJECTIVES REFERENCES

LABORATORY. Exploring Number Systems OBJECTIVES REFERENCES Dmitriy Shironosov/ShutterStock, Inc. LABORATORY Exploring Number Systems 2 OBJECTIVES Experiment with number systems. Gain practice adding in binary and converting between bases. REFERENCES Software needed:

More information

NCTM Content Standard/National Science Education Standard

NCTM Content Standard/National Science Education Standard Title: BASE-ic Space Travel Brief Overview: This unit introduces the concepts of bases and exponents (or powers) in order to gain a deeper understanding of place value. Students will assume the role of

More information

Fractions to decimals

Fractions to decimals Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of

More 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

CHAPTER 2. Set, Whole Numbers, and Numeration

CHAPTER 2. Set, Whole Numbers, and Numeration CHAPTER 2 Set, Whole Numbers, and Numeration 2.1. Sets as a Basis for Whole Numbers A set is a collection of objects, called the elements or members of the set. Three common ways to define sets: (1) A

More information

Fractional Numbers. Fractional Number Notations. Fixed-point Notation. Fixed-point Notation

Fractional Numbers. Fractional Number Notations. Fixed-point Notation. Fixed-point Notation 2 Fractional Numbers Fractional Number Notations 2010 - Claudio Fornaro Ver. 1.4 Fractional numbers have the form: xxxxxxxxx.yyyyyyyyy where the x es constitute the integer part of the value and the y

More information

Key. Introduction. What is a Fraction. Better Math Numeracy Basics Fractions. On screen content. Narration voice-over

Key. Introduction. What is a Fraction. Better Math Numeracy Basics Fractions. On screen content. Narration voice-over Key On screen content Narration voice-over Activity Under the Activities heading of the online program Introduction This topic will cover how to: identify and distinguish between proper fractions, improper

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

Fractions and Decimals

Fractions and Decimals Fractions and Decimals Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles December 1, 2005 1 Introduction If you divide 1 by 81, you will find that 1/81 =.012345679012345679... The first

More information

1 3 7 5. 2 3 1 6. The pattern going to the right or the left from the decimal point is the same but there are two big differences:

1 3 7 5. 2 3 1 6. The pattern going to the right or the left from the decimal point is the same but there are two big differences: Review of Place Values in Decimal Numbers A decimal number includes a decimal point and digit(s) to the right of the decimal point. Saying a decimal number aloud is very similar to saying a whole number

More information

Scilab Textbook Companion for Digital Electronics: An Introduction To Theory And Practice by W. H. Gothmann 1

Scilab Textbook Companion for Digital Electronics: An Introduction To Theory And Practice by W. H. Gothmann 1 Scilab Textbook Companion for Digital Electronics: An Introduction To Theory And Practice by W. H. Gothmann 1 Created by Aritra Ray B.Tech Electronics Engineering NIT-DURGAPUR College Teacher Prof. Sabyasachi

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

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

Style Guide for the Applied Dissertation

Style Guide for the Applied Dissertation Style Guide for the Applied Dissertation August 2009 The Style Guide for the Applied Dissertation describes the required format and style for applied dissertations at the Fischler School of Education and

More information

A Step towards an Easy Interconversion of Various Number Systems

A Step towards an Easy Interconversion of Various Number Systems A towards an Easy Interconversion of Various Number Systems Shahid Latif, Rahat Ullah, Hamid Jan Department of Computer Science and Information Technology Sarhad University of Science and Information Technology

More information

TCP/IP Cheat Sheet. A Free Study Guide by Boson Software, LLC

TCP/IP Cheat Sheet. A Free Study Guide by Boson Software, LLC boson_logo_tcpip.pdf 9/23/2010 11:28:19 AM TCP/IP Cheat Sheet A Free Study Guide by Boson Software, LLC Table 1 Address Class Summary Class s Hosts per Range of Network IDs (First Octet) Class A 126 16,777,214

More information

Subnetting Study Guide

Subnetting Study Guide Subnetting Study Guide by Boson Software, LLC An octet is a binary number of 8 bits, with the lowest possible number being 00000000 and the highest possible number being 11111111, or 28. The binary number

More information

Roman Numerals. Symbol Decimal Value I One (1) V Five (5) X Ten (10) L Fifty (50) C Hundred (100) D Five Hundred (500) M Thousand (1000)

Roman Numerals. Symbol Decimal Value I One (1) V Five (5) X Ten (10) L Fifty (50) C Hundred (100) D Five Hundred (500) M Thousand (1000) Roman Numerals Pre-requisite: Number System, Addition and Subtraction. Target Audience: Standard V to Standard VII. In Syllabus Standard V. Revision Standard VI & VII. Symbol Decimal Value I One (1) V

More information

Binary Adders: Half Adders and Full Adders

Binary Adders: Half Adders and Full Adders Binary Adders: Half Adders and Full Adders In this set of slides, we present the two basic types of adders: 1. Half adders, and 2. Full adders. Each type of adder functions to add two binary bits. In order

More information

4.3 TABLE 3 TABLE 4. 1342 five 1 125 3 25 4 5 2 1 125 75 20 2 222.

4.3 TABLE 3 TABLE 4. 1342 five 1 125 3 25 4 5 2 1 125 75 20 2 222. .3 Conversion Between Number Bases 169.3 Conversion Between Number Bases Although the numeration systems discussed in the opening section were all base ten, other bases have occurred historically. For

More information

IT:101 Cisco Networking Academy I Subnetting

IT:101 Cisco Networking Academy I Subnetting IT:101 Cisco Networking Academy I Subnetting The IPv4 address is 32 bits long and it is written in the form of dotted decimal notation. IP address in binary format: 11000000.00000001.00000001.00000020

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

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

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

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

0018 DATA ANALYSIS, PROBABILITY and STATISTICS

0018 DATA ANALYSIS, PROBABILITY and STATISTICS 008 DATA ANALYSIS, PROBABILITY and STATISTICS A permutation tells us the number of ways we can combine a set where {a, b, c} is different from {c, b, a} and without repetition. r is the size of of the

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

Lecture 11: Number Systems

Lecture 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 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

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

pi: 3.14159265... in the examples below.

pi: 3.14159265... in the examples below. Rounding Numbers When you have to round a number, you are usually told how to round it. It's simplest when you're told how many "places" to round to, but you should also know how to round to a named "place",

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