MATH 104B OCTAL, BINARY, AND HEXADECIMALS NUMBERS
|
|
- Nathan McDaniel
- 6 years ago
- Views:
Transcription
1 MATH 104B OCTAL, BINARY, AND HEXADECIMALS NUMBERS A: Review: Decimal or Base Ten 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 relative size of the 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. In Base 10, there are 10 different digits that can occupy a place. 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 The value of each place can be written as a power of 10. B: Octal or Base Eight Numbers In Octal there are only 8 different digits that can occupy a place. 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: 3, 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 is 8 3. Converting an Octal Number into a Decimal Number Suppose I have the number above: 3, (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.)
2 To convert the number 3, 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, 3, = 1, 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, 3, We saw that 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? Well, 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 Two Numbers Binary Numbers may look odd at first because they consist of zeros 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 is 2 4.
3 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, = 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. To convert 487 into Binary, we start by asking How many 1024s are there in 487? (Note: 1024 is the 11 th column.) 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
4 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, = D: Hexadecimal or Base Sixteen 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 just like Octal and Binary Numbers. In Octal there are only 8 different digits that can occupy a place. They are 0, 1, 2, 3, 4, 5, 6, and 7. In Binary there are only 2 different digits that can occupy a place. They are 0 and 1. In Hexadecimal there are 16 different digits that can occupy a place. 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 Base 10, you have 10. In Base 8, you have 12. In Base 2, you have In Base 16, you have A. Basically, in Base 16 we must be able to represent 10, 11, 12, 13, 14, or 15 items using just one digit. So we let A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. A couple of interesting Hexadecimal numbers are DEAD 16 and BEEF 16
5 Given the number: 3AD 16. 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 is Converting a Hexadecimal Number into a Decimal Number Suppose I have the number from above: 3AD 8 To convert the number 3AD 8 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, 3AD 168 = 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 Just like what we did for Octal and Binary Numbers, except in each base 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. 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, = 2EB 16.
6 Homework: 1. Convert the following Octal Numbers into Decimal Numbers: a b c d. 1, Convert the following Decimal Numbers into Octal Numbers: a. 29 b. 67 c. 130 d Convert the following Binary Numbers into Decimal Numbers: a b c d Convert the following Decimal Numbers into Binary Numbers: a. 7 b. 33 c. 140 d Convert the following Hexadecimal Numbers into Decimal Numbers: a. 1B 16 b. B2 16 c. ABC 16 d. 101F Convert the following Decimal Numbers into Hexadecimal Numbers: a. 17 b. 50 c. 239 d. 4108
The. Binary. Number System
The Binary Number System Why is Binary important? Everything on a computer (or other digital device) is represented by Binary Numbers One to Five in various systems 1 2 3 4 5 I II III IV V 1 10 11 100
More informationObjective 1.02 Understand Numbering Systems
Objective.0 Understand Numbering Systems C O M P U T E R P R O G R A M M I N G I Number Systems Number systems we will talk about: Decimal (Base 0 ) Binary (Base ) Hexadecimal (Base 6 ) Decimal The number
More informationCS & IT Conversions. Magnitude 10,000 1,
CS & IT Conversions There are several number systems that you will use when working with computers. These include decimal, binary, octal, and hexadecimal. Knowing how to convert between these number systems
More informationNumber Systems Using and Converting Between Decimal, Binary, Octal and Hexadecimal Number Systems
Number Systems Using and Converting Between Decimal, Binary, Octal and Hexadecimal Number Systems In everyday life, we humans most often count using decimal or base-10 numbers. In computer science, it
More informationBut I know what most of you will do: use a calculator to convert; that's fine, IF you understand the theory.
Numbers After you have read this, the next section will show how to use a This and other videos related to numbers and colors are available on the class web site. Why are there different numbering systems?
More informationChapter 3: Number Systems and Codes. Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc.
Chapter 3: Number Systems and Codes Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc., 5 th edition Decimal System The radix or base of a number system determines
More informationCHAPTER 2 Number Systems
CHAPTER 2 Number Systems Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish between non-positional and positional number systems.
More information2 Number Systems 2.1. Foundations of Computer Science Cengage Learning
2 Number Systems 2.1 Foundations of Computer Science Cengage Learning 2.2 Objectives After studying this chapter, the student should be able to: Understand the concept of number systems. Distinguish between
More informationComputer Systems and Networks. ECPE 170 Jeff Shafer University of the Pacific. Binary Numbers
ECPE 170 Jeff Shafer University of the Pacific Binary Numbers 2 Recap - von Neumann Model How does this run a stored program? 3 Objectives Chapter 2 in textbook Digital computers How do we represent numbers
More informationConversion Between Number Bases
Conversion Between Number Bases MATH 100 Survey of Mathematical Ideas J. Robert Buchanan Department of Mathematics Summer 2018 General Number Bases Bases other than 10 are sometimes used in numeration
More informationSubtraction Understand Subtraction on a Number Line Using a number line let s demonstrate the subtraction process using the problem 7 5.
Objective 1 Subtraction Understand Subtraction on a Number Line Using a number line let s demonstrate the subtraction process using the problem 7 5. -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 Using the number line
More informationNumber Systems MA1S1. Tristan McLoughlin. November 27, 2013
Number Systems MA1S1 Tristan McLoughlin November 27, 2013 http://en.wikipedia.org/wiki/binary numeral system http://accu.org/index.php/articles/1558 http://www.binaryconvert.com http://en.wikipedia.org/wiki/ascii
More informationComputer Systems and Networks. ECPE 170 Jeff Shafer University of the Pacific. Binary Numbers
ECPE 170 Jeff Shafer University of the Pacific Binary Numbers 2 Homework #1 Assigned today! h@p://ecs- network.serv.pacific.edu/ecpe- 170 Due Next Class Period (i.e. Wednesday) Class design: Smaller but
More informationIntroduction to Computer Science-103. Midterm
Introduction to Computer Science-103 Midterm 1. Convert the following hexadecimal and octal numbers to decimal without using a calculator, showing your work. (6%) a. (ABC.D) 16 2748.8125 b. (411) 8 265
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers & Number Systems
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers & Number Systems Introduction Numbers and Their Properties Multiples and Factors The Division Algorithm Prime and Composite Numbers Prime Factors
More informationMastering Binary Math
Cisco certification candidates, from the CCNA to the CCIE, must master binary math. This includes basic conversions, such as binary-to-decimal and decimal-to-binary, as well as more advanced scenarios
More informationMemory Addressing, Binary, and Hexadecimal Review
C++ By A EXAMPLE Memory Addressing, Binary, and Hexadecimal Review You do not have to understand the concepts in this appendix to become well-versed in C++. You can master C++, however, only if you spend
More informationNumber systems and binary
CS101 Fundamentals of Computer and Information Sciences LIU 1 of 8 Number systems and binary Here are some informal notes on number systems and binary numbers. See also sections 3.1 3.2 of the textbook.
More informationLogical Bases: Representation of Numbers Decimal number Positional notation Binary numbers
Logical Bases: Representation of Numbers Decimal numbers most commonly used by humans are in base 0 and consist of the ten decimal digits 0,,, 3, 4, 5, 6, 7, 8, 9. For example, the decimal number 373 is
More informationNumber Bases LESSON TWO. Computer Science. By John Owen
Number Bases LESSON TWO By John Owen Computer Science Objective In the last lesson you learned about different Number Bases used by the computer, which were Base Two binary Base Eight octal Base Sixteen
More informationBits and Bytes. Here is a sort of glossary of computer buzzwords you will encounter in computer use:
Bits and Bytes Here is a sort of glossary of computer buzzwords you will encounter in computer use: Bit Computer processors can only tell if a wire is on or off. Luckily, they can look at lots of wires
More informationBits. Binary Digits. 0 or 1
Data Representation Bits Binary Digits 0 or 1 Everything stored in a computer is stored as bits. Bits can mean different things depending on how the software or hardware interpret the bits Bits are usually
More informationNumbers!!...is that right? CSCI 255
Numbers!!...is that right? CSCI 255 BASE10 What do we know and use all the time? 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 zero through nine.decimals! Position matters too. 5874263 3 x 10 6 x 10 2 x 10 4 x 10 7 x 10
More informationDecimal/Binary Conversion on the Soroban
Decimal/Binary Conversion on the Soroban Conversion of a whole number from decimal to binary This method uses successive divisions by two, in place, utilizing a simple right-to-left algorithm. The division
More informationNumber Systems. The Computer Works in Binary, or how I learned to think like a computer. The computer s natural number system is binary not decimal.
PROGRAMMING CONCEPTS Number Systems The Computer Works in Binary, or how I learned to think like a computer Copyright 2013 Dan McElroy The computer s natural number system is binary not decimal. For example,
More informationLecture 1: Digital Systems and Number Systems
Lecture 1: Digital Systems and Number Systems Matthew Shuman September 26th, 2012 The Digital Abstraction 1.3 in Text Analog Systems Analog systems are continuous. Look at the analog clock in figure 1.
More informationNumeral Systems. -Numeral System -Positional systems -Decimal -Binary -Octal. Subjects:
Numeral Systems -Numeral System -Positional systems -Decimal -Binary -Octal Subjects: Introduction A numeral system (or system of numeration) is a writing system for expressing numbers, that is a mathematical
More informationIntroduction to Numbering Systems
NUMBER SYSTEM Introduction to Numbering Systems We are all familiar with the decimal number system (Base 10). Some other number systems that we will work with are Binary Base 2 Octal Base 8 Hexadecimal
More informationBSC & BIT Numbering Systems. ITU Lecture 3b
BSC & BIT -1 2017-18 Numbering Systems ITU 07102 Lecture 3b Introduction We use a number to present a quantity (value) of any thing that can be quantified. Quantities are measured, monitored, recorded,
More informationDigital Logic. The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer.
Digital Logic 1 Data Representations 1.1 The Binary System The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. The system we
More informationChapter 2: Number Systems
Chapter 2: Number Systems Logic circuits are used to generate and transmit 1s and 0s to compute and convey information. This two-valued number system is called binary. As presented earlier, there are many
More informationChapter 1 History & Hardware
Chapter 1 History & Hardware 1-1 Mechanical Machines History & Generations of Computing The first computers (some in the 17th century) were mechanical devices not electronic devices. While the technology
More informationNUMBER SENSE AND OPERATIONS. Competency 0001 Understand the structure of numeration systems and multiple representations of numbers.
SUBAREA I. NUMBER SENSE AND OPERATIONS Competency 0001 Understand the structure of numeration systems and multiple representations of numbers. Prime numbers are numbers that can only be factored into 1
More informationDLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR
UNIT I Digital Systems: Binary Numbers, Octal, Hexa Decimal and other base numbers, Number base conversions, complements, signed binary numbers, Floating point number representation, binary codes, error
More informationRadicals and Fractional Exponents
Radicals and Roots Radicals and Fractional Exponents In math, many problems will involve what is called the radical symbol, n X is pronounced the nth root of X, where n is 2 or greater, and X is a positive
More informationOverview. Suggestions for use
Overview Level Tables Questions Operations,2,, x 2,2,, x,2,,,, x,2,,,, x,2,,,,,, x,2,,,,,, x,2,,,,,,,, x,2,,,,,,,, x - x - x - x Extension levels - (multiples of & ) x - (multiples of & ) x - (decimals)
More informationDecimal/Hexadecimal Conversion
Decimal/Hexadecimal Conversion For these first two methods, you only need to know the multiples of fifteen from one through nine: 1-15 2-30 3-45 4-60 5-75 6-90 7-105 8-120 9-135 Conversion of Hexadecimal
More informationTHE LOGIC OF COMPOUND STATEMENTS
CHAPTER 2 THE LOGIC OF COMPOUND STATEMENTS Copyright Cengage Learning. All rights reserved. SECTION 2.5 Application: Number Systems and Circuits for Addition Copyright Cengage Learning. All rights reserved.
More informationChapter 1 Review of Number Systems
1.1 Introduction Chapter 1 Review of Number Systems Before the inception of digital computers, the only number system that was in common use is the decimal number system which has a total of 10 digits
More informationAppendix 2 Number Representations
Appendix 2 Number Representations There are many different ways to represent whole numbers. While we are comfortable counting in decimal (0,1,2,3,4,5,6,7,8,9,10,11,12, ), that is only one set of names
More informationComputer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2
Computer Architecture and System Software Lecture 02: Overview of Computer Systems & Start of Chapter 2 Instructor: Rob Bergen Applied Computer Science University of Winnipeg Announcements Website is up
More informationCSE 140 Homework One
CSE 140 Homewor One June 29, 2009 Only Problem Set Part B will be graded. Turn in only Problem Set Part B which will be due on July 13, 2009 (Monday) at 3:00pm. 1 Problem Set Part A textboo 1.3 textboo
More informationExcerpt from "Art of Problem Solving Volume 1: the Basics" 2014 AoPS Inc.
Chapter 5 Using the Integers In spite of their being a rather restricted class of numbers, the integers have a lot of interesting properties and uses. Math which involves the properties of integers is
More information1.3 Systems of numeration: To represent quantities in the different systems of numeration, specific symbols are used, which are also called ciphers.
Chapter One 1.1 Introduction: Numbers are used to express quantities. There are many numerations systems used in the field of digital electronics, one of the most important being the binary system of numeration
More informationME 461 C review Session Fall 2009 S. Keres
ME 461 C review Session Fall 2009 S. Keres DISCLAIMER: These notes are in no way intended to be a complete reference for the C programming material you will need for the class. They are intended to help
More informationNUMERIC SYSTEMS USED IN NETWORKING
NUMERIC SYSTEMS USED IN NETWORKING Decimal - Binary - Hexadecimal Table ASCII Code 128 64 32 16 8 4 2 1 The Letter A 0 1 0 0 0 0 0 1 Data Units Base 10 Numbering System Base 2 Numbering System Decimal
More informationChapter 2. Data Representation in Computer Systems
Chapter 2 Data Representation in Computer Systems Chapter 2 Objectives Understand the fundamentals of numerical data representation and manipulation in digital computers. Master the skill of converting
More informationDigital Systems and Binary Numbers
Digital Systems and Binary Numbers Mano & Ciletti Chapter 1 By Suleyman TOSUN Ankara University Outline Digital Systems Binary Numbers Number-Base Conversions Octal and Hexadecimal Numbers Complements
More informationBinary, Hexadecimal and Octal number system
Binary, Hexadecimal and Octal number system Binary, hexadecimal, and octal refer to different number systems. The one that we typically use is called decimal. These number systems refer to the number of
More informationExcerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997
Excerpt from: Stephen H. Unger, The Essence of Logic Circuits, Second Ed., Wiley, 1997 APPENDIX A.1 Number systems and codes Since ten-fingered humans are addicted to the decimal system, and since computers
More information0001 Understand the structure of numeration systems and multiple representations of numbers. Example: Factor 30 into prime factors.
NUMBER SENSE AND OPERATIONS 0001 Understand the structure of numeration systems and multiple representations of numbers. Prime numbers are numbers that can only be factored into 1 and the number itself.
More informationComputer Number Systems Supplement
Computer Number Systems Supplement Dr. Ken Hoganson, All Rights Reserved. SUPPLEMENT CONTENTS S.1 Decimal System: Powers-of-the-Base 2 S.2 Converting to Binary: Division/Remainder Algorithm. 3 S.3 Binary
More informationDigital Fundamentals
Digital Fundamentals Tenth Edition Floyd Chapter 2 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Decimal Numbers The position of each digit in a weighted
More informationIntroduction to Computer Science (I1100) With 1 coin 2 possibilities: Head / Tail or 0/1
With 1 coin 2 possibilities: Head / Tail or 0/1 77 What if I have 2 coins?! 0 0 With 2 coins, I can have 4 possibilities 0 1 1 0 1 1 With 3 coins, I can have 2*2*2=8 possibilities With 4 coins, I can have
More informationWorld Inside a Computer is Binary
C Programming 1 Representation of int data World Inside a Computer is Binary C Programming 2 Decimal Number System Basic symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Radix-10 positional number system. The radix
More informationAgenda EE 224: INTRODUCTION TO DIGITAL CIRCUITS & COMPUTER DESIGN. Lecture 1: Introduction. Go over the syllabus 3/31/2010
// EE : INTRODUCTION TO DIGITAL CIRCUITS & COMPUTER DESIGN Lecture : Introduction /9/ Avinash Kodi, kodi@ohio.edu Agenda Go over the syllabus Introduction ti to Digital it Systems // Why Digital Systems?
More informationLecture Notes: Floating-Point Numbers
Lecture Notes: Floating-Point Numbers CS227-Scientific Computing September 8, 2010 What this Lecture is About How computers represent numbers How this affects the accuracy of computation Positional Number
More informationOperations On Data CHAPTER 4. (Solutions to Odd-Numbered Problems) Review Questions
CHAPTER 4 Operations On Data (Solutions to Odd-Numbered Problems) Review Questions 1. Arithmetic operations interpret bit patterns as numbers. Logical operations interpret each bit as a logical values
More informationOutline. What Digit? => Number System. Decimal (base 10) Significant Digits. Lect 03 Number System, Gates, Boolean Algebra. CS221: Digital Design
Lect 3 Number System, Gates, Boolean Algebra CS22: Digital Design Dr. A. Sahu Dept of Comp. Sc. & Engg. Indian Institute of Technology Guwahati Outline Number System Decimal, Binary, Octal, Hex Conversions
More informationKorea University of Technology and Education
MEC52 디지털공학 Binary Systems Jee-Hwan Ryu School of Mechanical Engineering Binary Numbers a 5 a 4 a 3 a 2 a a.a - a -2 a -3 base or radix = a n r n a n- r n-...a 2 r 2 a ra a - r - a -2 r -2...a -m r -m
More informationECE 372 Microcontroller Design Assembly Programming Arrays. ECE 372 Microcontroller Design Assembly Programming Arrays
Assembly Programming Arrays Assembly Programming Arrays Array For Loop Example: unsigned short a[]; for(j=; j
More informationBeyond Base 10: Non-decimal Based Number Systems
Beyond Base : Non-decimal Based Number Systems What is the decimal based number system? How do other number systems work (binary, octal and hex) How to convert to and from nondecimal number systems to
More informationHOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE
MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number
More informationBINARY SYSTEM. Binary system is used in digital systems because it is:
CHAPTER 2 CHAPTER CONTENTS 2.1 Binary System 2.2 Binary Arithmetic Operation 2.3 Signed & Unsigned Numbers 2.4 Arithmetic Operations of Signed Numbers 2.5 Hexadecimal Number System 2.6 Octal Number System
More informationREPRESENTING INFORMATION:
REPRESENTING INFORMATION: BINARY, HEX, ASCII CORRESPONDING READING: WELL, NONE IN YOUR TEXT. SO LISTEN CAREFULLY IN LECTURE (BECAUSE IT WILL BE ON THE EXAM(S))! CMSC 150: Fall 2015 Controlling Information
More informationComputer Arithmetic. In this article we look at the way in which numbers are represented in binary form and manipulated in a computer.
Computer Arithmetic In this article we look at the way in which numbers are represented in binary form and manipulated in a computer. Numbers have a long history. In Europe up to about 400 numbers were
More informationInformation 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 informationPackaging and labelling
QRDvet template, opportunities for reduced label text and multi-lingual labels, recent examples EMA/IFAH-Europe Info Day 2014 Presented by: Jóhann M. Lenharðsson CVMP member (IS) An agency of the European
More informationFundamentals. Fundamentals. Fundamentals. We build up instructions from three types of materials
Fundamentals We build up instructions from three types of materials Constants Expressions Fundamentals Constants are just that, they are values that don t change as our macros are executing Fundamentals
More informationUnder the Hood: Data Representation. Computer Science 104 Lecture 2
Under the Hood: Data Representation Computer Science 104 Lecture 2 Admin Piazza, Sakai Up Everyone should have access Homework 1 Posted Due Feb 6 PDF or Plain Text Only: No Word or RTF Recommended: Learn
More informationDiscussion. Why do we use Base 10?
MEASURING DATA Data (the plural of datum) are anything in a form suitable for use with a computer. Whatever a computer receives as an input is data. Data are raw facts without any clear meaning. Computers
More informationNumber representations
Number representations Number bases Three number bases are of interest: Binary, Octal and Hexadecimal. We look briefly at conversions among them and between each of them and decimal. Binary Base-two, or
More informationCOUNTING AND CONVERTING
COUNTING AND CONVERTING The base of each number system is also called the radix. The radix of a decimal number is ten, and the radix of binary is two. The radix determines how many different symbols are
More informationUnit 7 Number System and Bases. 7.1 Number System. 7.2 Binary Numbers. 7.3 Adding and Subtracting Binary Numbers. 7.4 Multiplying Binary Numbers
Contents STRAND B: Number Theory Unit 7 Number System and Bases Student Text Contents Section 7. Number System 7.2 Binary Numbers 7.3 Adding and Subtracting Binary Numbers 7.4 Multiplying Binary Numbers
More informationDigital 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 information1010 2?= ?= CS 64 Lecture 2 Data Representation. Decimal Numbers: Base 10. Reading: FLD Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
CS 64 Lecture 2 Data Representation Reading: FLD 1.2-1.4 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 ) + (1x10 0 ) 1010 10?= 1010 2?= 1
More informationTOPICS. Other Number Systems. Other Number Systems 9/9/2017. Octal Hexadecimal Number conversion
Topic : Introduction To computers Faculty : Department of commerce and Management BY: Prof.Meeta R. Gujarathi E mail: meetargujarathi@gmail.com Octal Hexadecimal Number conversion TOPICS Other Number Systems
More informationDigital Systems. John SUM Institute of Technology Management National Chung Hsing University Taichung, ROC. December 6, 2012
Digital Systems John SUM Institute of Technology Management National Chung Hsing University Taichung, ROC December 6, 2012 Contents 1 Logic Gates 3 1.1 Logic Gate............................. 3 1.2 Truth
More informationReview of Data Representation & Binary Operations Dhananjai M. Rao CSA Department Miami University
Review of Data Representation & Binary Operations Dhananjai M. Rao () CSA Department Miami University 1. Introduction In digital computers all data including numbers, characters, and strings are ultimately
More informationDIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM
COURSE / CODE DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) NUMBER SYSTEM A considerable subset of digital systems deals with arithmetic operations. To understand the
More informationAudio Text for the Lesson: Counting Systems
Audio Text for the Lesson: Counting Systems Part 1: Introduction (2 minutes) Peace, mercy and blessings of Allah Welcome everyone in this lesson Allow me to introduce myself, my name is Abdullah Saleh
More informationCPSC 217 L01 Midterm
CPSC 217 L01 Midterm Duration: 50 minutes 4 March 2010 This exam has 55 questions and 10 pages. This exam is closed book. No notes, books, calculators or electronic devices, or other assistance may be
More informationSterler Subnetting System
Sterler Subnetting System The following paper is presented as a logic system to explain the mechanics of IP addressing, subnet masking and CIDR notation. I call it the Sterler Subnetting System. I have
More informationOctal & Hexadecimal Number Systems. Digital Electronics
Octal & Hexadecimal Number Systems Digital Electronics What, More Number Systems? Why do we need more number systems? Humans understand decimal Check out my ten digits! Digital electronics (computers)
More informationNumber Theory Algorithms
Number Theory Algorithms Zeph Grunschlag Copyright Zeph Grunschlag, 2 22. Agenda Euclidean Algorithm for GCD Number Systems Decimal numbers (base ) Binary numbers (base 2) One s complement Two s complement
More informationDATA REPRESENTATION. By- Neha Tyagi PGT CS KV 5 Jaipur II Shift, Jaipur Region. Based on CBSE curriculum Class 11. Neha Tyagi, KV 5 Jaipur II Shift
DATA REPRESENTATION Based on CBSE curriculum Class 11 By- Neha Tyagi PGT CS KV 5 Jaipur II Shift, Jaipur Region Neha Tyagi, KV 5 Jaipur II Shift Introduction As we know that computer system stores any
More informationNumber Systems. TA: Mamun. References: Lecture notes of Introduction to Information Technologies (ITEC 1011) by Dr Scott MacKenzie
Number Systems TA: Mamun References: Lecture notes of Introduction to Information Technologies (ITEC 1011) by Dr Scott MacKenzie Common Number Systems System Base Symbols Decimal 10 0, 1, 9 Binary 2 0,
More informationMoodle WILLINGDON COLLEGE SANGLI. ELECTRONICS (B. Sc.-I) Introduction to Number System
Moodle 1 WILLINGDON COLLEGE SANGLI ELECTRONICS (B. Sc.-I) Introduction to Number System E L E C T R O N I C S Introduction to Number System and Codes Moodle developed By Dr. S. R. Kumbhar Department of
More information1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM
1. NUMBER SYSTEMS USED IN COMPUTING: THE BINARY NUMBER SYSTEM 1.1 Introduction Given that digital logic and memory devices are based on two electrical states (on and off), it is natural to use a number
More informationObjectives. Connecting with Computer Science 2
Objectives Learn why numbering systems are important to understand Refresh your knowledge of powers of numbers Learn how numbering systems are used to count Understand the significance of positional value
More informationUNIT1: COMPUTERNUMBER SYSTEM
UNIT1: COMPUTERNUMBER SYSTEM Binary,Decimal, Octal and Hexadecimal Number-Base Conversions Addition, Subtraction and Multiplication of Computer Number System Compliment (1 s, 2's and r s complement) Signed
More informationIntro to C and Binary Numbers 8/27/2007
Intro to C and Binary Numbers 8/27/2007 1 Opening Discussion Let's look at three answers to the interclass question. What are the steps in building a C program? Do you have any questions about the class
More informationBeyond Base 10: Non-decimal Based Number Systems
Beyond Base : Non-decimal Based Number Systems What is the decimal based number system? How do other number systems work (binary, octal and hex) How to convert to and from nondecimal number systems to
More informationVoyager Mobile Entry Plus. (VME Plus) Installer Manual
Voyager - 50 Mobile Entry Plus (VME Plus) Installer Manual Device Telephone Number: 1 Installation Steps 1. If there is a SIM installed in the GSM device skip to step 3. 2. If there is no SIM installed
More informationDecimals Outcomes. Represent Q Using Decomposition
1 Decimals Outcomes Represent addition, subtraction, multiplication, and division in Q using number lines and decomposition. Perform addition, subtraction, multiplication, and division in Q. Convert between
More informationSlide Set 1. for ENEL 339 Fall 2014 Lecture Section 02. Steve Norman, PhD, PEng
Slide Set 1 for ENEL 339 Fall 2014 Lecture Section 02 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2014 ENEL 353 F14 Section
More informationCOMP Overview of Tutorial #2
COMP 1402 Winter 2008 Tutorial #2 Overview of Tutorial #2 Number representation basics Binary conversions Octal conversions Hexadecimal conversions Signed numbers (signed magnitude, one s and two s complement,
More informationEE 8351 Digital Logic Circuits Ms. J.Jayaudhaya, ASP/EEE
EE 8351 Digital Logic Circuits Ms. J.Jayaudhaya, ASP/EEE Numbering Systems Types Of Numbers Natural Numbers The number 0 and any number obtained by repeatedly adding a count of 1 to 0 Negative Numbers
More informationPython Numbers. Learning Outcomes 9/19/2012. CMSC 201 Fall 2012 Instructor: John Park Lecture Section 01 Discussion Sections 02-08, 16, 17
Python Numbers CMSC 201 Fall 2012 Instructor: John Park Lecture Section 01 Discussion Sections 02-08, 16, 17 1 (adapted from Meeden, Evans & Mayberry) 2 Learning Outcomes To become familiar with the basic
More informationDigital Logic Circuits Volume I Digital Number Systems
PDHonline Course E377 (5 PDH) Digital Logic Circuits Volume I Digital Number Systems Instructor: Lee Layton, P.E 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 22030-6658 Phone & Fax:
More information