# CS101 Lecture 11: Number Systems and Binary Numbers. Aaron Stevens 14 February 2011

Save this PDF as:

Size: px
Start display at page:

Download "CS101 Lecture 11: Number Systems and Binary Numbers. Aaron Stevens 14 February 2011"

## Transcription

1 CS101 Lecture 11: Number Systems and Binary Numbers Aaron Stevens 14 February

2 3!!! MATH WARNING!!! TODAY S LECTURE CONTAINS TRACE AMOUNTS OF ARITHMETIC AND ALGEBRA PLEASE BE ADVISED THAT CALCULTORS WILL BE ALLOWED ON THE QUIZ (and that you probably won t need them) 4 2

3 Overview/Questions What gives a number its value? What is a number system? I ve heard that computers use binary numbers. What s a binary number? What kind of numbers do computers store and manipulate? 5 Numbers Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645, 32 Negative Numbers A value less than 0, with a sign Examples: -24, -1, ,

4 Numbers Integers A natural number, a negative number, zero Examples: 249, 0, , -32 Rational Numbers An integer or the quotient of two integers Examples: -249, -1, 0, 3/7, -2/5 7 3 Numbering Systems A numbering system assigns meaning to the position of the numeric symbols. For example, consider this set of symbols: 642 What number is it? Why? 8 4 4

5 Numbering Systems It depends on the numbering system. 642 is in BASE 10 The base of a number determines the number of digits (e.g. symbols) and the value of digit positions 9 5 Positional Notation Continuing with our example 642 in base 10 positional notation is: 6 x 10 2 = 6 x 100 = x 10 1 = 4 x 10 = x 10º = 2 x 1 = 2 = 642 in base 10 This number is in base 10 The power indicates the position of the number

6 Positional Notation 642 = 6 3 * * * 10 0 As a general form: B is the base d n * B n-1 + d n-1 * B n d 1 * B 0 n is the number of digits in the number d is the digit in the i th position in the number 11 7 What Would Pooh Do? 12 6

7 Binary Numbers Digital computers are made up of electronic circuits, which have exactly 2 states: on and off. Computers use a numbering system which has exactly 2 symbols, representing on and off Binary Numbers Decimal is base 10 and has 10 digits: 0,1,2,3,4,5,6,7,8,9 Binary is base 2 and has 2, so we use only 2 symbols: 0,1 For a given base, valid numbers will only contain the digits in that base, which range from 0 up to (but not including) the base

8 Binary Numbers and Computers A binary digit or bit can take on only these two values. Low Voltage = 0 High Voltage = 1 all bits have 0 or 1 Binary numbers are built by concatenating a string of bits together. Example: Positional Notation: Binary Numbers Recall this general form: d n * B n-1 + d n-1 * B n d 1 * B 0 The same can be applied to base-2 numbers: 1011 bin = 1 * * * * bin = (1 * 8) + (0 * 4) + (1 * 2) + (1 * 1) 1011 bin = = 11 dec 16 8

9 Converting Binary to Decimal What is the decimal equivalent of the binary number ? (you try it! Work left-to-right) Converting Binary to Decimal What is the decimal equivalent of the binary number ? 0 x 2 7 = 0 x 128 = x 2 6 = 1 x 64 = x 2 5 = 1 x 32 = x 2 4 = 0 x 16 = x 2 3 = 1 x 8 = x 2 2 = 1 x 4 = x 2 1 = 1 x 2 = x 2º = 0 x 1 = 0 = 110 (decimal)

10 Converting Binary to Decimal Try another one. What is the decimal equivalent of the binary number ? (you try it! Work left-to-right) Converting Binary to Decimal Try another one. What is the decimal equivalent of the binary number ? 1 x 2 7 = 1 x 128 = x 2 6 = 0 x 64 = x 2 5 = 1 x 32 = x 2 4 = 0 x 16 = x 2 3 = 1 x 8 = x 2 2 = 0 x 4 = x 2 1 = 1 x 2 = x 2º = 1 x 1 = 1 = 171 (decimal)

11 Converting from Decimal to Other Bases Algorithm (process) for converting number in base 10 to other bases While (the quotient is not zero) Divide the decimal number by the new base* Make the remainder the next digit to the left in the answer Replace the original decimal number with the quotient * Using whole number (integer) division only. Example: 3 / 2 gives us a quotient of 1 and a remainder Converting Decimal to Binary What is the binary equivalent of the decimal number 103? 103 / 2 = 51, remainder 1 rightmost bit 51 / 2 = 25, remainder 1 25 / 2 = 12, remainder 1 12 / 2 = 6, remainder 0 6 / 2 = 3, remainder 0 3 / 2 = 1, remainder 1 1 / 2 = 0, remainder 1 leftmost bit 103 dec = bin 22 11

12 Converting Decimal to Binary Now you try one. What is the binary equivalent of the decimal number 201? Recall the algorithm: While (the quotient is not zero) Divide the decimal number by the new base* Make the remainder the next digit to the left in the answer Replace the original decimal number with the quotient 23 Converting Decimal to Binary What is the binary equivalent of the decimal number 201? 201 / 2 = 100, remainder 1 rightmost bit 100 / 2 = 50, remainder 0 50 / 2 = 25, remainder 0 25 / 2 = 12, remainder 1 12 / 2 = 6, remainder 0 6 / 2 = 3, remainder 0 3 / 2 = 1, remainder 1 1 / 2 = 0, remainder 1 leftmost bit 201 dec = bin 24 12

13 Binary and Computers Byte 8 bits a common unit of computer memory. Word A computer word is a group of bits which are passed around together during computation. The word length of the computer s processor is how many bits are grouped together. 8-bit machine (e.g. Nintendo Gameboy, 1989) 16-bit machine (e.g. Sega Genesis, 1989) 32-bit machines (e.g. Sony PlayStation, 1994) 64-bit machines (e.g. Nintendo 64, 1996) Just Call Me! Here s my phone number: What s wrong with this number? Hard to write on a napkin Vulnerable to transcription errors Won t make you popular at parties 26 13

14 Binary, Hexadecimal, Decimal Each four bits map to a hex digit. Hexadecimal prefix 0x???? No inherent value, just means treat as a hex number 0x94D3 27 Hexadecimal to Decimal Convert each hex digit into 4 bits. Convert binary to decimal. Example: 0x94D3 = = = = (decimal) 28 14

15 Conversions Between Number Systems Try some! My phone number: 0x16FF96419 (or: )

16 What You Learned Today Encoding: Symbols Represent Values Number Systems Binary Numbers, Bits, and Bytes Algorithms: converting binary to decimal and vice versa Encoding: Hexadecimal 31 Announcements and To Do List HW04 due Wednesday 2/16 Readings: Reed ch 5, pp 83-87, (today) Quiz 2 on Friday 2/18 Covers lectures 6,7,9,10,

### 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

### 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...

### 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

### 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

### Integer and Real Numbers Representation in Microprocessor Techniques

Brno University of Technology Integer and Real Numbers Representation in Microprocessor Techniques Microprocessor Techniques and Embedded Systems Lecture 1 Dr. Tomas Fryza 30-Sep-2011 Contents Numerical

### 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,

### 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

### 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

### MT1 Number Systems. In general, the number a 3 a 2 a 1 a 0 in a base b number system represents the following number:

MT1 Number Systems MT1.1 Introduction A number system is a well defined structured way of representing or expressing numbers as a combination of the elements of a finite set of mathematical symbols (i.e.,

### 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

### 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

### 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

### 1. True or False? A natural number is the number 0 or any number obtained by adding 1 to a natural number.

CS Illuminated, 5 th ed. Chapter 2 Review Quiz 1. True or False? A natural number is the number 0 or any number obtained by adding 1 to a natural number. 2. True or False? The category of numbers called

### 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

### 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:

### 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:

### CDA 3200 Digital Systems. Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012

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

### CS231: Computer Architecture I

CS231: Computer Architecture I Spring 2003 January 22, 2003 2000-2003 Howard Huang 1 What is computer architecture about? Computer architecture is the study of building entire computer systems. Processor

### 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

### Review of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement

Review of Number Systems Binary, Octal, and Hexadecimal Numbers and Two's Complement Topic 1: Binary, Octal, and Hexadecimal Numbers The number system we generally use in our everyday lives is a decimal

### 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

### CS101 Lecture 05: Logic Gates and Binary Addition

CS101 Lecture 05: Logic Gates and Binary Addition Logic Gates Binary Number Addition Some images copyright Jones and Bartlett Thanks to Charles Petzold for some diagrams and ideas Aaron Stevens (azs@bu.edu)

### 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

### 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

### 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

### Lecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor

Lecture 8 Binary Numbers & Logic Operations The focus of the last lecture was on the microprocessor During that lecture we learnt about the function of the central component of a computer, the microprocessor

### 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

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

Today Binary addition Representing negative numbers 2 Binary Addition Consider the following binary numbers: 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 1 How do we add these numbers? 3 Binary Addition 0 0 1 0 0 1 1

### 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

### Here 4 is the least significant digit (LSD) and 2 is the most significant digit (MSD).

Number System Introduction Number systems provide the basis for all operations in information processing systems. In a number system the information is divided into a group of symbols; for example, 26

### NUMBERING SYSTEMS C HAPTER 1.0 INTRODUCTION 1.1 A REVIEW OF THE DECIMAL SYSTEM 1.2 BINARY NUMBERING SYSTEM

12 Digital Principles Switching Theory C HAPTER 1 NUMBERING SYSTEMS 1.0 INTRODUCTION Inside today s computers, data is represented as 1 s and 0 s. These 1 s and 0 s might be stored magnetically on a disk,

### 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

### 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

### NUMBER REPRESENTATIONS IN THE COMPUTER for COSC 120

NUMBER REPRESENTATIONS IN THE COMPUTER for COSC 120 First, a reminder of how we represent base ten numbers. Base ten uses ten (decimal) digits: 0, 1, 2,3, 4, 5, 6, 7, 8, 9. In base ten, 10 means ten. Numbers

### 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

### 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

### 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

### 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

### Data Representation Binary Numbers

Data Representation Binary Numbers Integer Conversion Between Decimal and Binary Bases Task accomplished by Repeated division of decimal number by 2 (integer part of decimal number) Repeated multiplication

### 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

### Presented By: Ms. Poonam Anand

Presented By: Ms. Poonam Anand Know the different types of numbers Describe positional notation Convert numbers in other bases to base 10 Convert base 10 numbers into numbers of other bases Describe the

### 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

### 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

### 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

### 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

### 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

### Number Systems Richard E. Haskell

NUMBER SYSTEMS D Number Systems Richard E. Haskell Data inside a computer are represented by binary digits or bits. The logical values of these binary digits are denoted by and, while the corresponding

### 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

### The Mathematics Driving License for Computer Science- CS10410

The Mathematics Driving License for Computer Science- CS10410 Approximating Numbers, Number Systems and 2 s Complement by Nitin Naik Approximating Numbers There are two kinds of numbers: Exact Number and

### Chapter 2 Numeric Representation.

Chapter 2 Numeric Representation. Most of the things we encounter in the world around us are analog; they don t just take on one of two values. How then can they be represented digitally? The key is that

### 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

### 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

### Digital System Design Prof. D. Roychoudhury Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur

Digital System Design Prof. D. Roychoudhury Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture - 03 Digital Logic - I Today, we will start discussing on Digital

### The Power of Binary 0, 1, 10, 11, 100, 101, 110,

The Power of Binary 0, 1, 10, 11, 100, 101, 110, 111... What is Binary? a binary number is a number expressed in the binary numeral system, or base-2 numeral system, which represents numeric values using

### 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

### 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

### A Short Introduction to Binary Numbers

A Short Introduction to Binary Numbers Brian J. Shelburne Department of Mathematics and Computer Science Wittenberg University 0. Introduction The development of the computer was driven by the need to

### 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

### 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

### 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

### LECTURE 2: Number Systems

LECTURE : Number Systems CIS Fall 7 Instructor: Dr. Song Xing Department of Information Systems California State University, Los Angeles Learning Objectives Review Boolean algebra. Describe numbering systems

### 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

### 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

### Computer Architecture CPIT 210 LAB 1 Manual. Prepared By: Mohammed Ghazi Al Obeidallah.

Computer Architecture CPIT 210 LAB 1 Manual Prepared By: Mohammed Ghazi Al Obeidallah malabaidallah@kau.edu.sa LAB 1 Outline: 1. Students should understand basic concepts of Decimal system, Binary system,

### 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

### 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

### Signed Binary Arithmetic

Signed Binary Arithmetic In the real world of mathematics, computers must represent both positive and negative binary numbers. For example, even when dealing with positive arguments, mathematical operations

### CSE 1400 Applied Discrete Mathematics Naming and Number Systems

CSE 1400 Applied Discrete Mathematics Naming and Number Systems Department of Computer Sciences College of Engineering Florida Tech Spring 2012 Problems on Naming Systems Background Names are made from

### 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

### 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

### NUMBER SYSTEMS CHAPTER 19-1

NUMBER SYSTEMS 19.1 The Decimal System 19. The Binary System 19.3 Converting between Binary and Decimal Integers Fractions 19.4 Hexadecimal Notation 19.5 Key Terms and Problems CHAPTER 19-1 19- CHAPTER

### 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

### 1 Number systems 1.1 DECIMAL SYSTEM

A programmable logical controller uses the binary system rather than the decimal system to process memory cells, inputs, outputs, timers, flags etc.. DECIMAL SYSTEM In order to understand the binary number

### 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

### 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

### Chapter 3: Number Systems

Slide 1/40 Learning Objectives In this chapter you will learn about: Non-positional number system Positional number system Decimal number system Binary number system Octal number system Hexadecimal number

### 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

### 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

### Chapter 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

### 1 Number System (Lecture 1 and 2 supplement)

1 Number System (Lecture 1 and 2 supplement) By Dr. Taek Kwon Many different number systems perhaps from the prehistoric era have been developed and evolved. Among them, binary number system is one of

### EEM 232 Digital System I

EEM 232 Digital System I Instructor : Assist. Prof. Dr. Emin Germen egermen@anadolu.edu.tr Course Book : Logic and Computer Design Fundamentals by Mano & Kime Third Ed/Fourth Ed.. Pearson Grading 1 st

### Binary Which powers of 2 are we adding? Decimal answer 10101

1 CS 105 Lab #1 representation of numbers numbers are the dough we use to represent all information inside the computer. The purpose of this lab is to practice with some binary number representations.

### 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.

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

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

### 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)

### 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

### 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

### 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

### Integer Numbers. The Number Bases of Integers Textbook Chapter 3

Integer Numbers The Number Bases of Integers Textbook Chapter 3 Number Systems Unary, or marks: /////// = 7 /////// + ////// = ///////////// Grouping lead to Roman Numerals: VII + V = VVII = XII Better:

### 2. Number Systems - Positional Number Systems (1) - 2. Number Systems - Binary Numbers - 2. Number Systems - Positional Number Systems (2) -

Sistemas Digitais I LESI - 2º ano Lesson 2 - Number Systems Prof. João Miguel Fernandes (miguel@di.uminho.pt) Dept. Informática - Positional Number Systems (1) - We use daily a positional number system.

### 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

### 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,

### 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

### 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,

### 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

### Collin's Lab: Binary & Hex

Collin's Lab: Binary & Hex Created by Collin Cunningham Last updated on 2014-08-21 01:30:12 PM EDT Guide Contents Guide Contents Video Transcript Learn More Comparison Converters Mobile Web Desktop 2 3

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

REVIEW OF NUMBER SYSTEMS Notes Unit 2 BINARY NUMBER SYSTEM In the decimal system, a decimal digit can take values from to 9. For the binary system, the counterpart of the decimal digit is the binary digit,

### 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