Number Systems and Binary Arithmetic Quantitative Analysis II Professor Bob Orr.

Slides:



Advertisements
Similar presentations
DATA REPRESENTATION CONVERSION.
Advertisements

Company LOGO Edit your slogan here DKT 122/3 DIGITAL SYSTEM 1 WEEK #3 NUMBER SYSTEMS, OPERATION & CODES (PART 2)
Number Systems. 2 The total number of allowable symbols in a number system is called the radix or base of the system. Decimal Numbers: radix = 10 (symbols:
Chapter Chapter Goals Know the different types of numbers Describe positional notation.
Chapter 02 Binary Values and Number Systems Nell Dale & John Lewis.
1 Number Systems. 2 Numbers Each number system is associated with a base or radix – The decimal number system is said to be of base or radix 10 A number.
Converting Binary to Octal
Number Systems and Arithmetic
© Copyright 2000 Indiana University Board of Trustees Proficiency Quiz Study Guide Note: The following slides are provided courtesy of Dr. Bob Orr (Computer.
BASICS OF COMPUTER APPLICATIONS ASB 102. UNIT 1 Introducing computer system  Number system  What is number system?  Types of number system  Their.
Chapter 1 1 Number Systems. 2 Objectives  Understand why computers use binary (Base-2) numbering.  Understand how to convert Base-2 numbers to Base-
Data Representation in Computers. Data Representation in Computers/Session 3 / 2 of 33 Number systems  The additive approach – Number earlier consisted.
Binary and Hexadecimal Numbers
Number Systems.
EKT 121 / 4 ELEKTRONIK DIGIT 1 CHAPTER 1 : INTRODUCTION.
Numbering Systems CS208.
Digital Electronics. Digital circuits work on the basis of a transistor being used as a switch. Consider a light switch, a transistor can be considered.
Supplemental Chapter Number Bases
1-1 Lecture 1 Class Overview and Appendix A -- Number Systems.
Chapter 2 Binary Values and Number Systems. 2 2 Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645,
Binary Values and Number Systems Chapter Goals Distinguish among categories of numbers Describe positional notation Convert numbers in other bases.
Number systems, Operations, and Codes
Positional Notation 642 in base 10 positional notation is:
Number Base Conversions
Digital Electronics Octal & Hexadecimal Number Systems.
Chapter 2 Number Systems: Decimal, Binary, and Hex.
CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC
Binary01.ppt Decimal Decimal: Base 10 means 10 Unique numerical digits ,00010,000 Weight Positions 3,
WEEK #2 NUMBER SYSTEMS, OPERATION & CODES (PART 1)
Discrete Mathematics Numbering System.
Octal & Hexadecimal Number Systems
School of Computer and Communication Engineering, UniMAP Mohd ridzuan mohd nor DKT 122/3 - DIGITAL SYSTEM I Chapter.
Introduction To Number Systems Binary System M. AL-Towaileb1.
School of Computer and Communication Engineering, UniMAP Mohd ridzuan mohd nor DKT 122/3 - DIGITAL SYSTEM I Chapter.
Number Systems – Definitions page 214 The radix or base 밑 refers to the number b in an expression of the form b n. The number n is called the exponent.
Number Systems. Topics  The Decimal Number System  The Binary Number System  Converting from Binary to Decimal  Converting from Decimal to Binary.
ECE 2110: Introduction to Digital Systems Number Systems: conversions.
The Hexadecimal System is base 16. It is a shorthand method for representing the 8-bit bytes that are stored in the computer system. This system was chosen.
Chapter 5 NUMBER REPRESENTATION AND ARITHMETIC CIRCUITS.
Conversions 1)Binary to Denary Method 1 Work out the position values of the binary bits and add those values together So above would be
ECE 2110: Introduction to Digital Systems Number Systems: conversions.
Digital logic COMP214  Lecture 2 Dr. Sarah M.Eljack Chapter 1 1.
Binary Values. Numbers Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645, 32 Negative Numbers.
Prepared By: Norakmar Binti Mohd Nadzari CHAPTER 2 ARITHMETIC AND LOGIC UNIT.
Number Systems & Binary Arithmetic
Some basic concepts underlying computer archi­tecture
Introduction To Number Systems
Digital Design Chapter One Digital Systems and Binary Numbers
Numbering Systems.
Chapter 02 Nell Dale & John Lewis.
Octal to Decimal Decimal Octal Binary Hexadecimal.
Discrete Mathematics Numbering System.
Number Systems and Binary Arithmetic
Digital Electronics INTRODUCTION ANALOG VS DIGITAL NUMBER SYSTEMS.
CHAPTER 1 : INTRODUCTION
Number Systems.
Convert Decimal to Binary
Writer:-Rashedul Hasan. Editor:- Jasim Uddin
Tools of Web Development 1: Module A: Numbering Systems
Number System conversions
Number Systems and Binary Arithmetic
Introduction to IT By: Muhammed s. anwar.
Digital Electronics and Microprocessors
Chapter 2: Number Systems
Chapter 2 Number Systems.
Number Systems Rayat Shikshan Sanstha’s
Number Systems Rayat Shikshan Sanstha’s
Introduction To Number Systems
Chapter 2 Number Systems.
Presentation transcript:

Number Systems and Binary Arithmetic Quantitative Analysis II Professor Bob Orr

© Copyright 2000 Indiana University Board of Trustees Binary Number System Also called the “Base 2 system” The binary number system is used to model the series of electrical signals computers use to represent information 0 represents the no voltage or an off state 1 represents the presence of voltage or an on state

© Copyright 2000 Indiana University Board of Trustees Decimal to Binary Conversion The easiest way to convert a decimal number to its binary equivalent is to use the Division Algorithm This method repeatedly divides a decimal number by 2 and records the quotient and remainder –The remainder digits (a sequence of zeros and ones) form the binary equivalent in least significant to most significant digit sequence

© Copyright 2000 Indiana University Board of Trustees Division Algorithm Convert 67 to its binary equivalent: = x 2 Step 1: 67 / 2 = 33 R 1 Divide 67 by 2. Record quotient in next row Step 2: 33 / 2 = 16 R 1 Again divide by 2; record quotient in next row Step 3: 16 / 2 = 8 R 0 Repeat again Step 4: 8 / 2 = 4 R 0 Repeat again Step 5: 4 / 2 = 2 R 0 Repeat again Step 6: 2 / 2 = 1 R 0 Repeat again Step 7: 1 / 2 = 0 R 1STOP when quotient equals

© Copyright 2000 Indiana University Board of Trustees Octal Number System Also known as the Base 8 System Uses digits Readily converts to binary Groups of three (binary) digits can be used to represent each octal digit Also uses multiplication and division algorithms for conversion to and from base 10

© Copyright 2000 Indiana University Board of Trustees Decimal to Octal Conversion Convert to its octal equivalent: 427 / 8 = 53 R3Divide by 8; R is LSD 53 / 8 = 6 R5Divide Q by 8; R is next digit 6 / 8 = 0 R6Repeat until Q =

© Copyright 2000 Indiana University Board of Trustees Hexadecimal Number System Base 16 system Uses digits 0-9 & letters A,B,C,D,E,F Groups of four bits represent each base 16 digit

© Copyright 2000 Indiana University Board of Trustees Decimal to Hexadecimal Conversion Convert to its hexadecimal equivalent: 830 / 16 = 51 R14 51 / 16 = 3 R3 3 / 16 = 0 R3 33E 16 = E in Hex