Chapter 3: Number Systems and Codes. Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc.

Size: px
Start display at page:

Download "Chapter 3: Number Systems and Codes. Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc."

Transcription

1 Chapter 3: Number Systems and Codes Textbook: Petruzella, Frank D., Programmable Logic Controllers. McGraw Hill Companies Inc., 5 th edition

2 Decimal System The radix or base of a number system determines the total number of different symbols or digits used by the system. The decimal system has a base of 10. In the decimal system, 10 unique numbers or digits ( 0 through 9) are used: the total number of symbols is the same as the base, and the symbol with the largest value is 1 less than the base.

3 Decimal System The decimal system can be summarized as follows: Ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Base: 10 Weights: 1, 10, 100, 1000, (powers of base 10)

4 Decimal System Weighted value in the decimal system

5 Binary System The binary system has a base of 2. The only allowable digits are 0 and 1 Digital Signal Waveform: with digital circuits it is easy to distinguish between two voltage levels - +5 V and O V, which can be related to the binary digits 1 and 0. Volts +5 0 Time High (H) (1) Low (L) (0)

6 Binary System The binary system can be summarized as follows: Two digits: 0, 1 Base: 2 Weights: 1, 2, 4, 8, 16, 32, (powers of base 2)

7 Binary System Decimal Binary Since the binary system uses only two digits, each position of a binary number can go through only two changes, and then a 1 is carried to the immediate left position. To express the number in the binary system requires many more digits than in the decimal system

8 Converting For Binary To Decimal

9 Converting For Binary To Decimal Another Method In the binary number when you see a 1, multiply that 1 times the value that is directly over it. Where you see a 0 in the box, just ignore it If we add only those numbers which have a binary 1 in the box under them, we come up with which equals 173.

10 Bits Bytes - Words Each digit of a binary number is known as a bit. A group of 8 bits is known as a byte. A group of bits that occupies 16-Bit Word one or more storage locations MSB and is treated as a unit is known Bit as a word. A 16-bit word is made up of two bytes (Upper and Lower). The least Upper significant Byte bit (LSB) is the digit that represents LSB the smallest value. The most significant bit (MSB) is the digit that represents the largest value.

11 PLC Processor Memory Size The size of the programmable controller relates to the amount of user program that can be stored. The 1 K word memory size shown can store 1,024 words, or 16,380 (1,024 x 16) bits of information using 16-bit words or 32,768 (1,024 x 32) using 32 bit words.

12 Converting For Decimal To Binary

13 Binary Representation Of Data Even though the binary system has only two digits, it can be used to represent any quantity that can be represented in the decimal system. Computer memory is then a series of binary 1s and 0s. SLC 500 Modular Chassis Output Status File A Each One word 16-bit will represents be output created file the in word on the table is or reserved off only state if for the of each processor one slot The Made column up of on single the right bits lists grouped the output into 16-bit module words address. finds output the an point. chassis. output These module points residing are numbered in a particular 0 through15. slot.

14 1. The binary number system has a base of 8. (True/False) 2. The decimal number 7 would be written in binary as (True/False) 3. To express a number in decimal requires fewer digits than in the binary system. (True/False) 4. For a base 2 number system, the weight value associated with the 3rd digit would be 4. (True/False)

15 5. What is the decimal value of binary ? a. 48 c. 13 b. 26 d The decimal number 15 would be written in binary as: a c. 4C b d Data can be stored in one 16-bit word as two separate groups of 8-bit data. (True/False)

16 8. A group of 8 bits is known as a byte. (True/False) 9. The MSB is the digit that represents the smallest value. (True/False) 10. Since the binary system has only two digits, it is limited as far as representing very large quantities. (True/False)

17 Negative Numbers In the binary system it is not possible to use positive and negative symbols to represent the polarity of a number. One method is of representing a binary number as either a positive or negative value is to use an extra digit, or sign bit, at the MSB of the number. In the sign bit position, a 0 indicates that the number is positive, and a 1 indicates a negative number. Sign Sign Bit Bit Magnitude Bits Bits Decimal Value

18 Negative Numbers Another method of expressing a negative number in a digital system is by using the complement of a binary number. To represent a negative number in 1's complement you simply take the numbers magnitude and flip all the bits (i.e. 1 becomes 0, and 0 becomes 1). +3 binary representation: binary representation: 1100 (1 s complement)

19 Negative Numbers The most common way to express a negative binary number is to show it as a 2 s complement number. The 2 s complement is the binary number that results when 1 is added to the 1 s complement. +3 binary representation: binary representation: 1100 (1 s complement) -3 binary representation: 1101 (2 s complement)

20 Octal System The octal numbering system can be summarized as follows: Eight digits: 0, 1, 2, 3, 4, 5, 6, 7 Base: 8 Weights: 1, 8, 64, 512, (powers of base 8) The octal number system is sometimes used because 8 data bits make up a byte of information that can be easily addressed by the PLC user or programmer.

21 Octal System The Allen-Bradley PLC-5 family of PLCs uses the octal numbering systems for addressing of I/O modules. I:2/16 O:3/22

22 Octal System The digits range from 0 to 7; therefore, numbers 8 and 9 are not allowed!

23 Converting Octal To Decimal As in all other numbering system, each digit in an octal number has a weighted decimal value according to its position.

24 Converting Octal-to-Binary Octal is used to handle large binary numbers. One octal digit is used to express three binary digits.

25 Hexadecimal System The hexadecimal (hex) numbering system can be summarized as follows: Sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Base: 16 Weights: 1, 16, 256, (powers of base 16) The hex numbering system is used in PLCs because a word of data often consists of 16 data bits, or two 8-bit bytes.

26 Hexadecimal-to-Decimal Conversion To convert a hexadecimal number to its decimal equivalent, the hexadecimal digits in the columns are multiplied by the base 16 weight.

27 Hexadecimal-to-Binary Conversion Using the hex numbering system allows the status of a large number of binary bits to be represented in a small space such as a PLC programming display.

28 BCD (Binary-Coded Decimal) System The BCD (Binary-Coded Decimal) numbering system provides a convenient way of handling large numbers that need to be inputted to or outputted from a PLC. There is no easy way to go from binary to decimal and back. The BCD system provides a means of converting a code readily handled by humans (decimal) to a code readily handled by equipment (binary).

29 Examples Of Numeric Values In: Decimal, Binary, BCD, and Hexadecimal, Representation

30 BCD Representation Of Decimal Number Conversion from Decimal to BCD is straightforward. You merely use 4 bits to represent each decimal digit.

31 BCD Thumb-Wheel Switch Interface The circuit board has one connection for each bit s weight plus a common A decimal number is selected The thumb-wheel switch outputs the equivalent 4-bits of BCD data

32 Typical PLC Number Conversion Instruction Convert To Decimal Instruction This instruction will convert the binary bit pattern at the source address N7:23, into a BCD bit pattern of the same decimal value as the destination address, O:20. The instruction executes every time it is scanned and the instruction is true.

33 Gray Code The Gray code is a special type of binary code that does not use position weighting. It is set up so that as we progress from one number to the next, only one bit changes. For this reason, the Gray code is considered to be an error-minimizing code. Because only one bit changes at a time, the speed of transition for the Gray code is considerably faster than that for codes such as BCD.

34 Gray Code Gray codes are used with with position encoders for accurate control of the motion of robots, machine tools, and servomechanisms. Typical Encoder Disk The encoder disk is attached to a rotating shaft and outputs a digital Gray code signal that is used to determine the position of the shaft.

35 ASCII Code ASCII stands for American Standard Code for Information Interchange. It is an alphanumeric code because it indicates letters as well as numbers. The keystrokes on the keyboard of a computer are converted directly into ASCII for processing by the computer.

36 Parity Bit Some PLC communications systems use a parity bit to check the accuracy of data transmission. For example, when data are transferred between PLCs, one of the binary bits may accidentally change states. Parity is a system where each character transmitted contains one additional bit known as a parity bit. The bit may be binary 0 or binary 1, depending on the number of 1 s and 0 s in the character itself. Two systems of parity are normally used: odd and even.

37 Odd parity means that the total number of binary 1 bits in the character, including the parity bit, is odd. Parity Bit Even parity means that the total number of binary 1 bits in the character, including the parity bit, is even.

38 Binary Addition When adding with binary numbers, there are only four conditions that can occur.

39 Binary Addition When adding larger binary numbers, the resulting 1 s are carried into higher-order columns.

40 Binary Subtraction To subtract from larger binary numbers, subtract column by column, borrowing from the adjacent column when necessary. Remember that when borrowing from the adjacent column, there are two digits, i. e., 0 borrow 1 gives 10.

41 Binary Subtraction To subtract using the 1 s complement: 1. Change the subtrahend to 1 s complement 2. Add the two numbers 3. Remove the last carry and add it to the number 1 s complement

42 Binary Multiplication When multiplying binary numbers, there are only four conditions that can occur. 0 x 0 = 0 0 x 1 = 0 1 x 0 = 0 1 x 1 = 1

43 Binary Multiplication To multiply numbers with more than one digit, form partial products and add them together. 101 x

44 Binary Division The process for dividing one binary number by another is the same for both binary and decimal numbers

45 Typical PLC Add, Subtract, Multiply, and Divide Instructions

46 PLC Data Comparison Instructions Are used to compare the relative magnitude of two quantities. At times devices may need to be controlled when they are less than, equal to or greater than other data values or set points used in the application, like timer and counter values. A = B (A equals B) A > B (A is greater than B) A < B (A is less than B)

47 11. In the binary system + and symbols are used to indicate whether a number is positive or negative. (True/False) 12. Numbers 8 and 9 are not used in the octal number system. (True/False) 13. The octal number 153 would be written in binary as: a c b d

48 14. The hexadecimal (hex) numbering system is a base system. (a) 2 (b) 8 (c) 10 (d) What is the decimal equivalent for the BCD number ? (a) 8421 (b) 7863 (c) 1234 (d) 3728

49 16. The Gray code is set up so that as we progress from one number to the next, only one bit changes. (True/False) 17. Which code is used to convert the keystrokes on the keyboard of a computer for the processor? (a) BCD (b) HEX (c) ASCII (d) OCTAL

50 18. A parity bit is used to check the of data transmission. (a) speed (b) type (c) accuracy (d) time 19. What is the sum of binary numbers 1100 and 1011? a c b d

51 20. Which instruction is used to compare the relative magnitude of two quantities? (a) Add (b) Subtract (c) Multiply (d) Less Than

BINARY SYSTEM. Binary system is used in digital systems because it is:

BINARY 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 information

Digital Fundamentals

Digital 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 information

Chapter 2 Number Systems and Codes Dr. Xu

Chapter 2 Number Systems and Codes Dr. Xu Chapter 2 Number Systems and Codes Dr. Xu Chapter 2 Objectives Selected areas covered in this chapter: Converting between number systems. Decimal, binary, hexadecimal. Advantages of the hexadecimal number

More information

CHW 261: Logic Design

CHW 261: Logic Design CHW 261: Logic Design Instructors: Prof. Hala Zayed Dr. Ahmed Shalaby http://www.bu.edu.eg/staff/halazayed14 http://bu.edu.eg/staff/ahmedshalaby14# Slide 1 Slide 2 Slide 3 Digital Fundamentals CHAPTER

More information

Lecture (02) Operations on numbering systems

Lecture (02) Operations on numbering systems Lecture (02) Operations on numbering systems By: Dr. Ahmed ElShafee ١ Dr. Ahmed ElShafee, ACU : Spring 2018, CSE202 Logic Design I Complements of a number Complements are used in digital computers to simplify

More information

Number representations

Number 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 information

Review of Number Systems

Review of Number Systems Review of Number Systems The study of number systems is important from the viewpoint of understanding how data are represented before they can be processed by any digital system including a digital computer.

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

Logic and Computer Design Fundamentals. Chapter 1 Digital Computers and Information

Logic and Computer Design Fundamentals. Chapter 1 Digital Computers and Information Logic and Computer Design Fundamentals Chapter 1 Digital Computers and Information Overview Digital Systems and Computer Systems Information Representation Number Systems [binary, octal and hexadecimal]

More information

CS 121 Digital Logic Design. Chapter 1. Teacher Assistant. Hadeel Al-Ateeq

CS 121 Digital Logic Design. Chapter 1. Teacher Assistant. Hadeel Al-Ateeq CS 121 Digital Logic Design Chapter 1 Teacher Assistant Hadeel Al-Ateeq Announcement DON T forgot to SIGN your schedule OR you will not be allowed to attend next lecture. Communication Office hours (8

More information

Moodle WILLINGDON COLLEGE SANGLI. ELECTRONICS (B. Sc.-I) Introduction to Number System

Moodle 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 information

Chapter 1. Digital Systems and Binary Numbers

Chapter 1. Digital Systems and Binary Numbers Chapter 1. Digital Systems and Binary Numbers Tong In Oh 1 1.1 Digital Systems Digital age Characteristic of digital system Generality and flexibility Represent and manipulate discrete elements of information

More information

The Gray Code. Script

The Gray Code. Script Course: B.Sc. Applied Physical Science (Computer Science) Year & Sem.: IInd Year, Sem - IIIrd Subject: Computer Science Paper No.: IX Paper Title: Computer System Architecture Lecture No.: 9 Lecture Title:

More information

Number Systems. Dr. Tarek A. Tutunji Philadelphia University, Jordan

Number Systems. Dr. Tarek A. Tutunji Philadelphia University, Jordan Number Systems Dr. Tarek A. Tutunji Philadelphia University, Jordan Number Systems Programmable controllers use binary numbers in one form or another to represent various codes and quantities. Every number

More information

D I G I T A L C I R C U I T S E E

D I G I T A L C I R C U I T S E E D I G I T A L C I R C U I T S E E Digital Circuits Basic Scope and Introduction This book covers theory solved examples and previous year gate question for following topics: Number system, Boolean algebra,

More information

Computer Organization

Computer Organization Computer Organization Register Transfer Logic Number System Department of Computer Science Missouri University of Science & Technology hurson@mst.edu 1 Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5,

More information

Digital Fundamentals

Digital Fundamentals Digital Fundamentals Tenth Edition Floyd Chapter 2 2009 Pearson Education, Upper 2008 Pearson Saddle River, Education NJ 07458. All Rights Reserved Quiz 2 Agenda Lecture: Chapter 2 (2-7 through 2-11):

More information

Data Representation and Binary Arithmetic. Lecture 2

Data Representation and Binary Arithmetic. Lecture 2 Data Representation and Binary Arithmetic Lecture 2 Computer Data Data is stored as binary; 0 s and 1 s Because two-state ( 0 & 1 ) logic elements can be manufactured easily Bit: binary digit (smallest

More information

Digital Fundamentals

Digital Fundamentals Digital Fundamentals Tenth Edition Floyd Chapter 1 Modified by Yuttapong Jiraraksopakun Floyd, Digital Fundamentals, 10 th 2008 Pearson Education ENE, KMUTT ed 2009 Analog Quantities Most natural quantities

More information

UNIT 7A Data Representation: Numbers and Text. Digital Data

UNIT 7A Data Representation: Numbers and Text. Digital Data UNIT 7A Data Representation: Numbers and Text 1 Digital Data 10010101011110101010110101001110 What does this binary sequence represent? It could be: an integer a floating point number text encoded with

More information

CHAPTER 2 (b) : AND CODES

CHAPTER 2 (b) : AND CODES DKT 122 / 3 DIGITAL SYSTEMS 1 CHAPTER 2 (b) : NUMBER SYSTEMS OPERATION AND CODES m.rizal@unimap.edu.my sitizarina@unimap.edu.my DECIMAL VALUE OF SIGNED NUMBERS SIGN-MAGNITUDE: Decimal values of +ve & -ve

More information

Digital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes

Digital Fundamentals. CHAPTER 2 Number Systems, Operations, and Codes Digital Fundamentals CHAPTER 2 Number Systems, Operations, and Codes Decimal Numbers The decimal number system has ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 The decimal numbering system has a base of

More information

Digital Systems and Binary Numbers

Digital Systems and Binary Numbers Digital Systems and Binary Numbers Prof. Wangrok Oh Dept. of Information Communications Eng. Chungnam National University Prof. Wangrok Oh(CNU) 1 / 51 Overview 1 Course Summary 2 Binary Numbers 3 Number-Base

More information

DIGITAL SYSTEM DESIGN

DIGITAL SYSTEM DESIGN DIGITAL SYSTEM DESIGN UNIT I: Introduction to Number Systems and Boolean Algebra Digital and Analog Basic Concepts, Some history of Digital Systems-Introduction to number systems, Binary numbers, Number

More information

Digital Systems and Binary Numbers

Digital 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 information

Lecture 2: Number Systems

Lecture 2: Number Systems Lecture 2: Number Systems Syed M. Mahmud, Ph.D ECE Department Wayne State University Original Source: Prof. Russell Tessier of University of Massachusetts Aby George of Wayne State University Contents

More information

Korea University of Technology and Education

Korea 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 information

Lecture (03) Binary Codes Registers and Logic Gates

Lecture (03) Binary Codes Registers and Logic Gates Lecture (03) Binary Codes Registers and Logic Gates By: Dr. Ahmed ElShafee Binary Codes Digital systems use signals that have two distinct values and circuit elements that have two stable states. binary

More information

DIGITAL SYSTEM FUNDAMENTALS (ECE 421) DIGITAL ELECTRONICS FUNDAMENTAL (ECE 422) COURSE / CODE NUMBER SYSTEM

DIGITAL 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 information

CHAPTER TWO. Data Representation ( M.MORRIS MANO COMPUTER SYSTEM ARCHITECTURE THIRD EDITION ) IN THIS CHAPTER

CHAPTER TWO. Data Representation ( M.MORRIS MANO COMPUTER SYSTEM ARCHITECTURE THIRD EDITION ) IN THIS CHAPTER 1 CHAPTER TWO Data Representation ( M.MORRIS MANO COMPUTER SYSTEM ARCHITECTURE THIRD EDITION ) IN THIS CHAPTER 2-1 Data Types 2-2 Complements 2-3 Fixed-Point Representation 2-4 Floating-Point Representation

More information

Binary Systems and Codes

Binary Systems and Codes 1010101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101010 1010101010101010101010101010101010101010101010101010101010101010101010101010101010

More information

Binary Codes. Dr. Mudathir A. Fagiri

Binary Codes. Dr. Mudathir A. Fagiri Binary Codes Dr. Mudathir A. Fagiri Binary System The following are some of the technical terms used in binary system: Bit: It is the smallest unit of information used in a computer system. It can either

More information

MACHINE LEVEL REPRESENTATION OF DATA

MACHINE LEVEL REPRESENTATION OF DATA MACHINE LEVEL REPRESENTATION OF DATA CHAPTER 2 1 Objectives Understand how integers and fractional numbers are represented in binary Explore the relationship between decimal number system and number systems

More information

Ms Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES. 1.1 Introduction

Ms Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES. 1.1 Introduction Ms Sandhya Rani Dash UNIT 2: NUMBER SYSTEM AND CODES Structure 2.1 Introduction 2.2 Objectives 2.3 Binary Numbers 2.3.1 Binary-to-Decimal conversion 2.3.2 Decimal-to-Binary Conversion 2.4 Octal Numbers

More information

Chap 1. Digital Computers and Information

Chap 1. Digital Computers and Information Chap 1. Digital Computers and Information Spring 004 Overview Digital Systems and Computer Systems Information Representation Number Systems [binary, octal and hexadecimal] Arithmetic Operations Base Conversion

More information

Chapter 3 DATA REPRESENTATION

Chapter 3 DATA REPRESENTATION Page1 Chapter 3 DATA REPRESENTATION Digital Number Systems In digital systems like computers, the quantities are represented by symbols called digits. Many number systems are in use in digital technology

More information

CHAPTER V NUMBER SYSTEMS AND ARITHMETIC

CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V-1 CHAPTER V CHAPTER V NUMBER SYSTEMS AND ARITHMETIC CHAPTER V-2 NUMBER SYSTEMS RADIX-R REPRESENTATION Decimal number expansion 73625 10 = ( 7 10 4 ) + ( 3 10 3 ) + ( 6 10 2 ) + ( 2 10 1 ) +(

More information

Digital Logic. The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer.

Digital Logic. The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. Digital Logic 1 Data Representations 1.1 The Binary System The Binary System is a way of writing numbers using only the digits 0 and 1. This is the method used by the (digital) computer. The system we

More information

Numbering systems. Dr Abu Arqoub

Numbering systems. Dr Abu Arqoub Numbering systems The decimal numbering system is widely used, because the people Accustomed (معتاد) to use the hand fingers in their counting. But with the development of the computer science another

More information

plc numbers Encoded values; BCD and ASCII Error detection; parity, gray code and checksums

plc numbers Encoded values; BCD and ASCII Error detection; parity, gray code and checksums plc numbers - 3. 3. NUMBERS AND DATA Topics: Number bases; binary, octal,, hexa Binary calculations; s compliments, addition, subtraction and Boolean operations Encoded values; BCD and ASCII Error detection;

More information

Digital Systems and Binary Numbers

Digital Systems and Binary Numbers Digital Systems and Binary Numbers ( 范倫達 ), Ph. D. Department of Computer Science National Chiao Tung University Taiwan, R.O.C. Spring, 2018 ldvan@cs.nctu.edu.tw http://www.cs.nctu.edu.tw/~ldvan/ Outline

More information

Logic Circuits I ECE 1411 Thursday 4:45pm-7:20pm. Nathan Pihlstrom.

Logic Circuits I ECE 1411 Thursday 4:45pm-7:20pm. Nathan Pihlstrom. Logic Circuits I ECE 1411 Thursday 4:45pm-7:20pm Nathan Pihlstrom www.uccs.edu/~npihlstr My Background B.S.E.E. from Colorado State University M.S.E.E. from Colorado State University M.B.A. from UCCS Ford

More information

CS & IT Conversions. Magnitude 10,000 1,

CS & 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 information

Slide 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 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 information

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010

Number Systems and Conversions UNIT 1 NUMBER SYSTEMS & CONVERSIONS. Number Systems (2/2) Number Systems (1/2) Iris Hui-Ru Jiang Spring 2010 Contents Number systems and conversion Binary arithmetic Representation of negative numbers Addition of two s complement numbers Addition of one s complement numbers Binary s Readings Unit.~. UNIT NUMBER

More information

Numeral Systems. -Numeral System -Positional systems -Decimal -Binary -Octal. Subjects:

Numeral 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 information

Fundamentals of Programming (C)

Fundamentals of Programming (C) Borrowed from lecturer notes by Omid Jafarinezhad Fundamentals of Programming (C) Group 8 Lecturer: Vahid Khodabakhshi Lecture Number Systems Department of Computer Engineering Outline Numeral Systems

More information

Number System. Introduction. Decimal Numbers

Number System. Introduction. Decimal Numbers 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

More information

World Inside a Computer is Binary

World 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 information

Introduction to Numbering Systems

Introduction 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 information

Number Systems Base r

Number Systems Base r King Fahd University of Petroleum & Minerals Computer Engineering Dept COE 2 Fundamentals of Computer Engineering Term 22 Dr. Ashraf S. Hasan Mahmoud Rm 22-44 Ext. 724 Email: ashraf@ccse.kfupm.edu.sa 3/7/23

More information

Positional Number System

Positional Number System Positional Number System A number is represented by a string of digits where each digit position has an associated weight. The weight is based on the radix of the number system. Some common radices: Decimal.

More information

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-2700: Digital Logic Design Winter Notes - Unit 4. hundreds.

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-2700: Digital Logic Design Winter Notes - Unit 4. hundreds. UNSIGNED INTEGER NUMBERS Notes - Unit 4 DECIMAL NUMBER SYSTEM A decimal digit can take values from to 9: Digit-by-digit representation of a positive integer number (powers of ): DIGIT 3 4 5 6 7 8 9 Number:

More information

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-278: Digital Logic Design Fall Notes - Unit 4. hundreds.

ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-278: Digital Logic Design Fall Notes - Unit 4. hundreds. ECE-78: Digital Logic Design Fall 6 UNSIGNED INTEGER NUMBERS Notes - Unit 4 DECIMAL NUMBER SYSTEM A decimal digit can take values from to 9: Digit-by-digit representation of a positive integer number (powers

More information

that system. weighted value associated with it. numbers. a number. the absence of a signal. MECH 1500 Quiz 2 Review Name: Class: Date:

that system. weighted value associated with it. numbers. a number. the absence of a signal. MECH 1500 Quiz 2 Review Name: Class: Date: Name: Class: Date: MECH 1500 Quiz 2 Review True/False Indicate whether the statement is true or false. 1. The decimal system uses the number 9 as its base. 2. All digital computing devices perform operations

More information

LOGIC DESIGN. Dr. Mahmoud Abo_elfetouh

LOGIC DESIGN. Dr. Mahmoud Abo_elfetouh LOGIC DESIGN Dr. Mahmoud Abo_elfetouh Course objectives This course provides you with a basic understanding of what digital devices are, how they operate, and how they can be designed to perform useful

More information

Slide Set 1. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary

Slide Set 1. for ENEL 353 Fall Steve Norman, PhD, PEng. Electrical & Computer Engineering Schulich School of Engineering University of Calgary Slide Set 1 for ENEL 353 Fall 2017 Steve Norman, PhD, PEng Electrical & Computer Engineering Schulich School of Engineering University of Calgary Fall Term, 2017 SN s ENEL 353 Fall 2017 Slide Set 1 slide

More information

umber Systems bit nibble byte word binary decimal

umber Systems bit nibble byte word binary decimal umber Systems 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. To perform useful operations on these

More information

Get Free notes at Module-I One s Complement: Complement all the bits.i.e. makes all 1s as 0s and all 0s as 1s Two s Complement: One s complement+1 SIGNED BINARY NUMBERS Positive integers (including zero)

More information

Digital Systems COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals

Digital Systems COE 202. Digital Logic Design. Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Digital Systems COE 202 Digital Logic Design Dr. Muhamed Mudawar King Fahd University of Petroleum and Minerals Welcome to COE 202 Course Webpage: http://faculty.kfupm.edu.sa/coe/mudawar/coe202/ Lecture

More information

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1

IT 1204 Section 2.0. Data Representation and Arithmetic. 2009, University of Colombo School of Computing 1 IT 1204 Section 2.0 Data Representation and Arithmetic 2009, University of Colombo School of Computing 1 What is Analog and Digital The interpretation of an analog signal would correspond to a signal whose

More information

NUMBER SYSTEMS AND CODES

NUMBER SYSTEMS AND CODES C H A P T E R 69 Learning Objectives Number Systems The Decimal Number System Binary Number System Binary to Decimal Conversion Binary Fractions Double-Dadd Method Decimal to Binary Conversion Shifting

More information

Number Systems Prof. Indranil Sen Gupta Dept. of Computer Science & Engg. Indian Institute of Technology Kharagpur Number Representation

Number Systems Prof. Indranil Sen Gupta Dept. of Computer Science & Engg. Indian Institute of Technology Kharagpur Number Representation Number Systems Prof. Indranil Sen Gupta Dept. of Computer Science & Engg. Indian Institute of Technology Kharagpur 1 Number Representation 2 1 Topics to be Discussed How are numeric data items actually

More information

2. MACHINE REPRESENTATION OF TYPICAL ARITHMETIC DATA FORMATS (NATURAL AND INTEGER NUMBERS).

2. MACHINE REPRESENTATION OF TYPICAL ARITHMETIC DATA FORMATS (NATURAL AND INTEGER NUMBERS). 2. MACHINE REPRESENTATION OF TYPICAL ARITHMETIC DATA FORMATS (NATURAL AND INTEGER NUMBERS). 2.. Natural Binary Code (NBC). The positional code with base 2 (B=2), introduced in Exercise, is used to encode

More information

Agenda EE 224: INTRODUCTION TO DIGITAL CIRCUITS & COMPUTER DESIGN. Lecture 1: Introduction. Go over the syllabus 3/31/2010

Agenda 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 information

Decimal & Binary Representation Systems. Decimal & Binary Representation Systems

Decimal & Binary Representation Systems. Decimal & Binary Representation Systems Decimal & Binary Representation Systems Decimal & binary are positional representation systems each position has a value: d*base i for example: 321 10 = 3*10 2 + 2*10 1 + 1*10 0 for example: 101000001

More information

Semester Transition Point. EE 109 Unit 11 Binary Arithmetic. Binary Arithmetic ARITHMETIC

Semester Transition Point. EE 109 Unit 11 Binary Arithmetic. Binary Arithmetic ARITHMETIC 1 2 Semester Transition Point EE 109 Unit 11 Binary Arithmetic At this point we are going to start to transition in our class to look more at the hardware organization and the low-level software that is

More information

Excerpt 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 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 information

Chapter 1 Review of Number Systems

Chapter 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 information

Octal & Hexadecimal Number Systems. Digital Electronics

Octal & 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 information

UNIT 2 NUMBER SYSTEM AND PROGRAMMING LANGUAGES

UNIT 2 NUMBER SYSTEM AND PROGRAMMING LANGUAGES UNIT 2 NUMBER SYSTEM AND PROGRAMMING LANGUAGES Structure 2.0 Introduction 2.1 Unit Objectives 2.2 Number Systems 2.3 Bits and Bytes 2.4 Binary Number System 2.5 Decimal Number System 2.6 Octal Number System

More information

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation

Course Schedule. CS 221 Computer Architecture. Week 3: Plan. I. Hexadecimals and Character Representations. Hexadecimal Representation Course Schedule CS 221 Computer Architecture Week 3: Information Representation (2) Fall 2001 W1 Sep 11- Sep 14 Introduction W2 Sep 18- Sep 21 Information Representation (1) (Chapter 3) W3 Sep 25- Sep

More information

Number codes nibble byte word double word

Number codes nibble byte word double word Codes Number codes Digital circuits (like processors) represent information with two-valued binary codes. Why? Every signal wire in a digital system can transport one binary digit, or bit. A signal at

More information

ECE 20B, Winter Purpose of Course. Introduction to Electrical Engineering, II. Administration

ECE 20B, Winter Purpose of Course. Introduction to Electrical Engineering, II. Administration ECE 20B, Winter 2003 Introduction to Electrical Engineering, II Instructor: Andrew B Kahng (lecture) Email: abk@eceucsdedu Telephone: 858-822-4884 office, 858-353-0550 cell Office: 3802 AP&M Lecture: TuThu

More information

COMP Overview of Tutorial #2

COMP 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 information

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

SE311: Design of Digital Systems

SE311: Design of Digital Systems SE311: Design of Digital Systems Lecture 3: Complements and Binary arithmetic Dr. Samir Al-Amer (Term 041) SE311_Lec3 (c) 2004 AL-AMER ١ Outlines Complements Signed Numbers Representations Arithmetic Binary

More information

CHAPTER 2 Data Representation in Computer Systems

CHAPTER 2 Data Representation in Computer Systems CHAPTER 2 Data Representation in Computer Systems 2.1 Introduction 37 2.2 Positional Numbering Systems 38 2.3 Decimal to Binary Conversions 38 2.3.1 Converting Unsigned Whole Numbers 39 2.3.2 Converting

More information

TOPICS. Other Number Systems. Other Number Systems 9/9/2017. Octal Hexadecimal Number conversion

TOPICS. 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 information

SCR 1013 : Digital Logic Module 2: NUMBER SYSTEM & CODES

SCR 1013 : Digital Logic Module 2: NUMBER SYSTEM & CODES SCR 1013 : Digital Logic Module 2: NUMBER SYSTEM & CODES Module 2 Content Number system Decimal Number Binary Number Hexadecimal Numbers Octal Number Conversion between Number system Digital Codes (BCD,

More information

Digital Logic Lecture 4 Binary Codes

Digital Logic Lecture 4 Binary Codes Digital Logic Lecture 4 Binary Codes By Ghada Al-Mashaqbeh The Hashemite University Computer Engineering Department Outline Introduction. Character coding. Error detection codes. Gray code. Decimal coding.

More information

in this web service Cambridge University Press

in this web service Cambridge University Press 978-0-51-85748- - Switching and Finite Automata Theory, Third Edition Part 1 Preliminaries 978-0-51-85748- - Switching and Finite Automata Theory, Third Edition CHAPTER 1 Number systems and codes This

More information

The type of all data used in a C++ program must be specified

The type of all data used in a C++ program must be specified The type of all data used in a C++ program must be specified A data type is a description of the data being represented That is, a set of possible values and a set of operations on those values There are

More information

Microcomputers. Outline. Number Systems and Digital Logic Review

Microcomputers. Outline. Number Systems and Digital Logic Review Microcomputers Number Systems and Digital Logic Review Lecture 1-1 Outline Number systems and formats Common number systems Base Conversion Integer representation Signed integer representation Binary coded

More information

Chapter 2: Number Systems

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

More information

Data Representation COE 301. Computer Organization Prof. Muhamed Mudawar

Data Representation COE 301. Computer Organization Prof. Muhamed Mudawar Data Representation COE 30 Computer Organization Prof. Muhamed Mudawar College of Computer Sciences and Engineering King Fahd University of Petroleum and Minerals Presentation Outline Positional Number

More information

Level ISA3: Information Representation

Level ISA3: Information Representation Level ISA3: Information Representation 1 Information as electrical current At the lowest level, each storage unit in a computer s memory is equipped to contain either a high or low voltage signal Each

More information

Number Systems CHAPTER Positional Number Systems

Number Systems CHAPTER Positional Number Systems CHAPTER 2 Number Systems Inside computers, information is encoded as patterns of bits because it is easy to construct electronic circuits that exhibit the two alternative states, 0 and 1. The meaning of

More information

Chapter 2 Number System

Chapter 2 Number System Chapter 2 Number System Embedded Systems with ARM Cortext-M Updated: Tuesday, January 16, 2018 What you should know.. Before coming to this class Decimal Binary Octal Hex 0 0000 00 0x0 1 0001 01 0x1 2

More information

Memory Addressing, Binary, and Hexadecimal Review

Memory 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 information

1.1 Information representation

1.1 Information representation Fundamentals of Data Representation: Before we jump into the world of number systems, we'll need a point of reference; I recommend that you copy the following table that you can refer to throughout this

More information

1.1. INTRODUCTION 1.2. NUMBER SYSTEMS

1.1. INTRODUCTION 1.2. NUMBER SYSTEMS Chapter 1. 1.1. INTRODUCTION Digital computers have brought about the information age that we live in today. Computers are important tools because they can locate and process enormous amounts of information

More information

Rui Wang, Assistant professor Dept. of Information and Communication Tongji University.

Rui Wang, Assistant professor Dept. of Information and Communication Tongji University. Data Representation ti and Arithmetic for Computers Rui Wang, Assistant professor Dept. of Information and Communication Tongji University it Email: ruiwang@tongji.edu.cn Questions What do you know about

More information

Electronic Data and Instructions

Electronic Data and Instructions Lecture 2 - The information Layer Binary Values and Number Systems, Data Representation. Know the different types of numbers Describe positional notation Convert numbers in other bases to base 10 Convert

More information

CMPE223/CMSE222 Digital Logic Design. Positional representation

CMPE223/CMSE222 Digital Logic Design. Positional representation CMPE223/CMSE222 Digital Logic Design Number Representation and Arithmetic Circuits: Number Representation and Unsigned Addition Positional representation First consider integers Begin with positive only

More information

Chapter 2. Data Representation in Computer Systems

Chapter 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 information

CC411: Introduction To Microprocessors

CC411: Introduction To Microprocessors CC411: Introduction To Microprocessors OBJECTIVES this chapter enables the student to: Use number { base 2, base 10, or base 16 }. Add and subtract binary/hex numbers. Represent any binary number in 2

More information

User. Application program. Interfaces. Operating system. Hardware

User. Application program. Interfaces. Operating system. Hardware Operating Systems Introduction to Operating Systems and Computer Hardware Introduction and Overview The operating system is a set of system software routines that interface between an application program

More information

Dec Hex Bin ORG ; ZERO. Introduction To Computing

Dec Hex Bin ORG ; ZERO. Introduction To Computing Dec Hex Bin 0 0 00000000 ORG ; ZERO Introduction To Computing OBJECTIVES this chapter enables the student to: Convert any number from base 2, base 10, or base 16 to any of the other two bases. Add and

More information

Objectives. Connecting with Computer Science 2

Objectives. 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 information