ECE 3110: Introduction to Digital Systems Number Systems.

Slides:



Advertisements
Similar presentations
Number Systems and Codes
Advertisements

Representing Numbers: Integers
DATA REPRESENTATION CONVERSION.
Binary Representation
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.
Chapter 1 Number Systems and Codes William Kleitz Digital Electronics with VHDL, Quartus® II Version Copyright ©2006 by Pearson Education, Inc. Upper Saddle.
Computer Systems 1 Fundamentals of Computing
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.
Number Systems and Codes In PLC
+ CS 325: CS Hardware and Software Organization and Architecture Integers and Arithmetic.
Chapter 1 Number Systems and Codes 1. Outline 1. NUMBER SYSTEMS AND CODES 2. DIGITAL ELECTRONIC SIGNALS AND SWITCHES 3. BASIC LOGIC GATES 4. PROGRAMMABLE.
Binary and Hexadecimal Numbers
Number Systems.
ECE 2110: Introduction to Digital Systems Signed Number Conversions.
BR 8/99 Digital Devices Integrated Circuits that operate on Digital Data are in 95% of every electrical powered device in the U.S. The theory of operation.
CS231 Fundamentals1 Fundamentals What kind of data do computers work with? – Deep down inside, it’s all 1s and 0s What can you do with 1s and 0s? – Boolean.
Chapter 1 Basic Principles of Digital Systems. 2 Analog vs. Digital Analog: –A way of representing a physical quantity by a proportional continuous voltage.
Numbering systems.
Numbering Systems CS208.
1 Number SystemsLecture 8. 2 BINARY (BASE 2) numbers.
ECE 3110: Introduction to Digital Systems Review #1 (Chapter 1,2)
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.
Conversion of Number System Conversion Among Bases The possibilities: Hexadecimal DecimalOctal Binary
Engineering 1040: Mechanisms & Electric Circuits Spring 2014 Number Systems.
1-1 Lecture 1 Class Overview and Appendix A -- Number Systems.
Number Systems Number Systems Stone Age: knots, some stone marks Roman Empire: more systematic notation I, II, III, IV, V, VI, VII.VIII, IX, X, C=100,
1 CS103 Guest Lecture Number Systems & Conversion Bitwise Logic Operations.
Computer Arithmetic and the Arithmetic Unit Lesson 2 - Ioan Despi.
CPU Internal memory I/O interface circuit System bus
CCE-EDUSAT SESSION FOR COMPUTER FUNDAMENTALS Date: Session III Topic: Number Systems Faculty: Anita Kanavalli Department of CSE M S Ramaiah.
Number systems, Operations, and Codes
Number Systems and Codes
ECE 2110: Introduction to Digital Systems 2. Number Systems & Codes.
Number Base Conversions
Chapter 19 Number Systems. Irvine, Kip R. Assembly Language for Intel-Based Computers, Translating Languages English: Display the sum of A times.
ECE 3110: Introduction to Digital Systems Introduction (Contd.)
Positional Number Systems Decimal, Binary, Octal and Hexadecimal Numbers Wakerly Section
AEEE2031 Data Representation and Numbering Systems.
Digital Design Basics Analog vs Digital Why we need digital? Reproducibility, economy, programmability… Digital Devices Gates, FFs Combinational, sequential.
ECE 3110: Introduction to Digital Systems Number Systems.
ECE 2110: Introduction to Digital Systems Number Systems.
CSC 331: DIGITAL LOGIC DESIGN COURSE LECTURER: E. Y. BAAGYERE. CONTACT: LECTURE TIME: 15:40 – 17:45 hrs. VENUE: SP-LAB.
ECE 2110: Introduction to Digital Systems
ECE 3110: Introduction to Digital Systems Introduction (Contd.)
ECE 2110: Introduction to Digital Systems Number Systems: conversions.
CS151 Introduction to Digital Design Chapter 1: Digital Systems and Information Lecture 2 1Created by: Ms.Amany AlSaleh.
Number Systems and Binary Arithmetic Quantitative Analysis II Professor Bob Orr.
ECE 2110: Introduction to Digital Systems Number Systems: conversions.
1 Digital Logic Design (41-135) Chapter 5 Number Representation & Arithmetic Circuits Younglok Kim Dept. of Electrical Engineering Sogang University Spring.
Positional Number Systems Decimal, Binary, Octal and Hexadecimal Numbers Wakerly Section
Digital Design Chapter One Digital Systems and Binary Numbers
Numbering Systems.
Octal to Decimal Decimal Octal Binary Hexadecimal.
Number Systems and Binary Arithmetic
Data Representation Binary Numbers Binary Addition
CHAPTER 1 : INTRODUCTION
ECE 3110: Introduction to Digital Systems
Number Systems.
Digital Devices Integrated Circuits that operate on Digital Data are in 95% of every electrical powered device in the U.S. The theory of operation of these.
Number System conversions
Fundamentals & Ethics of Information Systems IS 201
IT 0213: INTRODUCTION TO COMPUTER ARCHITECTURE
University of Gujrat Department of Computer Science
Chapter 1 Number Systems & Conversions
Number Systems and Binary Arithmetic
Numbering System TODAY AND TOMORROW 11th Edition
Digital Electronics and Microprocessors
Number Systems Rayat Shikshan Sanstha’s
Number Systems Rayat Shikshan Sanstha’s
Presentation transcript:

ECE 3110: Introduction to Digital Systems Number Systems

2 Previous class Summary Electronics/sw aspects of digital design Integrated Circuits (wafer,die,SSI,MSI,LSI,VLSI) PLDs: PLAs,PALs,CPLD,FPGA ASIC

3 Digital Design Levels Many representations of digital logic Device Physics and IC manufacturing Moore’s Law [1965, Gordon Moore]: Transistor level --->Logic design, functional building blocks The number of transistors per square inch in an IC doubles every year [18months].

4 Digital Design Levels Transistor-level circuit diagrams Example: Multiplexor

5 Truth tables Gate-level Logic diagrams

6 Prepackaged building blocks, e.g. multiplexer Equations: Z = S  A  + S  B

7 Various hardware description languages ABEL VHDL

8 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 1, 0, 56 True, False, Maybe Hot, Cold, LukeWarm, Cool On, Off, Leaky

9 Number Systems To talk about binary data, we must first talk about number systems The decimal number system (base 10) you should be familiar with! Positional number system

10 Positional Notation Value of number is determined by multiplying each digit by a weight and then summing. The weight of each digit is a POWER of the BASE and is determined by position.

11 The decimal number system (base 10) you should be familiar with! A digit in base 10 ranges from 0 to 9. A digit in base 2 ranges from 0 to 1 (binary number system). A digit in base 2 is also called a ‘bit’. A digit in base R can range from 0 to R-1 A digit in Base 16 can range from 0 to 16-1 (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F). Use letters A-F to represent values 10 to 15. Base 16 is also called Hexadecimal or just ‘Hex’.

= 9 x x x x x = = = 1x x x x x x2 -2 = = A2F 16 = 10x x x16 0 = 10 x x x 1 = = 2607 Base 10, Base 2, Base 16

13 Common Powers 2 -3 = = = = = = = = = = = = = = = = = 1 = = 16 = = 256 = = 4096 = = 1024 = 1 K 2 20 = = 1 M (1 Megabits) = 1024 K = 2 10 x = = 1 G (1 Gigabits)

14 Least Significant Digit Most Significant Digit = Most Significant Digit (has weight of 2 5 or 32). For base 2, also called Most Significant Bit (MSB). Always LEFTMOST digit. Least Significant Digit (has weight of 2 0 or 1). For base 2, also called Least Significant Bit (LSB). Always RIGHTMOST digit.

15 Hex (base 16) to Binary Conversion Each Hex digit represents 4 bits. To convert a Hex number to Binary, simply convert each Hex digit to its four bit value. Hex Digits to binary (cont): 9 16 = A 16 = B 16 = C 16 = D 16 = E 16 = F 16 = Hex Digits to binary: 0 16 = = = = = = = = =

16 Hex to Binary, Binary to Hex A2F 16 = = Binary to Hex is just the opposite, create groups of 4 bits starting with least significant bits. If last group does not have 4 bits, then pad with zeros for unsigned numbers = = Padded with a zero

Hex to Binary, Binary to Hex A2F 16 = = Binary to Hex is just the opposite, create groups of 4 bits starting with least significant bits. If last group does not have 4 bits, then pad with zeros for unsigned numbers = = Padded with a zero

Octal to Binary, Binary to Octal = Binary to Octal is just the opposite, create groups of 3 bits starting with least significant bits. If last group does not have 3 bits, then pad with zeros for unsigned numbers = = Padded with a zero

Conversion of Any Base to Decimal Converting from ANY base to decimal is done by multiplying each digit by its weight and summing = 1x x x x x x2 -2 = = Binary to Decimal Hex to Decimal A2F 16 = 10x x x16 0 = 10 x x x 1 = = 2607

A Trick! If faced with a large binary number that has to be converted to decimal, I first convert the binary number to HEX, then convert the HEX to decimal. Less work! = = D 16 F = 13 x x x16 0 = 13 x x x 1 = = Of course, you can also use the binary, hex conversion feature on your calculator. Calculators won’t be allowed on the first test, though…...

21 Conversion of Decimal Integer To ANY Base Divide Number N by base R until quotient is 0. Remainder at EACH step is a digit in base R, from Least Significant digit to Most significant digit.

Conversion of Decimal Integer To ANY Base Example Convert 53 to binary 53/2 = 26, rem = 1 26/2 = 13, rem = 0 13/2 = 6, rem = 1 6 /2 = 3, rem = 0 3/2 = 1, rem = 1 1/2 = 0, rem = = = 1x x x x x x2 0 = = 53 Least Significant Digit Most Significant Digit

23 More Conversions Convert 53 to Hex 53/16 = 3, rem = 5 3 /16 = 0, rem = = = 3 x x 16 0 = = =??? 16

24 Binary Numbers Again Recall that N binary digits (N bits) can represent unsigned integers from 0 to 2 N bits = 0 to 15 8 bits = 0 to bits = 0 to Besides simply representation, we would like to also do arithmetic operations on numbers in binary form. Principle operations are addition and subtraction.

25

26 Next… Additions/subtractions