1. Digital logic COMP214  Lecture 1 Dr. Sarah M.Eljack Chapter 1 1

2. مقرر المنطق الرقمي 1. Concepts and basic components of computer hardware and software.  2. Systems numbers  3. binary Systems  4. Boolean algebra  5. Logical expressions  6. Logic gates  7. Digital circuit design Structural  8. Sequential digital circuits Chapter 1 2

3. References المراجع:  1. Digital Design, Mano, M. Morris, 3 rd edition, ISBN 0-13-062121-8, Prentice- Hall, 2002.  2. Fundamentals of logic Design, 5 th edition, Brooks/Cole Thomson Learning, 2004.  3. Introduction to Digital Systems, M. Ercegovac, T. Lang, and J. Moreno, Wiley and Sons. 1998.  Chapter 1 3

4. Outline  Introduction  Numbering Systems  Binary & Hexadecimal Numbers  Base Conversions  Integer Storage Sizes  Binary and Hexadecimal Addition  Signed Integers and 2's Complement Notation  Binary and Hexadecimal subtraction  Carry and Overflow  Character Storage

5. Chapter 1 5 Overview  Digital Systems and Computer Systems  Information Representation  Number Systems [binary, octal and hexadecimal]

6. Chapter 1 6 Digital System  Takes a set of discrete information inputs and discrete internal information (system state) and generates a set of discrete information outputs. System State Discrete Information Processing System Discrete Inputs Discrete Outputs

7. Chapter 1 7 Digital System Example: A Digital Counter (e. g., odometer): 1300564 Count Up Reset Inputs: Count Up, Reset Outputs:Visual Display State: "Value" of stored digits Synchronous or Asynchronous?

8. Chapter 1 8 A Digital Computer Example Synchronous or Asynchronous? Inputs: Keyboard, mouse, modem, microphone Outputs: CRT, LCD, modem, speakers

9. Chapter 1 9 Signal  An information variable represented by physical quantity.  For digital systems, the variable takes on discrete values.  Two level, or binary values are the most prevalent values in digital systems.  Binary values are represented abstractly by: digits 0 and 1 words (symbols) False (F) and True (T) words (symbols) Low (L) and High (H) and words On and Off.  Binary values are represented by values or ranges of values of physical quantities

10. Chapter 1 10 Signal Examples Over Time Analog Asynchronous Synchronous Time Continuous in value & time Discrete in value & continuous in time Discrete in value & time Digital

11. Chapter 1 11 Signal Example – Physical Quantity: Voltage Threshold Region

12. Chapter 1 12  What are other physical quantities represent 0 and 1? CPU Voltage Disk CD Dynamic RAM Binary Values: Other Physical Quantities Magnetic Field Direction Surface Pits/Light Electrical Charge

13. Introduction  Computers only deal with binary data (0s and 1s), hence all data manipulated by computers must be represented in binary format.  Machine instructions manipulate many different forms of data: Numbers:  Integers: 33, +128, -2827  Real numbers: 1.33, +9.55609, -6.76E12, +4.33E-03 Alphanumeric characters (letters, numbers, signs, control characters): examples: A, a, c, 1,3, ", +, Ctrl, Shift, etc. Images (still or moving): Usually represented by numbers representing the Red, Green and Blue (RGB) colors of each pixel in an image, Sounds: Numbers representing sound amplitudes sampled at a certain rate (usually 20kHz).  So in general we have two major data types that need to be represented in computers; numbers and characters. Chapter 1 13

14. Chapter 1 14 Number Systems – Representation  Positive radix, positional number systems  A number with radix r is represented by a string of digits: A n - 1 A n - 2 … A 1 A 0. A - 1 A - 2 … A - m  1 A - m in which 0  A i < r and. is the radix point.  The string of digits represents the power series:  (Number) r =   j = - m j j i i = 0 i rArA (Integer Portion) + (Fraction Portion) i = n - 1 j = - 1

15. .  Numbering systems are characterized by their base number.  In general a numbering system with a base r will have r different digits (including the 0) in its number set. These digits will range from 0 to r-1  The most widely used numbering systems are listed in the table below: Chapter 1 15

16. Chapter 1 16

17. Chapter 1 17 Number Systems – Examples GeneralDecimalBinary Radix (Base)r102 Digits0 => r - 10 => 90 => 1 0 1 2 3 Powers of 4 Radix 5 -2 -3 -4 -5 r 0 r 1 r 2 r 3 r 4 r 5 r -1 r -2 r -3 r -4 r -5 1 10 100 1000 10,000 100,000 0.1 0.01 0.001 0.0001 0.00001 1 2 4 8 16 32 0.5 0.25 0.125 0.0625 0.03125

18. Chapter 1 18 Special Powers of 2  2 10 (1024) is Kilo, denoted "K"  2 20 (1,048,576) is Mega, denoted "M"  2 30 (1,073, 741,824)is Giga, denoted "G"

19. Binary Numbers  Each digit (bit) is either 1 or 0  Each bit represents a power of 2  Every binary number is a sum of powers of 2