1 / 42

Digital Logic & Design Lecture 01

Digital Logic & Design Lecture 01. Analogue Quantities. Continuous Quantity Intensity of Light Temperature Velocity. Digital Values. Discrete set of values. Continuous Signal. Continuous Signal. Digital Representation. Under Sampling. Electronic Processing. Analogue Systems

devin
Télécharger la présentation

Digital Logic & Design Lecture 01

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Digital Logic & Design Lecture 01

  2. Analogue Quantities Continuous Quantity • Intensity of Light • Temperature • Velocity

  3. Digital Values • Discrete set of values

  4. Continuous Signal

  5. Continuous Signal

  6. Digital Representation

  7. Under Sampling

  8. Electronic Processing • Analogue Systems • Digital Systems • Representing quantities in Digital Systems

  9. 39 0C ? Representing Digital Values 39mV DigitalSystem 6.25 x 1015 V !! 6.25 x 1018 ?

  10. Digital Systems • Two Voltage Levels • Two States • On/Off • Black/White • Hot/Cold • Stationary/Moving

  11. Binary Number System • Binary Numbers • Representing Multiple Values • Combination of 0v & 5v

  12. Merits of Digital Systems • Efficient Processing & Data Storage • Efficient & Reliable Transmission • Detection and Correction of Errors • Precise & Accurate Reproduction • Easy Design and Implementation • Occupy minimum space

  13. Information Processing • Numbers • Text • Formula and Equations • Drawings and Pictures • Sound and Music

  14. Logic Gates • Building Blocks • AND, OR and NOT Gates • NAND, NOR, XOR and XNOR Gates • Integrated Circuits (ICs)

  15. c 3 2 1 0 c 9 8 1 1 1 1 V 7400 D N 4 5 6 1 2 3 G Logic Gate Symbol and ICs

  16. Combinational Circuits • Combination of Logic Gates • Adder Combinational Circuit

  17. Sum Carry Adder Combinational Circuit

  18. Functional Devices • Functional Devices • Adders • Comparators • Encoders/Decoders • Multiplexers/Demultiplexers

  19. Sequential Circuits • Memory Element • Current & Previous State • Flip-Flops • Counters & Registers

  20. Block Diagram of a Sequential Circuit

  21. Programmable Logic Devices (PLDs) • Configurable Hardware • Combinational Circuits • Sequential Circuits • Low chip count • Lower Cost • Short development time

  22. Memory • Storage • RAM (Random Access Memory) • Read-Write • Volatile • ROM (Read-Only Memory) • Read-Only • Non-Volatile

  23. A/D & D/A Converters • Processing of Continuous values • Conversion • Analogue to Digital A/D • Digital to Analogue D/A • Industrial Control Application

  24. Digital Industrial Control Digital * / * * / * x u x u 1 1 1 1 Controller A/D D/A Converter Converter Thermocouple Reaction Vessel Heater Control

  25. Summary • Continuous Signals • Digital Representation in Binary • Information Processing • Logic Gates

  26. Summary • Combinational & Sequential Circuits • Programmable Logic Devices (PLDs) • Memory (RAM & ROM) • A/D & D/A Converters

  27. Number Systems and Codes • Decimal Number System • Caveman Number System • Binary Number System • Hexadecimal Number System • Octal Number System

  28. Decimal Number System • Ten unique numbers 0,1..9 • Combination of digits • Positional Number System • 275 = 2 x 102 + 7 x 101 + 5 x 100 • Base or Radix 10 • Weight 1, 10, 100, 1000 ….

  29. Representing Fractions • Fractions can be represented in decimal number system in a manner = 3 x 102 + 8 x 101 + 2 x 100 + 9 x 10-1 + 1 x 10-2 = 300 + 80 + 2 + 0.9 + 0.01 = 382.91

  30. Caveman Number System • ∑, ∆, >, Ω and ↑ • Base – 5 Number System • ∆Ω↑∑ = 220

  31. Caveman Number System

  32. Caveman Number System • Mr. Caveman is using a base 5 number system. Thus the number ∆Ω↑∑ in decimal is = ∆ x 53 + Ω x 52 + ↑ x 51 + ∑ x 50 = ∆ x 125 + Ω x 25 + ↑ x 5 + ∑ x 1 = (1) x 125 + (3) x 25 + (4) x 5 + (0) x 1 = 125 + 75 + 20 + 0 = 220

  33. Binary Number System • Two unique numbers 0 and 1 • Base – 2 • A binary digit is a bit • Combination of bits to represent larger values

  34. Binary Number System

  35. Combination of Binary Bits • Combination of Bits • 100112 = 1910 = (1 x 24) + (0 x 23) + (0 x 22) + (1 x 21) + (1 x 20) = (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2) + (1 x 1) = 16 + 0 + 0 + 2 + 1 = 19

  36. Fractions in Binary • Fractions in Binary • 1011.1012 = 11.625 = (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20) + (1 x 2-1) + (0 x 2-2) + (1 x 2-3) = (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1) + (1 x 1/2) + (0 x 1/4) + (1 x 1/8) = 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125 = 11.625 • Floating Point Notations

  37. Decimal-Binary Conversion • Binary to Decimal Conversion • Sum-of-Weights • Adding weights of non-zero terms • Decimal to Binary Conversion • Sum-of-Weights (in reverse) • Repeated Division by 2

  38. Decimal to binary conversion using Sum of weight

  39. Decimal-Binary Conversion • Binary to Decimal Conversion • Sum-of-Weights • Adding weights of non-zero terms Terms 16,0,0.2 and 1 19

  40. Decimal-Binary Conversion • Binary to Decimal Conversion • Sum-of-Weights • Adding weights of non-zero terms

  41. Decimal-Binary Conversion • Binary to Decimal Conversion • Sum-of-Weights • Adding weights of non-zero terms

  42. Lecture No. 1 Number Systems A Summary

More Related