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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

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Digital Logic & Design Lecture 01

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  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

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