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### digital-logic-design-cs302-power-point-slides-lecture-01.ppt

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 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 time temperature 0 C
5. Continuous Signal 1 2 4 7 34 25 23 37 29 42 41 25 22 18 35 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 time temperature 0 C
6. Digital Representation 1 2 4 7 18 34 25 23 35 37 29 42 41 25 22 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 samples temperature 0 C
7. Under Sampling 0 5 10 15 20 25 30 35 40 45 1 3 5 7 9 11 13 15 samples temperature 0 C
8. Electronic Processing  Analogue Systems  Digital Systems  Representing quantities in Digital Systems
9. Representing Digital Values 39 0C ? a1 1 a2 2 3 a3 4 a4 b1 b2 b3 b4 5 6 7 8 Vcc1 0 GND 0 1mV = 1 39mV 6.25 x 1015 V !! Digital System 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. Logic Gate Symbol and ICs AND Gate OR Gate NOT Gate 1 2 3 4 5 6 GND Vcc 13 12 11 10 9 8 7400 NAND Gate NOR Gate XOR Gate XNOR Gate NAND Gate IC
16. Combinational Circuits  Combination of Logic Gates  Adder Combinational Circuit
17. Adder Combinational Circuit Sum Carry
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 a1 1 a2 2 b1 b2 5 6 Combinational Logic Circuit Output Input a1 1 b1 5 Memory Element
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 Controller Thermocouple A/D Converter u1 x1 * / * D/A Converter u1 x1 * / * Reaction Vessel Heater Control
25. Summary  Continuous Signals  Digital Representation in Binary  Information Processing  Logic Gates
26.  Combinational & Sequential Circuits  Programmable Logic Devices (PLDs)  Memory (RAM & ROM)  A/D & D/A Converters Summary
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 Decimal Number Caveman Number Decimal Number Caveman Number 0 ∑ 10 >∑ 1 ∆ 11 >∆ 2 > 12 >> 3 Ω 13 >Ω 4 ↑ 14 >↑ 5 ∆∑ 15 Ω∑ 6 ∆∆ 16 Ω∆ 7 ∆> 17 Ω> 8 ∆Ω 18 ΩΩ 9 ∆↑ 19 Ω↑
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 Decimal Number Binary Number Decimal Number Binary Number 0 0 10 1010 1 1 11 1011 2 10 12 1100 3 11 13 1101 4 100 14 1110 5 101 15 1111 6 110 16 10000 7 111 17 10001 8 1000 18 10010 9 1001 19 10011
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. Number Weight Result after subtraction Binary 392 256 392-256=136 1 136 128 136-128=8 1 8 54 0 8 32 0 8 16 0 8 8 8-8=0 1 0 4 0 0 2 0 0 1 0 Decimal to binary conversion using Sum of weight
39. Decimal-Binary Conversion 2 4 3 2 1 0 10011 (1 2 ) (0 2 ) (0 2 ) (1 2 ) (1 2 )          Terms 16,0,0.2 and 1 19  Binary to Decimal Conversion  Sum-of-Weights  Adding weights of non-zero terms
40. Decimal-Binary Conversion  Binary to Decimal Conversion  Sum-of-Weights  Adding weights of non-zero terms
41.  Binary to Decimal Conversion  Sum-of-Weights  Adding weights of non-zero terms Decimal-Binary Conversion 2 2 10011 16 2 1 19 1 1 1011.101 8 2 2 8 5 11 8 11.625           
42. Lecture No. 1 Number Systems A Summary
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