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EE/CS120A: Logic Design Prof. Usagi (a.k.a. Hung-Wei Tseng) - PowerPoint PPT Presentation

Aug 21, 2022 •135 likes •783 views

EE/CS120A: Logic Design Prof. Usagi (a.k.a. Hung-Wei Tseng) Greetings Whats your Whats your feeling about name? stay-at-home? 2 Zoom Lecture Experience Discussion/Answer/ Dis Lecture Poll Lecture Poll Questions Think/Mute/

  1. EE/CS120A: Logic Design Prof. Usagi (a.k.a. Hung-Wei Tseng)

  2. Greetings What’s your What’s your feeling about name? stay-at-home? 2

  3. Zoom Lecture Experience Discussion/Answer/ Dis Lecture Poll Lecture Poll Questions Think/Mute/ Raise Hands/ Think/Mute/ Listen/Learn/Think/Mute Listen/Learn/Think/Mute Answer Unmute/Speak Answer Un 3

  4. Logic Design? https://www.britannica.com/technology/logic-design 4

  5. “Digital” Computers 5

  6. Computer 6

  7. Digital Computers 7

  8. Fermiac — 1947 Computers that are not “digital” MNIAC — 1949 Photo Credit By Kaihsu Tai, https://commons.wikimedia.org/w/index.php?curid=3956307 Photo Credit By Mark Pellegrini, CC BY- SA 1.0, https://commons.wikimedia.org/ 8 w/index.php?curid=7878402

  9. Poll close in Why are digital computers more popular now? • Please identify how many of the following statements explains why digital computers are now more popular than analog computers. ① The cost of building systems with the same functionality is lower by using digital computers. ② Digital computers can express more values than analog computers. ③ Digital signals are less fragile to noise and defective/low-quality components. ④ Digital data are easier to store. A. 0 B. 1 C. 2 D. 3 E. 4 9

  10. (1) Moore’s Law ICs are widely applicable ICs are increasingly popular ICs are more reliable ICs are well established Heat is a solvable issue Moore’s Law is the most important driver for historic CPU performance ICs are easy to manufacture gains and they’re getting smaller and ICs are small smaller! Designing ICs can be easy (1) Moore, G. E. (1965), 'Cramming more components onto integrated circuits', Electronics 38 (8) . 10

  11. (1) Moore’s Law • The number of transistors we can build in a fixed area of silicon doubles every 12 ~ 24 months. 10,000,000,000 1,000,000,000 100,000,000 Transistor Count 10,000,000 1,000,000 100,000 Moore’s Law is the most 10,000 important driver for 1,000 historic CPU performance 100 gains 10 1 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 (1) Moore, G. E. (1965), 'Cramming more components onto integrated circuits', Electronics 38 (8) . 11

  12. Why are digital computers more popular now? • Please identify how many of the following statements explains why digital computers are now more popular than analog computers. ① The cost of building systems with the same functionality is lower by using digital computers. ② Digital computers can express more values than analog computers. ③ Digital signals are less fragile to noise and defective/low-quality components. ④ Digital data are easier to store. A. 0 B. 1 C. 2 D. 3 E. 4 12

  13. Analog v.s. digital signals 0.5? 0.4? 0.45? 0.445? 0.4445? or 0.4444444444459? Infinite possible values! 1 0 sampling cycle 13

  14. Analog v.s. digital signals 3 2 1 0 sampling cycle 14

  15. Why are digital computers more popular now? • Please identify how many of the following statements explains why digital computers are now more popular than analog computers. ① The cost of building systems with the same functionality is lower by using digital computers. ② Digital computers can express more values than analog computers. ③ Digital signals are less fragile to noise and defective/low-quality components. ④ Digital data are easier to store. A. 0 B. 1 C. 2 D. 3 E. 4 15

  16. Analog v.s. digital signals 0.5? 0.4? 0.45? Anything within this wide 0.445? 0.4445? or range is considered as “1” 0.4444444444459? Infinite possible values! 1 0 sampling cycle 16

  17. Why are digital computers more popular now? • Please identify how many of the following statements explains why digital computers are now more popular than analog computers. ① The cost of building systems with the same functionality is lower by using digital computers. ② Digital computers can express more values than analog computers. ③ Digital signals are less fragile to noise and defective/low-quality components. ④ Digital data are easier to store. A. 0 B. 1 C. 2 D. 3 E. 4 17

  18. Analog data storage 18

  19. https://www.youtube.com/watch?v=NVpOdpRDYF4 19

  20. Why are digital computers more popular now? • Please identify how many of the following statements explains why digital computers are now more popular than analog computers. ① The cost of building systems with the same functionality is lower by using digital computers. ② Digital computers can express more values than analog computers. ③ Digital signals are less fragile to noise and defective/low-quality components. ④ Digital data are easier to store. A. 0 B. 1 C. 2 D. 3 E. 4 20

  21. 10-based number systems is the human-nature 21

  22. 10-based number system is popular since thousands of years ago 1: 𓏻 10: 𓎇 100: 𓍣 𓆽𓆽 𓎇 𓎇 = 2020 1000: 𓆽 10000: 𓂮 100000: 𓆑 1000000: 𓁩 22

  23. But digital circuits only have 0s and 1s… 1 0 23

  24. Binary numbers 24

  25. The brief history of binary numbers • The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz • The concept of binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. • Leibniz was specifically inspired by the Chinese I Ching. 25

  26. The basic idea of a number system • Each position represents a quantity; symbol in position means how many of that quantity 10 2 10 1 10 0 × × × • Decimal (base 10) 3 2 1 + + =300 • Ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 +20 • More than 9: next position +1 • Each position is incremented by power of 10 =321 • Binary (base 2) 2 3 2 2 2 1 2 0 × × × × • Two symbols: 0, 1 × =1 2 3 + + + 1 0 0 1 • More than 1: next position × +1 2 0 • Each position is incremented by power of 2 × =1 8 × +1 1 =9 26

  27. 27

  28. Poll close in How many does Prof. Usagi have? • Prof. Usagi says that he has a few eggs that he cannot count with all his fingers. However, if we consider each finger as a position in a binary number, then we only need five fingers to count all of them. How many eggs he may have? A. 4 B. 8 C. 12 D. 24 E. 32 28

  29. How many does Prof. Usagi have? • Prof. Usagi says that he has a few eggs that he cannot count with all his fingers. However, if we consider each finger as a More than 10 position in a binary number, then we only need five fingers to Some binary number needs 4 digits count all of them. How many eggs he may have? A. 4 0b10000 < x < 0b11111 and 10 < x B. 8 C. 12 2^4+0=16 < x < 2^4+2^3+2^2+2^1+2^0=16+8+4+2+1=31 D. 24 10 < 16 < x < 31 E. 32 29

  30. Converting from decimal to binary 2 321 2 160 …… 1 2 80 …… 0 2 40 …… 0 2 20 …… 0 2 10 …… 0 2 5 …… 0 2 2 …… 1 1 …… 0 321 = 0b 101000001 30

  31. Other frequently used number systems • Octal — base of 8 • 8 symbols: 0, 1, 2, 3, 4, 5, 6, 7 321 = 0b 101000001 • More than 7: next position 321 = 0b 101 000 001 • Each position is incremented by power of 8 = 0 5 0 1 • Easy conversion from binary — merge 3-digit into one • Hexdecimal — base of 16 • 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F 321 = 0b 1 0100 0001 • More than 15: next position = 0x 1 4 1 • Each position is incremented by power of 16 • Easy conversion from binary — merge 4-digit into one 31

  32. Poll close in Prof. Usagi’s age? • Prof. Usagi and some of you mentioned the age to each other and claim both of them are at their “21”s. Assume none of them are lying. Both of them completed their high school at the age of 18 (decimal) in their lives. Prof. Usagi got his bachelor’s degree already without earlier completion through his student life, what number systems are they using? A. Prof. Usagi is using octal, the student is using decimal B. Prof. Usagi is using decimal, the student is using octal C. Prof. Usagi is using hexdecimal, the student is using decimal D. Prof. Usagi is using octal, the student is using hexadecimal E. Both of them are using decimal, Prof. Usagi is just incredibly young. 32

  33. Prof. Usagi’s age? • Prof. Usagi and some of you mentioned the age to each other and claim both of them are at their “21”s. Assume none of them are lying. Both of them completed their high school at the age of 18 (decimal) in their lives. Prof. Usagi got his bachelor’s degree already without earlier completion through his student life, what number systems are they using? A. Prof. Usagi is using octal, the student is using decimal B. Prof. Usagi is using decimal, the student is using octal C. Prof. Usagi is using hexdecimal, the student is using decimal D. Prof. Usagi is using octal, the student is using hexadecimal E. Both of them are using decimal, Prof. Usagi is just incredibly young. 33

  34. Logic Design? https://www.britannica.com/technology/logic-design 34

  35. Beyond these, you will also learn… 35

  36. Topics of this quarter • Combinational Logic • Logic gates • Boolean Algebra • K-map • Sequential Logic • Finite state machines • Clock • Flip-flops • Datapath Components • Adder/mux/multipliers … • Registers • Counter/timers • RTL Design • Verilog 36

  37. Why learning logic design? 37

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