Description of the achievements in digital circuitry in the area of random number generation, where data are unique in nature and can be sorted in linear function of measurable variables. Software available, develop it in Microsoft Excel, with =RAND () function within. Trust measurement (modelling trust) is use to show the application of having seven (7) distinct governing factors, to model the rigid equation(s) that calculates the results/trust level/performance measurement, well-known techniques such as Moving Average and Exponential Smoothing Techniques.

1. DIGITAL CIRCUITRY AND SYSTEM WITH RANDOM
NUMBER GENERATOR:
Weightings on the Variables of Trust
(Trust Measurement_Part 3)
By Gan Chun Chet (Ir., PEng (M‘sia))
23th October, 2023
MSc Operations Management 1997
[Manchester School Management]
University of Manchester Institute of Science and Technology (UMIST),
United Kingdom.
BEng (Hons) Mechanical Engineering 1996
[Simon Building]
University of Manchester, United Kingdom

2. The Initial Part
Boolean Algebra
Demorgan Theorem
Derive a Delay “D” Flip Flop

3. Boolean Algebra (1) : AND and OR GATE

4. Boolean Algebra (2) : NOT GATE

5. Boolean Algebra (3) : NAND (NOT AND) GATE

6. Boolean Algebra (4) : NOR (NOT OR) GATE

7. We could invert other composite functions like,

8. In addition…

9. …with an example

10. Demorgan’s
Theorem

11. Karnaugh
Maps
(K – Maps)
(1)

12. Karnaugh
Maps
(K – Maps)
(2)

13. How to Derive a Delay “D” Flip Flop :
SR-FF (NAND Implementation) (1)

14. How to Derive a Delay “D” Flip Flop :
SR-FF (NAND Implementation) (2)

15. How to Derive a Delay “D” Flip Flop :
SR-FF (NAND Implementation) (3)

16. How to Derive a Delay “D” Flip Flop :
Master_Slave SR-FF (1)

17. How to Derive a Delay “D” Flip Flop :
Master_Slave SR-FF (2)

18. How to Derive a Delay “D” Flip Flop :
Master_Slave JK-FF

19. How to Derive a Delay “D” Flip Flop :
Delay FF (D-Type) (1)

20. How to Derive a Delay “D” Flip Flop :
Delay FF (D-Type) (2)

21. How to Derive a Delay “D” Flip Flop :
Toggle FF (1)

22. How to Derive a Delay “D” Flip Flop :
Toggle FF (2)

23. Implementing a Linear
Feedback Shift Register
Random Number Generation : 5, 6, 7 & 9 Bit

24. Linear Feedback Shift Register (no. of bits, length and tap
positions)
Item No. of bits Length of
loop
Tap
positions
1 5 31 1 & 4
2 6 63 0 & 5
3 7 127 0 & 6
4 9 511 3 & 8

25. The Basic Way to Generate Random Numbers (1)
This is a “5-bit Linear Feedback Shift Register”
- All numbers generated are unique, and the
numbers never repeat

26. The Basic Way to Generate Random Numbers (2)
This is a “6-bit Linear Feedback Shift Register”
- All numbers generated are unique, and the
numbers never repeat

27. The Basic Way to Generate Random Numbers (3)
This is a “7-bit Linear Feedback Shift Register”
- All numbers generated are unique, and the
numbers never repeat

28. The Basic Way to Generate Random Numbers (4)
This is a “9-bit Linear Feedback Shift Register”
- All numbers generated are unique, and the
numbers never repeat

29. The Application of RANDOM
Number Generation in EXCEL -
Weightings on the Variables of
Trust
Trust Measurement_Part 3 : The Details (based on a simulation).

30. The Application of RANDOM
Number Generation in EXCEL -
Weightings on the Variables of
Trust
• Ideally, RANDOM Number are generated in EXCEL
by the function =RAND()
• As the previous slides shows the hardware of
generating unique Randomized Numbers (in
detail), the subsequent slides shows the
application - equation(s) aspect of weighting on
the Variables of Trust to obtain a plausible
trendline that models the real world (observations
– based on random data generation, currently)
• What are the future trends to be establish/govern,
that could prevent similar occurrence in the past,
to ensure foreseeable gains/ and phase-in/depict
systemic risks?

31. Individually Weightings on the Variables of Trust
GENERATED FROM RANDOM NUMBERS =RAND() IN EXCEL
WEIGHTINGS ON THE FACTORS TOTAL TO 1.0
SIMULATION RESULT

32. Trust Measurement Level – Performance
Measurement based on the Components of Trust
SIMULATION RESULT

33. Trust Measurement Level – Performance
Measurement based on the Components of Trust
SIMULATION RESULT

34. Trust Measurement Level – Performance
Measurement based on the Components of Trust
SIMULATION RESULT

35. The Analogy of “Profitable Trending
Transactions”
• The analogy of “profitable trending transactions” is similar to the idea
of comparing past occurrences with the current situation(s), and to
forecasting (or predict) future value figuratively.
• Random Number Generation is utilized here to show that the number
generated is uniquely generated and when sorting the complete
number range - will be incrementally a linear trendline (i.e. lawful
within an organized system). It is able to depict (perceptive) that this
nature model, in practice, will represent the real world we live in
today.

36. Example in Excel File_1…
SIMULATION RESULT

37. Categorical of Trust Level by Chance in Four
Quadrants_By Charting (sample)

38. Example of Calculation (1) SIMULATION RESULT

39. Example in Excel File_2… SIMULATION RESULT

40. Example of Calculation (2) SIMULATION RESULT

41. Example in Excel File_3…
SIMULATION RESULT

42. Example of Calculation (3) SIMULATION RESULT
AVERAGING THOSE ITEMS
THAT ARE “MORE THAN
AVERAGE” CURRENT
PERFORMANCE

43. Example in Excel File_4…
SIMULATION RESULT

44. Example in Excel File_5…
SIMULATION RESULT

45. Discussions on the Methods
• Probability of a Count of Chance in The Respective Quadrants, most
probable in Category 2 -averaging to be between 50 to 80, but
averaging to about above 54%
• Categorization of Trust Level by Limits (considering the data within
the governing limits, “between lower and upper limit” – mean area),
average is about 53% to 62%
• Moving Average within a defined window of view, shows tremendous
improvement, about 64% to 69%

46. _Final Error Calculations
• Small error detected within the method, as stipulated, during
modelling the random numbers, raw data, generated from digital
circuitry – preliminary/fundamental derivation depicts, as shown.
• Low level of error, roughly 1-2% error is acceptable, over a period of
time (about 20 years period cycle, in this case - 20 delivery items –
about 4 weeks or 1 month; 20 years on average for 12 data plot
within each point).

47. Thank you for
your attention