seminar on BASICS OF PROBABILITIES

AND RANDOM LOGIC SIGNALS

BY TEJASHREE PATIL

1DS15LVS12

CONTENTS

Basics of probabilities Relative frequency and classical definition of probability Conditional probability, PDF and theorem of total probability Introduction to probabilistic power analysis Random logic signals Conclusion References

1. Basics of probabilities

Probability is the measure of the likelihood that an event

will occur or chance of getting an expected outcome.

It deals with the result of an experiment whose outcome is

not known in advance.

Tossing a coin involves only two outcomes : head and

tail. 

The higher the probability of an event, the more certain

we are that the event will occur.

Continued..

Let “ S ” is the sample space which is the collection of all possible outcomes of an experiment. For tossing a coin experiment S={ H, T } Here ‘H’ and ‘T’ are called sample points. Event: It is a subset of sample space ‘S’ Operations with events : If A and B are any two events then ,

(AᴗB) is an event which occurs if A occurs or B occurs or when both A and B occurs together.

(AᴖB) is an event which occurs if A occurs and B occurs.

Ᾱ is an event which occurs only when A does not occur.

2. Relative frequency and classical definition of probability

Let ‘E’ be the statistical experiment which repeats ‘n’ number of times.

Let A and B are events associated with E. and be the number of time event A and B occurs in

Experiment E respectively.

The relative frequency of A= ; for B =

Classical definition of probability =

3. Conditional probability, PDF and theorem of total probability

P(B/A)= P(AᴗB)/ P(A)

P(A/B)= (AᴖB)/ P(B)

Probability density function : Probability density function or density of a continuous random

variable, is a function that describes the relative likelihood for this random variable to take on a

given value. Theorem of total probability: Let ‘S’ be the sample space, B1,B2…….Bn are the events.

which are mutually exclusive and are not null events. Then , probability of a random event

‘A’ is given by,

Continued…….

4. Introduction to probabilistic power analysis

A logic signal is viewed as a random zero-one process with certain statistical

characteristics.

This approach is used at gate level abstraction and above.

The primary reason for probabilistic analysis is its high computational efficiency.

The biggest drawback is loss in its accuracy.

5. Random logic signals

Fig. 1 A logic signal and its characterization

Fig 2. two different logic signals with identical frequency

Continued..

from figure 1, :- Initial state=1

:- Time value when each transition can occur is ( 5, 15, 20, 35, 45 )

Frequency = (number of times signal changes its state / period)

From figure 2, both the signals have identical number of transitions irrespective of their periods.

Power dissipation,

5.1 Continuous and Discrete random signals

Continuous signal model : it reflects the precise time of signal transition.

Discrete signal model : signal switching is based on clock.

advantages : simplicity in signal representation and processing

6. CONCLUSION

To improve computational efficiency, we move for probabilistic power analysis. But there

is a loss of accuracy.

This presentation is mainly focused on basics of probabilities and we have come across

introduction to probabilistic power analysis.

7. REFERENCES

Text book - Gray Yeap , “ Practical low power digital VLSI design”

Text book- K. Giridhar , “Information theory and coding”

Probability - Wikipedia, the free encyclopedia

Probability density function - Wikipedia, the free encyclopedia

THANK YOU