Probability

Q. 100 coins are tosses together find the probability of getting heads odd no. of times

DIMENSIONS

Dimensions

When a derived quantity is expressed in terms of fundamental quantities, it is written as a product of different powers of the fundamental quantities. The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.

Here the physical quantity that is expressed in terms of the basic quantities is enclosed in square brackets to indicate that the equation is among the dimensions and not among the magnitudes.

Thus equation (i) can be written as [force] = [MLT²].

Such an expression for a physical quantity in terms of the fundamental quantities is called the dimensional equation. If we consider only the R.H.S. of the equation, the expression is termed as dimensional formula.

Thus, dimensional formula for force is [MLT^–2].

advance computer architecture

PROBABILITY

In our daily life, we often used phrases such as 'It may rain today', or 'India may win the match' or ' I may be selected for this post.' These phrases involve an element of uncertainty. How can we measure this uncertainty ? A measure of this uncertainty is provided by a branch of Mathematics, called the theory of probability.
Probability Theory is designed to measure the degree of uncertainty regarding the happening of a given event. The dictionary meaning of probability is ' likely though not certain to occur. Thus, when a coin is tossed, a head is likely to occur but may not occur. Similarly, when a die is thrown, it may or may not show the number 6.

Mathematics Fact

1.       Jean Robert Argand (1768-1822) was Swiss Mathematician who publish the idea of geometrical representation of complex number known as Argand Diagram

combinational logic

In digital circuit theory, combinational logic (sometimes also referred to as time-independent logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has memory while combinational logic does not.

DIGITAL ELECTRONIC

 

 

QS.1(i) What is the binary equivalent of the decimal number (368)₁₀

Ans.

The Binary equivalent of the Decimal number (368)₁₀ is (101110000)_2.

 

QS.1(ii) The decimal equivalent of hex number 1A53 is

Ans. The decimal equivalent of Hex Number 1A53 is 6739

(Conversion from Hex Number to Decimal Number is given below)

1 A 5 3 Hexadecimal

16³ 16² 16¹ 16° Weights

(1A53)16 = (1X16³) + (10 X 16²) + (5 X 16¹) + (3 X 16º)

= 4096 + 2560 + 80 + 3

= 6739

 

QS.2 The simplification of the Boolean expression (ABC)+ (ABC) is

Ans.  The Boolean expression is (ABC)+ (ABC) is equivalent to 1

(ABC)+ (ABC) = A + B +C + A + B +C = A + B + C + A + B + C

= (A+ A )(B+ B )(C+C ) = 1.1.1 = 1

 

QS.3The Gray code for decimal number 6 is equivalent to?

Ans. The Gray code for decimal number 6 is equivalent to 0101

Decimal number 6 is equivalent to binary number is 0110

 

QS.4. Simplify the following expression into sum of products using Karnaugh map

F(A,B,C,D) = _(1,3,4,5,6,7,9,12,13).

Ans. Simplification of the following expression into sum of products using Karnaugh

Map:

F(A,B,C,D) = S (1,3,4,5,6,7,9,12,13)

Karnaugh Map for the expression F(A,B,C,D) = S (1,3,4,5,6,7,9,12,13)

is shown in Fig.5(a). The grouping of cells is also shown in the Figure.

Fig.4(a)

 

QS.5 Simplify and draw the logic diagram for the given expression

F = ABC+ ABC+ ABC+ ABC+ ABC.

Ans. Simplification of the logic expression

F = ABC + AB C + ABC + A BC + A B C

F = ABC + AB C + ABC + A BC + A B C

F = A + B +C + ( A + B )C + ABC + A ( B +C ) + A B C

(Q ABC = A + B +C and AB = A + B by using Demorgan’s Law)

= A + B +C + AC + B C + ABC + A B + AC + A B C

= A + AC+ B + B C +C + AC + ABC +A B + A B C

= A (1+C)+ B (1 + C) +C (1 + A) + ABC + A B + A B C

= A + B +C + ABC + A B + A B C {Q (1+C) = 1 and (1+A) = 1}

= ( A + A B ) + B (1 + AC) +C (1+ AB)

= ( A + B )+ B +C {Q ( A + A B ) = ( A + B ); (1+AC) = 1 and (1+ AB) =1}

F = ( A + B +C ) (Q B + B = B )

The logic diagram for the simplified expression F = ( A + B +C ) is given in fig.6 (a)

Fig.5(a) Logic diagram for the expression F = ( A + B +C )

 

Important Questions on DIGITAL & ANALOG COMMUNICATION

Q1. Effect of Limited Bandwidth on Digital Signal. Explain.

Q2. Define and explain Shannon limit theorem.

Q3. Discuss different communication modes. Differentiate between asynchronous and synchronous transmission.

Q4. Difference between Secret key cryptography and public Key cryptography.

Q5. Explain with diagram different components of a communication system.

Q6. Explain properties of Fourier transform.

Q7. If f(t)-F(w) is Fourier transform pair. Find the Fourier transform of the following:

(i) f(t) coswot (ii) f2(t) (iii) F(-2t)

Q8. Explain the two physical layer interfaces i.e., RS232 and X.21

Q9. The bit sequence 1011101011 is to be transmitted using formats:

i) Unipolar RZ & NRZ

ii) Bipolar RZ & NRZ

Q10. Explain different transmission media:

(i) Fiber Optics (ii) Twisted pair (iii) Coaxial Pair

Q11. Explain following terms:

(i) Nyquist rate (ii)Shannon Limit

 

Q12. Differentiate between TDM and WDM.

Q13. Explain ISDN with applications, advantages & Disadvantages.

Q14. Differentiate between circuit switching and packet switching systems.

Q15. Explain the sliding window protocol in detail.

Q16. Explain the following:

(i) Data compression (ii) Run Length encoding

Q17. Draw and explain the basic block diagram of communication system.

Q18. What are the properties of signal? Compare analog signal and digital signal.

Q19. What are ESD and PSD? Derive expression for both.

Q20. Explain error detection and parity check.

Q21. Define Modulation: Amplitude, Phase and frequency.

Q22. Differentiate between connection oriented and connectionless service.

Q23. What are transmission impairments?

Q24. Explain Huffman encoding with the help of example.

Q25. Describe PSTN.

Unit - 4 ACA

Advance computer architecture unit4.ppt

Shared memory multiprocessor

https://www.dropbox.com/s/99zo2hc4al3zb8k/unit5.ppt

Advance Computer Architecture unit3.ppt