Q. Let 𝐻(𝑋) denote the entropy of a discrete random variable 𝑋 taking 𝐾 possible distinct real values. Which of the following statements is/are necessarily true?    (A) 𝐻(𝑋)≤logH𝐾 bits   (B) 𝐻(𝑋)≤𝐻(2𝑋)   (C) 𝐻(𝑋)≤𝐻(𝑋^2)   (D) 𝐻(𝑋)≤𝐻(2^X)  Answer: Option 1,2, and 4 Solution:  Option A:  (Correct) if K symbols having equal probability the maximum entropy = log2(K); other wise 𝐻(𝑋)≤logH𝐾 bits  Option B: (Correct) -plog2p ≤ -2plog2p Option C: (false) Think about X^2 = 4 then. X = 1,-1. Whenever different outcomes merge into one outcome, entropy decreases. Option D: (Correct) If every value of 2^X produces a unique output, the probabilities are just relabeled. The uncertainty is unchanged, so the entropy stays the same. If exactly one value of XXX maps to yyy, the probability stays the same. If two or more values of XXX map to yyy, you add their probabilities. GATE EC Previo...

Q. Select the correct statement(s) regarding CMOS implementation of NOT gates.   (A) Noise Margin High (𝑁𝑀H) is always equal to the Noise Margin Low (𝑁𝑀H), irrespective of the sizing of transistors.   (B) Dynamic power consumption during switching is zero.   (C) For a logical high input under steady state, the nMOSFET is in the linear regime of operation.   (D) Mobility of electrons never influences the switching speed of the NOT gate.   Answer: Option C Solution Option A : NMH and NML are generally not equal because electron mobility is about 2–3 times hole mobility. Designers often make pMOS wider (roughly 2–3×) to equalize them. Option B:  Whenever the output changes, the load capacitor charges/discharges. Therefore dynamic power is non-zero during switching. Option C:   (Correct)  Hence the nMOS is indeed in the linear (triode) region at steady state.  Option D:  Higher electron mobility ⇒ higher cu...

  Select the Boolean function(s) equivalent to 𝑥+𝑦𝑧, where 𝑥,𝑦, and 𝑧 are Boolean variables, and + denotes logical OR operation.   (A) 𝑥+𝑧+𝑥𝑦   (B) (𝑥+𝑦)(𝑥+𝑧)   (C) 𝑥+𝑥𝑦+𝑦𝑧   (D) 𝑥+𝑥𝑧+𝑥𝑦  Answers: Options B and C Solution: Option B:  (𝑥+𝑦)(𝑥+𝑧) = x.x + x.z + x.y + yz = x(1+y+z) + yz =  x+yz Option C:  𝑥+𝑥𝑦+𝑦𝑧 = x(1+y)+yz = x+yz GATE EC Previous Year Papers with Solutions → Electronics and Communication Study Material →

  An ideal OPAMP circuit with a sinusoidal input is shown in the figure. The 3 dB frequency is the frequency at which the magnitude of the voltage gain decreases by 3 dB from the maximum value. Which of the options is/are correct?  Answer: Option B and C Solution: Vout/Vin = -Rf/Rin = -2/(1+1/jwC) at, w = infinite, Vout/Vin = -2 at, w = 0, Vout/Vin = 0 So, it is highpassfilter and 3 dB cutoff frequency of the OPAMP is  1/2*pi*RC = 1000 rad/sec Further Reading What is - 3dB Frequency Response? And applications GATE EC Previous Year Papers with Solutions → Electronics and Communication Study Material →

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