Q. Consider the four-variable Boolean function, f(𝑤,𝑥,𝑦,𝑧)=∑𝑚(0,2,5,7,8,10,13,14,15) with ‘w’ as MSB and ‘z’ as LSB. Which of the following expressions is/are the valid form(s) of 𝑓(𝑤,𝑥,𝑦,𝑧)?   (A) 𝑥̅𝑧̅+𝑥𝑧+𝑤𝑥𝑦 (B) 𝑥𝑧+𝑤𝑥𝑦+ 𝑤𝑥̅𝑧̅+𝑤 𝑥𝑦𝑧̅ (C) 𝑥̅𝑧̅+𝑤𝑥𝑦+𝑤𝑥̅𝑧̅+𝑤 𝑥𝑦𝑧̅ (D) 𝑥̅𝑧̅+𝑥𝑧+𝑤𝑦𝑧̅ Solution Group 1: (0, 2, 8, 10) → x ′ z ′ x ′ z ′ Group 2: (5, 7, 13, 15) → x z x z Group 3: (10, 14) → w y z ′ w y z ′ xz + wyz^ + w^x^y^z^ + wx^y^z^ + w^x^yz^ + wx^yz^ = xz + wyz^ + x^y^z^ + x^yz^ = xz + wyz^ + x^z^ or,  Group 1: (0, 2, 8, 10) → x ′ z ′ x ′ z ′ Group 2: (5, 7, 13, 15) → x z x z Group 3: ( 14, 15) → w y z ′ wxy Answer A, D

  Q. For an ideal photodiode (η = 1), the responsivity (R) is equal to: Given Options: 1. λ / 2.14 (A/W) 2. 2.14 / λ (A/W) 3. λ / 1.24 (A/W) 4. 1.24 / λ (A/W) Correct Answer: Option 3 R = λ / 1.24 A/W Step-by-Step Solution Step 1: Write the Responsivity Formula The responsivity of a photodiode is defined as the ratio of photocurrent to incident optical power. R = ηq / hν Where: R = Responsivity (A/W) η = Quantum efficiency q = Electronic charge h = Planck's constant ν = Frequency of incident light Step 2: Convert Frequency into Wavel...

  The Casimir effect is a quantum mechanical phenomenon in which two uncharged, parallel conducting plates experience an attractive force when placed very close to each other in a vacuum. It occurs due to quantum fluctuations of the electromagnetic field (vacuum fluctuations). 1. Basic concept Imagine two parallel metal plates placed very close to each other in a vacuum. Electromagnetic field fluctuations exist even in a vacuum. Only certain electromagnetic modes can exist between the plates. The vacuum energy between the plates differs from that outside. This difference produces an attractive force between the plates. Important: Vacuum is not completely empty according to quantum field theory. 2. Casimir force formula For two ideal, perfectly conducting parallel plates: F = − π 2 ℏ c A 240 d 4 \boxed{F=-\frac{\pi^2\hbar c A}{240d^4}} Where: F F = Casimir force ℏ \hbar = Re...