Minimization PYQ QUIZ GATE CS

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz') is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes "don't care"

Minimum sum of product expression for f(w, x, y, z) shown in Karnaugh-map below is  

Given the following Karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?  

Which function does NOT implement the Karnaugh map given below?

The number of min-terms after minimizing the following Boolean expression is _________.

      [D′ + AB′ + A′C + AC′D + A′C′D]′

Which one of the following circuits implements the Boolean function given below?

f(x,y,z) = m0 + m1 + m3 + m4 + m5 + m6 

where mi is the ith minterm.

Consider the Karnaugh map given below, where X represents “ don’t care” and blank represents 0.

Assume for all inputs (a, c, d) the respective complements (a', b', c', d')are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________. Note: This questions appeared as Numerical Answer Type.

Consider three 4-variable functions f₁, f₂ and f₃, which are expressed in sum-of-minterms

f1 = Σ(0, 2, 5, 8, 14)
f2 = Σ(2, 3, 6, 8, 14, 15)
f3 = Σ(2, 7, 11, 14) 

For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

What is the minimum number of 2-input NOR gates required to implement 4-variable function expressed in sum-of-minterms from as f = Σ(0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer ________ .



Note: This was Numerical Type question.

Given the following Karnaugh Map for a Boolean function 𝐹(𝑤, 𝑥, 𝑦, 𝑧):

Which one or more of the following Boolean expression(s) represent(s) 𝐹?