GATE CS Minimization (K-Maps etc.) questions

Consider a Boolean function $F$ with the following minterm expression: $$F(P, Q, R, S)=\sum m(1,2,3,4,5,7,10,12,13,14)$$ Which of the following options is/are the minimal sum-of-products expression(s) of $F$ ?

Consider the following $4$-variable Boolean function $$F(A, B, C, D)=\Sigma m(0,1,2,3,8,9,10,11)$$ Consider $A$ as MSB, $D$ as LSB. Which one of the following options represents the minimal sum of products form for the above function? Note: ${+}$ is OR operation, ${\cdot}$ is AND operation, ${\prime}$ is NOT operation

Consider the following four variable Boolean function in sum-of-product form $$F\left(b_{3}, b_{2}, b_{1}, b_{0}\right)=\sum(0,2,4,8,10,11,12)$$ where the value of the function is computed by considering $b_{3} b_{2} b_{1} b_{0}$ as a $4$-bit binary number, where $b_{3}$ denotes the most significant bit and $b_{0}$ denotes the least significant bit. …

​​​​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) $F$ ?

Consider a Boolean expression given by $\text{F(X, Y, Z)}=\sum(3,5,6,7)$. Which of the following statements is/are CORRECT?

Consider $4$-variable functions $f 1, f 2, f 3, f 4$ expressed in sum-of-minterms form as given below. $$\begin{array}{l} f 1=\sum(0,2,3,5,7,8,11,13) \\ f 2=\sum(1,3,5,7,11,13,15) \\ f 3=\sum(0,1,4,11) \\ f 4=\sum(0,2,6,13) \end{array}$$ With respect to the circuit given above, which of the following options is/are CORRECT?

Consider the minterm list form of a Boolean function $F$ given below. $$F(P, Q, R, S) = \Sigma m(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)$$ Here, $m$ denotes a minterm and $d$ denotes a don't care term. The number of essential prime implicants of the function $F$ is ___

Consider the Karnaugh map given below, where $X$ represents "don't care" and blank represents $0$. Assume for all inputs $\left ( a,b,c,d \right )$, the respective complements $\left ( \bar{a}, \bar{b}, \bar{c}, \bar{d} \right )$ are also available. The above logic is implemented using $2$-input $\text{NOR}$ gates only. The minimum number of …

Given $f(w, x, y, z) = \Sigma_m(0,1, 2, 3, 7, 8, 10) + \Sigma_d(5, 6, 11, 15)$; where $d$ represents the 'don't-care' condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of $f(w, x, y, z)$?

Consider the following Boolean expression for F: $F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S$ The minimal sum$-$of$-$products form of $F$ is

Consider the following minterm expression for $F$: $$F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15$$ The minterms $2$, $7$, $8$ and $13$ are 'do not care' terms. The minimal sum-of-products form for $F$ is

What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term

The simplified SOP (Sum of Product) from the Boolean expression $$(P + \bar{Q} + \bar{R}) . (P + \bar{Q} + R) . (P + Q +\bar{R})$$ is

In the Karnaugh map shown below, $X$ denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

Consider the following Boolean function of four variables: $$f(w, x, y, z) = \Sigma(1, 3, 4, 6, 9, 11, 12, 14)$$ The function is

Consider a Boolean function $f(w,x,y,z)$. Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors $i_{1}=\left \langle w_{1}, x_{1}, y_{1},z_{1}\right \rangle$ and $i_{2}=\left \langle w_{2}, x_{2}, y_{2},z_{2}\right \rangle$ , we would like the function to remain true as the input …

The switching expression corresponding to $f(A,B,C,D)=\Sigma(1, 4, 5, 9, 11, 12)$ is:

Which are the essential prime implicants of the following Boolean function? $f(a, b, c)= a' c+ ac'+b' c$

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 $\left(xy+xz'\right)$ 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, …

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