GATE CS 2012 Q30 — Minimization (K-Maps etc.)

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?