Consider a Boolean function $F$ with the following minterm expression:

$$ F(P, Q, R, S)=\Sigma m(1,2,3,4,5,7,10,12,13,14) $$

Which of the following options is/are the minimal sum-of-products expression(s) of $F$ ?

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 the following four variable Boolean function in sum-of-product form

$$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$

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. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for $F$ ?

What is the minimum number of 2-input NOR gates required to implement a 4-variable function function expressed in sum-of-minterms form as

f = Σ(0, 2, 5, 7, 8, 10, 13, 15)?

Assume that all the inputs and their complements are available.