Consider the following four variable Boolean function in sum-of-product form $$F(b3, b2, b1, b0) = \sum(0, 2, 4, 8, 10, 11, 12)$$ where the value of the function is computed by considering $b3b2b1b0$ as a $4$-bit binary number, where $b3$ denotes the most significant bit and $b0$ 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 $F$?

Consider a finite state machine (FSM) with one input $X$ and one output $f$, represented by the given state transition table. The minimum number of states required to realize this FSM is \\\\\\\. (Answer in integer) !image(https://uadmin.udsfgecw.tech/file/download/public/public:0fda99fb-d8d4-40ac-ae15-c568c40bf1af.png)

Let $X$ be a 3-variable Boolean function that produces output as ‘$1$’ when at least two of the input variables are ‘$1$’. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

The number $-6$ can be represented as $1010$ in 4-bit 2’s complement representation. Which of the following is/are CORRECT 2’s complement representation(s) of $-6$?

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

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively. image needed to be inserted here For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is

For the Boolean function $F(A, B, C, D) = \sum m(0, 2, 5, 7, 8, 10, 12, 13, 14, 15)$, the essential prime implicants are .