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)

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is \\\\\\\. (Answer in integer) !image(https://uadmin.udsfgecw.tech/file/download/public/public:022d328e-9cfc-4383-b577-5157783c1302.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 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 .