Consider a system $S$ represented in state space as

$$\frac{dx}{dt} = \begin{bmatrix} 0 & -2 \\ 1 & -3 \end{bmatrix}x + \begin{bmatrix} 1 \\ 0 \end{bmatrix}r , \quad y = \begin{bmatrix} 2 & -5 \end{bmatrix}x.$$

Which of the state space representations given below has/have the same transfer function as that of $S$?

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 _________.

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is __________.

In a number system of base $r$, the equation $x^2 - 12x + 37 = 0$ has $x = 8$ as one of its solutions. The value of $r$ is _______.