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 _______.

A 4-bit priority encoder has inputs $D_3, D_2, D_1,$ and $D_0$ in descending order of priority. The two-bit output $AB$ is generated as 00, 01, 10, and 11 corresponding to inputs $D_3, D_2, D_1,$ and $D_0$, respectively. The Boolean expression of the output bit $B$ is _______.

The propagation delay of the 2 x 1 MUX shown in the circuit is 10 ns. Consider the propagation delay of the inverter as 0 ns.

If S is set to 1 then the output Y is _______.

The sequence of states $(Q_1 Q_0)$ of the given synchronous sequential circuit is ________.