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 _______.

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 _______.