Consider a hypothetical $48-$bit microprocessor having $48-$bit instructions composed of two fields. The first byte contains the opcode, and the remainder an immedidate operand or an operand address.

$($a$)$ What is the maximum directly addressable memory capacity $($in bytes$)?$ You can specify this in powers of two if you want.

$($b$)$ How many bits are needed for the program counter and the instruction register?