$.$ Consider the below control unit representation diagram. The control unit is represented using $32$ bits. There are two fields in the control portion of the microinstruction format. The $15-$bit micro$-$operation field specifies the type of micro$-$operation to be selected. An address selection field indicates the circumstance under which a microinstruction brarich will occur based on the flags. There are a total of $16$ flags. Answer the following:

$107$

a$.$ Number of bits available for address selection field.

b$.$ Number of bits in the address field.

c$.$ Total size of the control memory

B$.$ As mentioned, while studying the arithmetic left shift and logical left shift corresponds to a multiplication by $2$ considering the scenario where there is no overflow. Now let's suppose if there occurs an overflow while performing the multiplication using both the shifts, then both the arithmetic and logical left shift produces different results, while arithmetic left shift is capable of retaining the sign of the number. Show that these statements are valid for $6-$bit twos complement integers.