$(12$ pt$)$ A block diagram of the faster multiplier discussed in class is given below. Answer the following

questions assuming this functional unit is used to multiple two $16-$bit numbers.

a$.$ What is the size of multiplicand register?

bits

b$.$ What is the size of product register?

bits

c$.$ What is the maximum width of the product?

bits

d$.$ How many additions $($at most$)$ should be performed by the ALU?

e$.$ How many additions $($at least$)$ should be performed by the ALU?

f$.$ How many shifts should be done?