You have been asked to improve the security of a computer encryption system from $16-$bit encryption to a $22-$bit encryption system.

Answer the following questions. For each answer, you must show your working.

i$.$How many possible keys are available in the $16-$bit system?

ii$.$How many possible keys are available in the $22-$bit system?

iii.How much more secure is the new $22-$bit system than the $16-$bit system?