Q$\mathrm{.}2.(20$ points$)$ A computer has the following memory and cache characteristics:

$-1$ GB main memory

$-256$ KB cache

$-$ The cache is $4-$way set associative

$-$ There are $16$ words in a block

$-$ Each word is $4$ bytes

Answer the following questions. Show all calculations.

a$.$ How many bits are there in a main memory address?

b$.$ How many blocks are there in the main memory?

c$.$ How many sets are there in the cache?

d$.$ Show the tag, set and word fields of the memory addresses. How many bits are there in each field? tag set word