$(20$ 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.

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

$$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 held?