Consider a computer system with the following specifications:

$$ Main memory has a word size of $32$ bits.

$4-$way set$-$associative cache.

$$ Address length is $24$ bits.

$$ Cache line size is $32$ words $($each word is $16$ bits$).$

$$ The total size of the cache is $64$ Kbytes.

Questions:

$1.$ Compute the line size in bytes. Deduce the main memory block size in bytes. $(6$ points$)$

$2.$ Compute the number of possible addressable words in the main memory. Deduce the memory size in bytes and the number of blocks. $(13$ points$)$

$3.$ Compute the set size in bytes and the number of sets. $(6$ points$)$

$4.$ Show the format of main memory addresses. $(10$ points$)$