Consider a cache that has $4096$ blocks. Assuming a $32-$bit address, find the total number of tags

bits, index bits and offset bits used in addressing, and capacity of this cache $($in KB$)$ when it is:

a$)[4$ points$]$ direct mapped cache and each block contains $16$ words

b$)[4$ points$]4-$way set associative and each block contains $16$ words

c$)[4$ points$]8-$way set associative and each block contains $32$ words

d$)[3$ points$]$ fully$-$associative cache and each block contains $32$ words