Question $1(10$ points$)-$ Suppose the physical addresses $($address bus$)$ are $32$ bits wide. Suppose there is a cache containing $32$ K cache blocks, and each cache block contains $8$ bytes. Assume that the cache is direct mapped.

Determine the total size of the memory.

Specify how the $32-$bit address would be partitioned. For example, you would need to specify which $($how many$)$: bits are used for selecting the byte within the block $($byte offset$),$ bits are used to index the cache $($index bits$),$ and bits are used to compare against the tag stored in the cache entry $($tag bits$).$