A$)$ A memory system has $256MB.$ The memory is organized into blocks of $256B$ each, and the cache has total $512$KB$,$ organized into cache block frames of $256$B each.

I$)$ How many bits are needed to address all bytes in the memory system?

II$)$ How many memory blocks we have in the memory system? How many bits are needed to address all memory blocks?

III$)$ How many block frames are there in the cache? how many bits are needed to address all block frames?

IV$)$ For direct cache mapping, what would be the Block address $($concatenate the Tag and BF index$),$ Tag, BF index and Byte Offset in Hex form for the following byte addresses?

$\backslash$table$[[$Address$,$Block Address,Tag,Block Frame Index,Byte Offset$],[$A$1=$ ADB$86$E$2$h$,,,,]]$

B$)$ If cache is organized into $8-$way set associative cache, how many bits are required for the Tag,

Set and Byte Offet? What are the Tag, Set and Word values for the following byte addresses?

Address Tag Set Word

$\backslash$table$[[$Address$,$Tag,Set index,Byte Offset$],[$ADB$86$E$2$h$,,,]]$