$($b$)$ A computer has $4$ K Word RAM with each memory word of $8$ bits. It has cache memory, having $16$ blocks, having a size of $16$ bits $(2$ memory words$).$ Show how the main memory address $(3$AC$)$h will be mapped to the cache address, if $($i$)$ Direct cache mapping is used $($ii$)$ Associative cache mapping is used $($iii$)$Two$-$way set associative cache mapping is used. You should show the size of the tag, index, main memory block address and offset in your answer. $(3$ Marks$)$