Suppose a computer using direct mapped cache has $1048576$ words of main memory, and a cache of $32$ blocks, where each cache block contains $16$ words.

a$.$ How many blocks of main memory are there?

b$.$ What is the format of a memory address as seen by the cache, i$.$e$.,$ what are the sizes of the tag, block, and word fields?

c$.$ To which cache block will the memory reference $0DB{63}_{16}$ map?