$(1)$A word addressable computer system uses a direct mapped cache with $1$G Byte of main memory and a cache consisting of $256$ blocks, where each cache block holds $16$ words, and each word is $4$ bytes.

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

b$.$ What is the format of a memory address as interpreted by the cache $($Tag$,$ Block, and Word fields$)?$

c$.$ To which cache block will the memory reference $00$AB$3$D$28$ in Hex map?