$1.(15$ pts$)$ Consider a system with a direct mapped cache with $256$ KB of data and $8-$word blocks. The smallest addressable unit is a byte, $1$ word is defined as $32$ bits, and memory addresses are $32$ bits long.$($a$)$ Calculate the total number of kilo bits $($Kbits$)$ required to implement the cache.$($b$)$ Show the partitioning of a memory address into the appropriate fields with the numbers of bits.