Consider a byte$-$addressable computer with $16-$bit addresses, a cache capable of storing a total of $2$K bytes of data, and blocks of $8$ bytes. Show the format $($include field names and sizes$)$ of a $16-$bit memory address for:

a$)$ direct mapped

b$)$ fully associative

c$)4-$way set associative

d$)$ Where $($which block or set$)$ in cache would the memory address BAD$016$ be mapped for each of the three mapping techniques above? Specify the answer in decimal.

$6.$ Given a cache access time of $20$ns$,$ a main memory access time of $1000$ns$,$ and a cache hit ratio of $90$ percent. Assuming fetches to main memory are started in parallel with look$-$ups in cache, calculate the effective $($average$)$ access time of this system. $($There is no virtual memory on this system, no page table, no TLB$).$