Consider a memory system with the following characteristics:

$64-$bit virtual address

$2-$way set associative TLB

$256$ total TLB entries

$2KB$ page size

$42-$bit physical address

$4-$way set associative cache

$512KB$ cache

$64-$byte cache line $($block$)$

a$)$ Determine the size $($in bits$)$ of each of the labeled fields below:

Virtual Address

A

D$.$

B

E

C

F

b$)$ To what set in the cache does the physical address $0000058$C$942$ map to$?$

c$)$ To what set in the TLB does the virtual address $0000000004$ AB$5870$ map to$?$