Suppose we have a $4$ KB direct$-$mapped data cache with $4-$byte blocks. a$)$ Show how a $32-$bit memory address is divided into tag, index and offset. Show clearly how many bits are in each field. $(10$ points$)$ b$)$ How many total bits are there in this cache? $(10$ points$)$ c$)$ Consider this address trace: $0$x$480145540$x$480145480$x$480147540$x$480347600$x$480145540$x$480145600$x$480147600$x$48014554$ For this cache, for each address in the above trace, show the tag, index and offset in binary $($or hex$).$ Indicate whether each reference is a hit or a miss. What is the miss rate? $(15$ points$)$