Suppose you have to decide if you would like to use a one Level cache or a $2$ Level cache processor in a system with a memory which exhibits $50$ ns access. The cache exhibits the following performance characteristics:

Level $1$ cache:

Split configuration with:

I miss rate $4\%$

D miss rate $8\%$

Frequency of data accesses $20\%$

Hit time at Level $1$ is $0\mathrm{.}25$ns

Level $2$ cache:

Unified configuration with:

Miss rate $5\%$

Hit time at Level $2$ is $2$ ns

Compare the AMAT for the system with only L$1,$ and the system with L$1$ and L$2.$