$1.$ A system has a $2-$level cache hierarchy with the following parameters:

$$ L$1$ cache: $32$ KB$,$ direct$-$mapped, hit time: $2$ ns

$$ L$2$ cache: $256$ KB$,4-$way set associative, hit time: $10$ ns

$$ Main memory access time: $100$ ns

Assume that the L$1$ cache has a miss rate of $10\%$ and the L$2$ cache has a local miss rate of $20\%.$ Calculate the average memory access time $($AMAT$)$ for this system.