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consider a 2-level $L_1$ and $L_2$ memory hierarchy system.The associativity of $L_1$ towards processor is more .$L_1$(cache ) has accessing time of 15 ns and $L_2$ (main memory) has an accessing time of 100 ns .writing takes 30 ns for $L_1$ and 150 ns for $L_2$.assume 30% read misses in $L_1$ memory .50% of the program instructions are read only instructions .what is the average access time for the system if it uses write through protocol?

answer given-95.25 ns

my attempt-

since here nothing is mention about hit ratio or miss ratio for write means writing is done simultaneously  

so  $T_w=150 ns$

$T_r=.7*15ns+.3*(100ns+15ns)=45ns$

$T_{avg}=.5*45+.5*150=97.5ns$

please verify it.
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