Question

Suppose a computer having 5 GHz processor with cycle time of 4ns and main memory access time

200ns with CPI is 1 cycle.

i. Calculate the processor performance without cache.

ii. Calculate the performance with L1 cache, assume L1 hit rate is 85% and access time is 0.4ns.

iii. Calculate the performance with L2 cache, assume L2 hit rate is 80% and access time is 10ns.

iv. Calculate the performance with L3 cache, assume L3 hit rate is 75% and access time is 10ns.

Answer 1

Given,

A computer having 5ghz processor

cycle time = 4hrs

Main Memory = 200ns wit CPI as 1 cycle

(i)Performance without cache =1cycle/instruction

               $=4 hrs$

            $\Rightarrow 4hrs+\text{ memoery access}=4+200=204ns$

(ii)  The Performance with $L_1$ cache, assume $L_1$ hit rate is 85% and access time is 0.4ns.

      $=0.85\times 0.4+0.15[200+0.4]\\=30.4ns$

(iii) The performance with $L_2$ cache, assume $L_2$ hit rate is 80% and access time is 10ns

$=0.85+0.4+0.15[0.4+10]\times 0.8+0.15\times 0.2\times 210.4\\=7.9ns$

(iv) The performance with $L_3$ cache, assume $L_3$ hit rate is 75% and access time is 10ns

      $=0.85\times 0.4+0.15\times 0.8\times 10.4+0.15\times 0.2\times 0.75\times 20.4+0.15\times 0.2\times 0.25\times 220.4\\=3.7ns$