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Examples of calculation Effect Access Time using TLB

Effective memory Access Time (EMAT) for single-level paging with TLB hit and miss ratio:

Or, 

EMAT for Multi-level paging with TLB hit and miss ratio:

Or, 

From the above two formulas we can calculate EMAT, TLB access time, hit ratio, memory access time.

Example 1: Here calculating Effective memory Access Time (EMAT) where TLB hit ratio, TLB access time, and memory access time is given.

Example 2: Here calculating Effective memory Access Time (EMAT) for Multi-level paging system, where TLB hit ratio, TLB access time, and memory access time is given. 

Example 3: Here calculating the hit ratio, where EMAT, TLB access time, and memory access time is given.

Example 4: Here calculating TLB access time, where EMAT, TLB hit ratio and memory access time is given.

Example 5: Here calculating memory access time, where EMAT, TLB access time, and the hit ratio is given.

Example 1:

Consider a paging system, it takes 10ns to search translation lookaside buffer (TLB) and 80ns to access main memory. If the TLB hit ratio is 80%, the effective memory access time is 

Solution:

In question, if the level of paging is not mentioned, we can assume that it is single-level paging.

Effective memory Access Time (EMAT) for single-level paging with TLB hit ratio:

Here hit ratio (h) = 80% means here taking 0.8, memory access time (m) = 80ns and TLB access time (t) = 10ns.

So, 

So, Effective memory Access Time (EMAT) = 106 ns

We can solve it by another formula:

Here hit ratio = 80%, so miss ration = 20%

Note: We can use any formula answer will be same.

Example 2:

A 3 level paging scheme uses a Translation Look-aside Buffer (TLB). A TLB-access takes 20 ns and the main memory access takes 70 ns. What is the effective access time (in ns) if the TLB hit ratio is 70%?

Solution:

Here it is multi-level paging where 3-level paging means 3-page table is used.

EMAT for Multi-level paging with TLB hit and miss ratio:

Here hit ratio (h) = 70% means we are taking 0.7, memory access time (m) = 70ns, TLB access time (t) = 20ns and page level (k) = 3

So, 

So, Effective memory Access Time (EMAT) = 153 ns

We can solve it by another formula for multi-level paging:

Here hit ratio = 70%, so miss ration =30%

Note: We can use any formula answer will be same.

Example 3:

Consider a paging system, it takes 10ns to search translation lookaside buffer (TLB) and 80ns to access main memory. If the effective memory access time (EMAT) is 106ns, then find the TLB hit ratio.

Solution:

In question, if the level of paging is not mentioned, we can assume that it is single-level paging.

Effective memory Access Time (EMAT) for single-level paging with TLB hit ratio:

Here hit ratio = h, memory access time (m) = 80ns , TLB access time (t) = 10ns and Effective memory Access Time (EMAT) = 106ns

So, 

So, Hit ratio= 0.8 means 80%. 

Example 4:

A single-level paging system uses a Translation Look-aside Buffer (TLB) where memory access takes 100ns and hit ratio of TLB 80%. If Effective memory Access Time (EMAT) is 140ns, then find TLB access time.

Solution:

Effective memory Access Time (EMAT) for single level paging with TLB hit ratio:

Here hit ratio = 80% means we are taking 0.8, memory access time (m) = 100ns,Effective memory Access Time (EMAT) = 140ns and let TLB access time = t

So, 

So, TLB access time = 20ns. 

Example 5:

A single-level paging system uses a Translation Look-aside Buffer (TLB). A TLB-access takes 20 ns as well as a TLB hit ratio of 80%. What is the main memory access takes (in ns) if Effective memory Access Time (EMAT) is 140ns access time?

Solution:

Effective memory Access Time (EMAT) for single-level paging with TLB hit ratio:

Here hit ratio = 80% means we are taking 0.8,TLB access time = 20ns,Effective memory Access Time (EMAT) = 140ns and let memory access time = m.

So, 

So, main memory access time = 100 ns.