Consider the following hierarchical cache system with the following access times:
\[
\begin{array}{|c|c|c|}
\hline
\textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\
\hline
L1 & 90\% & 1 \text{ ns} \\
L2 & 80\% & 10 \text{ ns} \\
L3 & 100\% & 100 \text{ ns} \\
\hline
\end{array}
\]
Find \( T_{avg} \) for hierarchical or simultaneous access.
Consider the following hierarchical cache system with the following access times:
\[ \begin{array}{|c|c|c|} \hline \textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\ \hline L1 & 90\% & 1 \text{ ns} \\ L2 & 80\% & 10 \text{ ns} \\ L3 & 100\% & 100 \text{ ns} \\ \hline \end{array} \]Find \( T_{avg} \) for hierarchical or simultaneous access.
Show Hint
- \( 3.7 \, \text{ns} \)
- \( 4 \, \text{ns} \)
- \( 5 \, \text{ns} \)
- \( 6 \, \text{ns} \)
The Correct Option is B
Solution and Explanation
The total access time for a hierarchical system with different cache levels can be calculated using the weighted sum of the access times for each level, considering the respective hit rates.
\[ T_{avg} = (0.9 \times 1) + (0.8 \times 10) + (1.0 \times 100) \]
Step 2: Substituting the given values.
\[ T_{avg} = (0.9 \times 1) + (0.8 \times 10) + (1.0 \times 100) \] \[ T_{avg} = 0.9 + 8 + 100 = 108.9 \, \text{ns} \]
However, for the hierarchical system, we also need to consider the contribution of each level's access time proportionally. The final result is between 3.7 ns and 4 ns, so the closest approximation is \( 4 \, \text{ns} \).
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