Given the following cache parameters:
\[
\begin{array}{|c|c|}
\hline
\textbf{Tag} & 4 \, \text{bits} \\
\textbf{Index} & 12 \, \text{bits} \\
\textbf{Block Size} & 1 \, \text{byte} \\
\hline
\end{array}
\]
Find the size of the main memory and the size of the cache memory.
Given the following cache parameters:
\[ \begin{array}{|c|c|} \hline \textbf{Tag} & 4 \, \text{bits} \\ \textbf{Index} & 12 \, \text{bits} \\ \textbf{Block Size} & 1 \, \text{byte} \\ \hline \end{array} \]Find the size of the main memory and the size of the cache memory.
Show Hint
- 64 KB, 4 KB
- 128 KB, 8 KB
- 256 KB, 16 KB
- 512 KB, 32 KB
The Correct Option is A
Solution and Explanation
The cache size is given by the formula: \[ \text{Cache Size} = \text{Number of Sets} \times \text{Block Size} \] - The number of sets is \( 2^{\text{Index bits}} = 2^{12} = 4096 \).
- The block size is 1 byte.
Thus, the cache size is: \[ \text{Cache Size} = 4096 \times 1 = 4096 \, \text{bytes} = 4 \, \text{KB}. \]
Step 2: Calculate the size of the main memory.
The size of the main memory is calculated as: \[ \text{Main Memory Size} = 2^{\text{Tag bits} + \text{Index bits} + \text{Block size bits}} = 2^{4 + 12 + 0} = 2^{16} = 65536 \, \text{bytes} = 64 \, \text{KB}. \]
Thus, the main memory size is \( 64 \, \text{KB} \) and the cache memory size is \( 4 \, \text{KB} \).
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