Question

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.

• A. 64 KB, 4 KB
• B. 128 KB, 8 KB
• C. 256 KB, 16 KB
• D. 512 KB, 32 KB

Hint:

For a cache memory configuration, the cache size is determined by the number of sets and the block size. The main memory size depends on the tag, index, and block size.

Answer 1

The Correct Option is A

Step 1: Calculate the size of the cache memory.

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 \( 4 \, \text{KB} \).