Question

what is the hit rate of this call on a unified l2 instruction and data cache that is 2-way set associative, 1024b capacity, with 16b lines?

Answer 1

The hit rate for a unified L2 cache, 2-way set associative, 1024B capacity, with 16B lines is 50%. This is calculated based on the cache's set-associativity, capacity, and line size.

To calculate the hit rate, we need to know the number of sets in the cache, which is determined by the set-associativity and the capacity. The formula for calculating the number of sets (S) is given by:

`\[ S = \frac{\text{Cache Capacity}}{\text{Set Associativity} * \text{Line Size}} \]`

- Cache capacity = 1024 bytes

- Set associativity = 2-way

- Line size = 16 bytes

`\[ S = \frac{1024 \, \text{bytes}}{2 * 16 \, \text{bytes}} = (1024)/(32) = 32 \]`

Now, the hit rate for a 2-way set-associative cache can be calculated using the formula:

`\[ \text{Hit Rate} = 1 - \left( \frac{1}{\text{Set Associativity}} \right) \]`

For a 2-way set-associative cache, the hit rate is:

`\[ \text{Hit Rate} = 1 - \left( (1)/(2) \right) = (1)/(2) \]`

So, the hit rate for this unified L2 cache is
`\( (1)/(2) \)` or 50%.