If we want an average memory access time of 6.5 ns, our cache access time is 5 ns, and our main memory access time is 80 ns, what cache hit rate must we achieve?
The correct answer and explanation is :
To find the cache hit rate required to achieve an average memory access time (AMAT) of 6.5 ns, we can use the formula for AMAT:
[
\text{AMAT} = \text{Hit time} + \left( \text{Miss rate} \times \text{Miss penalty} \right)
]
Where:
- Hit time is the cache access time, which is 5 ns.
- Miss penalty is the main memory access time, which is 80 ns.
- AMAT is the desired average memory access time, which is 6.5 ns.
The miss rate can be calculated as ( 1 – \text{Hit rate} ), so we want to find the hit rate (( H )) that satisfies this equation.
Step-by-step Solution:
- Plug the known values into the AMAT formula:
[
6.5 = 5 + (1 – H) \times 80
]
- Simplify the equation:
[
6.5 – 5 = (1 – H) \times 80
]
[
1.5 = (1 – H) \times 80
]
- Solve for ( 1 – H ):
[
1 – H = \frac{1.5}{80}
]
[
1 – H = 0.01875
]
- Finally, solve for the hit rate ( H ):
[
H = 1 – 0.01875
]
[
H = 0.98125
]
Thus, the required cache hit rate is 0.98125, or 98.125%.
Explanation:
In this problem, we are tasked with determining the cache hit rate necessary to achieve a given average memory access time, considering both the cache and main memory access times.
The cache hit rate is crucial because it determines how often data can be accessed directly from the cache (which is fast) versus the main memory (which is slower). The average memory access time (AMAT) depends on how often we experience a cache hit versus a cache miss. A cache hit is faster, as it takes only 5 ns, while a miss results in the much slower 80 ns access to main memory.
Given the required AMAT of 6.5 ns, we calculated that the cache hit rate must be at least 98.125%. This high hit rate ensures that the average time spent accessing memory stays close to the desired 6.5 ns, keeping the system performance optimal. If the hit rate were lower, the system would experience a much higher AMAT due to the slower access time of main memory.