A CPU is equipped with a cache. If it takes 5 ns to access the data from the cache and 60 ns to access data from the main memory. What should be the hit ratio if the effective memory access time is 8 ns? Answer=

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**Question:**

A CPU is equipped with a cache. If it takes 5 ns to access the data from the cache and 60 ns to access data from the main memory, what should be the hit ratio if the effective memory access time is 8 ns?

**Answer = ________________%**

**Explanation:**

To find the hit ratio, you can use the formula for effective memory access time:

\[ \text{Effective Access Time (EAT)} = (\text{Hit Ratio} \times \text{Cache Access Time}) + ((1 - \text{Hit Ratio}) \times \text{Main Memory Access Time}) \]

Given:
- Cache Access Time = 5 ns
- Main Memory Access Time = 60 ns
- Effective Access Time = 8 ns

Substitute the values:

\[ 8 = (\text{Hit Ratio} \times 5) + ((1 - \text{Hit Ratio}) \times 60) \]

Solve for Hit Ratio:

1. Expand the equation: 
   \[ 8 = 5 \times \text{Hit Ratio} + 60 - 60 \times \text{Hit Ratio} \]

2. Combine like terms:
   \[ 8 = 60 - 55 \times \text{Hit Ratio} \]

3. Rearrange:
   \[ 55 \times \text{Hit Ratio} = 60 - 8 \]

4. Simplify:
   \[ 55 \times \text{Hit Ratio} = 52 \]

5. Divide both sides by 55:
   \[ \text{Hit Ratio} = \frac{52}{55} \approx 0.9455 \]

Therefore, the hit ratio should be approximately 94.55%.

Fill in the answer:
**Answer = 94.55%**
Transcribed Image Text:**Question:** A CPU is equipped with a cache. If it takes 5 ns to access the data from the cache and 60 ns to access data from the main memory, what should be the hit ratio if the effective memory access time is 8 ns? **Answer = ________________%** **Explanation:** To find the hit ratio, you can use the formula for effective memory access time: \[ \text{Effective Access Time (EAT)} = (\text{Hit Ratio} \times \text{Cache Access Time}) + ((1 - \text{Hit Ratio}) \times \text{Main Memory Access Time}) \] Given: - Cache Access Time = 5 ns - Main Memory Access Time = 60 ns - Effective Access Time = 8 ns Substitute the values: \[ 8 = (\text{Hit Ratio} \times 5) + ((1 - \text{Hit Ratio}) \times 60) \] Solve for Hit Ratio: 1. Expand the equation: \[ 8 = 5 \times \text{Hit Ratio} + 60 - 60 \times \text{Hit Ratio} \] 2. Combine like terms: \[ 8 = 60 - 55 \times \text{Hit Ratio} \] 3. Rearrange: \[ 55 \times \text{Hit Ratio} = 60 - 8 \] 4. Simplify: \[ 55 \times \text{Hit Ratio} = 52 \] 5. Divide both sides by 55: \[ \text{Hit Ratio} = \frac{52}{55} \approx 0.9455 \] Therefore, the hit ratio should be approximately 94.55%. Fill in the answer: **Answer = 94.55%**
A CPU is equipped with a cache. If it takes 5 ns to access the data from the cache and 60 ns to access data from the main memory, what is the effective memory access time if the hit ratio is 90%?

Answer = _______________ ns

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Transcribed Image Text:A CPU is equipped with a cache. If it takes 5 ns to access the data from the cache and 60 ns to access data from the main memory, what is the effective memory access time if the hit ratio is 90%? Answer = _______________ ns [Input box]
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