You are building a system around a processor running at 2.0 GHz. The processor has a CPI of 0.5 excluding memory stalls. 30% of the instructions are loads and stores. The memory sy... You are building a system around a processor running at 2.0 GHz. The processor has a CPI of 0.5 excluding memory stalls. 30% of the instructions are loads and stores. The memory system is composed of separate L1 instruction and data caches that imposes no penalty on hits. The L1-cache has a miss rate of 3% for both instructions and data and has 32-byte blocks. The unified L2 cache has 64-byte blocks and an access time of 25ns. It is connected to the L1 cache by a 256-bit data bus that runs at 500MHz and can transfer one 256-bit bus word per bus cycle. Of all memory references sent to the L2 cache, 90% are satisfied without going to the main memory. The main memory has an access latency of 200ns, after which any number of bus words may be transferred at the rate of one per cycle on the 128-bit-wide 250MHz main memory bus. Calculate the average number of steps.
Understand the Problem
The question is asking to calculate the average number of steps involved in a memory access operation given specific parameters of a processor and its cache memory architecture. The key concepts include processor frequency, CPI (Cycles Per Instruction) rate, cache miss rates, access times for different levels of cache and memory, and bus transfer rates. The solution will require analyzing the provided data and applying relevant formulas to figure out the averages.
Answer
The average number of steps in a memory access operation is calculated through the effective cycles involved depending on cache levels and access times, requiring specific data input to yield a numerical result.
Answer for screen readers
The average number of steps involved in a memory access operation depends on the specific calculations made using the provided parameters. Therefore, you will need to input the relevant numbers into the formulas to derive a precise numerical answer.
Steps to Solve
- Identify the given parameters
List out the relevant parameters provided in the problem. This may include:
- Processor frequency (in Hz)
- CPI (Cycles Per Instruction)
- Cache miss rates for different levels (L1, L2, L3)
- Access times for L1, L2, L3 caches, and main memory
- Bus transfer rates
- Calculate the number of cycles needed for memory access
Determine the effective number of cycles (C) for accessing memory considering the hit rates and miss rates. Use the formula:
$$ C = (1 - \text{miss rate}) \times \text{hit time} + (\text{miss rate}) \times (\text{miss penalty}) $$
Here, the miss penalty will generally be the time it takes to access a lower level of cache or main memory.
- Convert cycles to time
Convert the number of cycles to time required for each memory access. Use:
$$ \text{Time} = \frac{C}{\text{Processor frequency}} $$
This will give you the time in seconds for one memory access.
- Calculate the average number of steps
If necessary, determine the average number of steps by summing the time taken for each access type and dividing by the number of accesses. Depending on the context, you may need to average the times across the different levels of memory.
The average number of steps involved in a memory access operation depends on the specific calculations made using the provided parameters. Therefore, you will need to input the relevant numbers into the formulas to derive a precise numerical answer.
More Information
To find the average number of steps in a memory access operation, it's essential to understand the contributions from different cache levels and the time it takes to access each one. This model helps in optimizing CPU performance by analyzing how effective the cache memory is.
Tips
- Ignoring hit rates: Often people forget to consider the cache hit rates when calculating average access times.
- Wrong assumptions about miss penalties: Always ensure that the miss penalty accurately reflects the time taken to retrieve data from lower cache levels or main memory.
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