Application Of Amdahl's Law: Answer The Following Two Questi

Application Of Amdahl's Lawanswer The Following Two Questio

The provided questions primarily focus on computational performance analysis using Amdahl's Law, as well as topics related to memory technologies and their applications. The core assignment tasks are:

  1. Calculate the overall speedup when making specific portions of a program faster, based on given parameters, utilizing Amdahl's Law.
  2. Determine the percentage of total memory operation time required for refresh cycles in a dynamic RAM system.
  3. List and briefly define three emerging nonvolatile solid-state memory technologies.
  4. Explain the differences between DRAM and SRAM in terms of application, speed, size, and cost.

Paper For Above instruction

Analyzing the performance enhancements achievable through Amdahl's Law provides invaluable insights into optimizing computing systems. Amdahl's Law estimates the maximum expected improvement to an overall system when a particular component or task is improved or accelerated. It emphasizes the principle that the potential speedup is limited by the portion of the system that remains unchanged.

Application of Amdahl's Law in Performance Optimization

To understand the impact of performance improvements in specific parts of a program, it is essential to quantify the overall speedup. Consider the first scenario where 15% of a program is upgraded to run 85 times faster. The remaining 85% of the program remains unchanged. Using Amdahl’s Law, the overall speedup (S) is calculated as:

S = 1 / [(1 - P) + (P / S_p)]

Where:

  • P = proportion of execution time affected (0.15 in this case)
  • S_p = speedup of the improved portion (85) in this case

Substituting the values:

S = 1 / [(1 - 0.15) + (0.15 / 85)] = 1 / [0.85 + 0.00176] ≈ 1 / 0.85176 ≈ 1.174

Thus, the overall speedup when 15% of the program is improved by a factor of 85 results in approximately a 17.4% reduction in execution time, indicating modest benefits due to the limited portion being optimized.

In the second scenario, 85% of the program is made 15 times faster. Applying Amdahl's Law again:

S = 1 / [(1 - 0.85) + (0.85 / 15)] = 1 / [0.15 + 0.0567] ≈ 1 / 0.2067 ≈ 4.84

This results in an overall speedup of approximately 4.84 times, demonstrating a significant performance gain because a larger fraction of the program benefits from the acceleration.

Memory Refresh Cycles in Dynamic RAM

Dynamic RAM requires periodic refresh cycles to retain data, involving dedicated operations that temporarily block normal memory access. Given that the RAM must be refreshed 64 times per millisecond (ms), and each refresh takes 150 nanoseconds (ns), along with memory cycles taking 250 ns, we determine the percentage of total memory operation time dedicated to refreshes.

First, calculate total refresh time per ms:

Total refresh time = number of refreshes × time per refresh = 64 × 150 ns = 9600 ns

Next, compute total memory cycle time per ms:

Total memory cycles per ms = total time in ns = 1 ms = 1,000,000 ns

Now, the percentage of total time used for refreshes is:

(9600 ns / 1,000,000 ns) × 100 ≈ 0.96%

Therefore, approximately 0.96% of the total operating time of the memory is spent performing refresh cycles, which is necessary to maintain data integrity without significantly impacting system performance.

Emerging Nonvolatile Solid-State Memory Technologies

Recent advancements have led to the development of several nonvolatile memory technologies that combine high speed, durability, and non-volatility. Three notable technologies include:

  1. Phase-Change Memory (PCM): Utilizes the reversible phase change between amorphous and crystalline states in chalcogenide glass to store data with high speed and durability.
  2. Resistive Random-Access Memory (ReRAM): Stores data by changing the resistance across a dielectric solid-state material, offering fast switching times and scalability.
  3. Spin-Transfer Torque Magnetic RAM (STT-MRAM): Uses magnetic storage elements controlled by spin-polarized currents to provide nonvolatile, high-speed memory with low power consumption.

Differences Between DRAM and SRAM

Dynamic RAM (DRAM) and Static RAM (SRAM) serve distinct roles in computer architecture, primarily characterized by their operational mechanisms, speed, size, and costs.

Application

  • DRAM: Primarily used as the main system memory due to its high density and cost-efficiency, suitable for storing large amounts of data that the CPU can access quickly.
  • SRAM: Often employed for cache memory, given its faster access times and simpler design, although it is less dense and more expensive.

Characteristics

  • Speed: SRAM offers much faster access times (typically nanoseconds) compared to DRAM, which requires periodic refresh cycles.
  • Size and Density: DRAM can be manufactured at higher densities, making it suitable for larger memory capacities, whereas SRAM chips are physically larger for the same capacity.
  • Cost: Due to its complexity, SRAM is more expensive per bit than DRAM, which is simpler and more economical for large memory systems.

Conclusion

In summary, DRAM is used predominantly as main memory due to its affordability and capacity, despite being slower, while SRAM is favored for cache memory that demands high speed and low latency. Their differences in characteristics are fundamental to their respective applications in modern computing systems.

References

  • Hennessy, J. L., & Patterson, D. A. (2019). Computer Architecture: A Quantitative Approach (6th ed.). Morgan Kaufmann.
  • Simon, M. K., & Chern, W. (2020). Nonvolatile Memory Technologies and Their Applications. Journal of Emerging Technologies, 45(3), 112-125.
  • Anderson, P. M., & Myrvold, W. (2021). Memory Technologies: An Overview of Emerging Nonvolatile Memories. IEEE Transactions on Electron Devices, 68(4), 1690-1697.
  • Kawasaki, T., et al. (2022). Recent Advances in ReRAM Technology. Materials Today, 55, 103-110.
  • Kim, S., et al. (2020). Spin-Transfer Torque MRAM: A Review of Recent Progress. Journal of Magnetism and Magnetic Materials, 512, 167063.
  • Williams, R. S., et al. (2019). Phase-Change Memory Technology. IEEE Journal of Solid-State Circuits, 54(3), 776-785.
  • Sze, S. M. (2012). Semiconductor Devices: Physics and Technology. Wiley-Interscience.
  • Fowler, M., & Harari, H. (2020). High-Performance Memory Technologies. ACM Computing Surveys, 52(2), 1-36.
  • Yee, K. S., & Islam, M. T. (2022). The Future of Memory Technologies: Emerging Trends and Challenges. Nature Electronics, 5(2), 102-109.
  • Chen, W., & Lee, S. (2021). Memory Hierarchies and Their Impact on System Design. IEEE Micro, 41(1), 8-17.

Related Assignments