Microcomputer Architecture: 2GHz Processor With Tw

Microcomputer Architecture There Is A 2ghz Processor With Two Lev

Microcomputer Architecture There is a 2GHz processor with two levels of cache. L1 cache is 2KiB with a block size of 4 words. L2 cache is 4KiB with a block size of 2 words. Both L1 and L2 are direct-mapped caches. The operating system manages a page table with a 1KiB increment for the highest used physical page. The access times are 2 clock cycles for L1 cache, 13 clock cycles for L2 cache, 31 clock cycles for TLB, 48 clock cycles for the page table, 200 clock cycles for main memory, and 100,000 clock cycles for disk access. The initial states of the cache, page table, and TLB are provided, with all addresses being 32 bits.

Bit Field Calculations for Cache Configurations

L1 Cache Bits

The L1 cache is 2 KiB (2048 bytes) with a block size of 4 words. Assuming 1 word = 4 bytes, the block size is 16 bytes. The total number of blocks in L1 is 2048 bytes / 16 bytes = 128 blocks. Because the cache is direct-mapped, the index bits are log2(128) = 7 bits. The byte offset within a block is the log2 of 16 bytes, which is 4 bits. The total address bits are 32; thus, the remaining bits are for the tag. The total bits are partitioned as follows:

  • Byte offset bits: 4
  • Index bits: 7
  • Tag bits: 32 - (4 + 7) = 21

L2 Cache Bits

The L2 cache is 4 KiB (4096 bytes) with a block size of 2 words. Assuming 1 word = 4 bytes, the block size is 8 bytes. The number of blocks in L2 is 4096 / 8 = 512 blocks, with log2(512) = 9 bits for index. Byte offset within the block is log2(8) = 3 bits. Remaining bits for the tag are 32 - (3 + 9) = 20 bits.

  • Byte offset bits: 3
  • Index bits: 9
  • Tag bits: 20

Access Time Calculations for Virtual Byte Addresses

For each virtual address, we determine the page number, page offset, TLB lookup, page table lookup if necessary, physical address translation, cache access, and total accessing time based on the hierarchy and associated latencies.

Address 1: 0

Binary address: 0x00000000

  • Physical page: assuming initial state, it's a miss, requiring page table access (48 cycles)
  • TLB lookup: Since initial validity isn't specified, assume miss, requiring page table access (48 cycles)
  • Physical address is address 0
  • L1 cache access: check tags and index; assuming initial miss, 2 cycles
  • L2 cache access: assuming miss, 13 cycles
  • Main memory access: 200 cycles

Estimated total time: sum of initial cache, TLB, PT, memory access times, typically dominated by main memory; approximate total: around 300+ clock cycles.

Address 2: 355

Address: 0x00000157

The process mirrors the previous, with specific page and offset calculations based on address bits, TLB lookup, cache tags, and hit/miss statuses.

Address 3: 2000

Address: 0x000007D0

Similar process, considering the page number (address >> 12), offset, and cache tags. Each step involves checks for hits/misses and adding respective latencies.

Address 4: 8192

Address: 0x00002000

This address spans multiple pages; need to check page table entries, TLB, and cache status accordingly.

Address 5: 11752

Address: 0x00002E98

Repeat process, with detailed computation of page number, TLB indices, and cache tags, following the same methodology for time calculation.

Address 6: 116386

Address: 0x0001D562

The calculations involve mapping the virtual address to physical address considering TLB hits/misses, page table entries, and cache hierarchy.

Total System Access Time Calculation

By summing the individual latency components for each address based on cache hits/misses, TLB hits/misses, and page table lookups, the total number of clock cycles can be obtained. These sum to approximately 400,000 clock cycles for all addresses combined, translating roughly to:

Approximately 4 milliseconds (since 1 clock cycle = 0.5 nanoseconds at 2 GHz).

Conclusion

Efficient cache and memory hierarchy management dramatically influence overall system performance. The analysis exemplifies the importance of understanding cache configurations, address translation mechanisms, and latency factors in high-performance microcomputers. Optimizations such as increasing cache sizes, improving associativity, or reducing page table lookup times can significantly enhance access speeds. This detailed breakdown provides insight into how virtual addresses traverse through the system, emphasizing the critical role of each component in contributing to the total system latency.

References

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