256Mb DRAM is organized as a 32M × 8 memory externally and as a 16K × 16K…
2023
256Mb DRAM is organized as a 32M × 8 memory externally and as a 16K × 16K square array internally. Each row must be refreshed at least once every 50 milliseconds to forestall loss of data; refreshing one row takes 100 nanoseconds. What fraction of the total memory bandwidth is lost to refresh cycles?
Answer: B. 3.3% — ConceptA DRAM refresh temporarily uses the memory interface, so the bandwidth fraction lost equals the total refresh time within one refresh interval divided…
- A.
6.6%
- B.
3.3%
- C.
9.9%
- D.
4.3%
Attempted by 158 students.
Show answer & explanation
Correct answer: B
Concept
A DRAM refresh temporarily uses the memory interface, so the bandwidth fraction lost equals the total refresh time within one refresh interval divided by that interval.
For a two-dimensional memory array, refreshing every row once requires as many refresh operations as there are rows.
Application
The internal organization is 16K × 16K, so the number of rows is 16K = 16 × 1024 = 16,384.
Refreshing all rows once takes 16,384 × 100 ns = 1,638,400 ns.
Convert the refresh time to milliseconds: 1,638,400 ns = 1.6384 ms.
Divide by the 50 ms refresh interval: 1.6384 ms ÷ 50 ms = 0.032768 = 3.2768%, which rounds to 3.3%.
Cross-check
At 3.3% of 50 ms, refresh occupies about 1.65 ms, which agrees with the independently computed 1.6384 ms after rounding.
Result
The fraction of total memory bandwidth lost to refresh cycles is approximately 3.3%.
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