256 Mb DRAM is organized as a 32M × 8 memory externally and as a 16K × 16K…
2023
256 Mb 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 millisecond to forestall loss of data; refreshing one row takes 100 nanoseconds. What fraction of the total memory bandwidth is lost to refresh cycles?
- A.
6.6%
- B.
3.3%
- C.
9.9%
- D.
4.3%
Attempted by 72 students.
Show answer & explanation
Correct answer: B
Key idea: compute the fraction of time spent refreshing all rows within the required refresh interval.
Number of rows: the internal array is 16K × 16K, so there are 16K = 16,384 rows.
Time to refresh one row: 100 ns (100 × 10⁻⁹ s).
Total time to refresh all rows once = 16,384 × 100 ns = 1,638,400 ns = 1.6384 ms.
Refresh interval requirement = 50 ms.
Fraction of time lost to refresh = total refresh time / refresh interval = 1.6384 ms / 50 ms ≈ 0.032768 = 3.2768% ≈ 3.3%.
Check: internal array size 16,384 × 16,384 = 268,435,456 cells = 256 Mb, consistent with the external organization. Therefore about 3.3% of total memory bandwidth is lost to refresh cycles.
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