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?
- A.
6.6%
- B.
3.3%
- C.
9.9%
- D.
4.3%
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Correct answer: B
The DRAM has an internal 16K × 16K array, meaning there are 16,384 rows (16 × 1024). Each row requires a refresh every 50ms, taking 100ns per row. Total refresh time = 16,384 rows × 100ns/row = 1,638,400ns = 1.6384ms. The fraction of bandwidth lost is refresh time divided by total cycle time: 1.6384ms / 50ms ≈ 0.032768, or approximately 3.3%.
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