A 32 bit wide main memory with a capacity of 1 GB is built using \( 256 \mathrm{~M} \times 4 \) bits DRAM chips. The number of rows memory cells in the DRAM chip is \( 2^{14} \) . The time taken to perform one refresh operation is 50 nanoseconds. The refresh period is 2 milli seconds The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is \( \qquad \) .
Number of chips: 1 GB = \(2^{33}\) bits. Each chip = 256M × 4 = \(2^{30}\) bits. So 8 chips.
All chips are refreshed in parallel, so refreshing one chip = refreshing the whole memory.
Refresh time per period: each chip has \(2^{14}\) rows and each row refresh takes 50 ns.
Time = \(2^{14} \times 50\) ns = \(16384 \times 50\) ns = 819.2 µs = 0.8192 ms.
The refresh period is 2 ms, so the fraction used for refresh = \(0.8192 / 2 = 40.96\%\).
Time available for read/write = \(100 - 40.96 = 59.04\%\).
Answer: (B) 59.04
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