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A 32-bit wide main memory with a capacity of $1$ GB is built using $256\text{M}\times4$ bits DRAM chips. The number of rows per chip is $2^{14}$. The time taken to perform one refresh operation is $50$ nanoseconds. The refresh period is $2$ milliseconds. The percentage (rounded to the nearest integer) of time available for performing memory read/write operations in the main memory unit is ______.





Solution

Rows to be refreshed $=2^{14}=16384$

Time for one refresh $=50$ ns

Total refresh time:
$16384\times50\text{ ns}=819200\text{ ns}=0.8192\text{ ms}$

Refresh period $=2$ ms

Percentage of time used for refresh:
$\displaystyle \frac{0.8192}{2}\times100\approx41%$

Percentage available for read/write:
$100-41=59%$


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