A 32-bit wide main memory unit with a capacity of 1 GB is built using 256M $\times$ 4-bit DRAM chips. The number of rows of 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 milliseconds. The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is _______.

To maintain DRAM contents, all rows must be refreshed within the refresh period.

1. Number of rows to refresh:

   $$\text{Rows} = 2^{14} = 16384$$

2. Time spent on refreshing during one refresh period:

   $$\text{Time for one refresh} = 50\text{ ns}$$

   $$T_{\text{refresh}} = 16384 \times 50\text{ ns} = 819200\text{ ns} = 0.8192\text{ ms}$$

3. Refresh period:

   $$T_{\text{period}} = 2\text{ ms}$$

4. Percentage of time spent refreshing:

   $$\text{Percentage}_{ ext{refresh}} = \frac{0.8192\text{ ms}}{2\text{ ms}} \times 100\% = 40.96\%$$

5. Percentage of time available for read/write operations:

   $$\text{Available time percentage} = 100\% - 40.96\% = 59.04\%$$

Rounding to the closest integer gives 59 (acceptable range: 59.0 to 60.0).