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Official PYQ · 2018Q23Memory Hierarchy: Cache, Main Memory and Secondary StorageNAT1 mark

GATE CS 2018 Q23 — Memory Hierarchy: Cache, Main Memory and Secondary Storage

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A 32-bit32\text{-bit} wide main memory unit with a capacity of 1  GB1\;\textsf{GB} is built using 256M×4-bit256\textsf{M} \times 4\text{-bit} DRAM chips. The number of rows of memory cells in the DRAM chip is 2142^{14}. The time taken to perform one refresh operation is 50  nanoseconds50\;\text{nanoseconds}. The refresh period is 2  milliseconds.2\;\text{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 _________.
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Answer: 59 : 60

To find the percentage of time available for performing memory read/write operations, we first calculate the total time spent on refreshing the DRAM cells during one refresh period.

Step 1: Calculate the total refresh time

Each DRAM chip is refreshed row by row. The given parameters are:

  • Number of rows in the DRAM chip = 214=16,3842^{14} = 16,384
  • Time taken for one refresh operation = 50 ns50\text{ ns}
  • Refresh period = 2 ms=2×106 ns2\text{ ms} = 2 \times 10^6\text{ ns}

Since all chips in the memory unit are refreshed in parallel, the total time spent on refreshing all rows in one refresh period is:

Total Refresh Time=Number of rows×Time per refresh operation\text{Total Refresh Time} = \text{Number of rows} \times \text{Time per refresh operation} Total Refresh Time=16,384×50 ns=819,200 ns=0.8192 ms\text{Total Refresh Time} = 16,384 \times 50\text{ ns} = 819,200\text{ ns} = 0.8192\text{ ms}

Step 2: Calculate the percentage of time spent on refreshing

Refresh Overhead (%)=(0.8192 ms2 ms)×100%=40.96%\text{Refresh Overhead (\%)} = \left( \frac{0.8192\text{ ms}}{2\text{ ms}} \right) \times 100\% = 40.96\%

Step 3: Calculate the percentage of time available for read/write operations

Available Time (%)=100%−40.96%=59.04%\text{Available Time (\%)} = 100\% - 40.96\% = 59.04\%

Rounding to the closest integer, we get 59%59\%.

Note: The official GATE answer key accepted any value in the range 59 to 60.

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