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Cache Memory and Hierarchy

GATE CSE 2014 Set 2 · Q55

NAT2 marksMedium

Time

Consider a main memory system that consists of 8 memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for 100 nanoseconds (ns) by the data, address, and control signals. During the same 100 ns, and for 500 ns thereafter, the addressed memory module executes one cycle accepting and storing the data. The (internal) operation of different memory modules may overlap in time, but only one request can be on the bus at any time. The maximum number of stores (of one word each) that can be initiated in 1 millisecond is ________

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Official answer: 10000 (±0)

Cache Memory and Hierarchy

To find the maximum number of store operations that can be initiated in 1 millisecond1\text{ millisecond}:

  1. Memory Module Cycle Time: Each memory module takes 100 ns+500 ns=600 ns100\text{ ns} + 500\text{ ns} = 600\text{ ns} to complete one write operation.

  2. Bus Occupation Time: The system bus is occupied for 100 ns100\text{ ns} per write request.

  3. Interleaving / Overlapping Operations: Since there are 88 modules and the bus is occupied for 100 ns100\text{ ns} per request, the memory can accept a new request every 100 ns100\text{ ns} by interleaving across different modules. Because 8×100 ns=800 ns>600 ns8 \times 100\text{ ns} = 800\text{ ns} > 600\text{ ns}, a module will always be free when addressed in round-robin fashion, making the bus the only bottleneck.

  4. Initiation Rate: A new store operation can be initiated every 100 ns100\text{ ns}.

  5. Total Stores in 1 ms1\text{ ms}:

    1 ms=10−3 s=106 ns1\text{ ms} = 10^{-3}\text{ s} = 10^6\text{ ns}
    Maximum number of stores=106 ns100 ns=10000\text{Maximum number of stores} = \frac{10^6\text{ ns}}{100\text{ ns}} = 10000

Thus, the maximum number of stores that can be initiated is 10000.

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This Cache Memory and Hierarchy previous year question is Q55 of the GATE CSE 2014 Set 2 paper. Find more GATE CSE PYQs on Cache Memory and Hierarchy in Computer Organization and Architecture, or browse all GATE CSE PYQs.

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Cache Memory and Hierarchy in GATE CSE

Cache Memory and Hierarchy has 47 GATE CSE PYQs across 23 papers from 2011 to 2026. 16 of them are 2-mark NAT questions like this one, and GATE CSE 2014 Set 2 has 4.

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GateAI solution cardGATE CSE 2014 Set 2 · Q55 · NAT

Consider a main memory system that consists of 8 memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for 100 nanoseconds (ns) by the data, address, and control signals. During the same 100 ns, and for 500 ns thereafter, the addressed memory module executes one cycle accepting and storing the data. The (internal) operation of different memory modules may overlap in time, but only one request can be on the bus at any time. The maximum number of stores (of one word each) that can be initiated in 1 millisecond is …

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