GATE CS 2025 Set 2 Q46 — Instruction Pipelining

To find the total time taken to process $1000$ instructions in the given $5$-stage pipeline, we proceed as follows:

1. Determine the Clock Cycle Time ($T_p$)

The clock cycle time of a pipelined processor is determined by the maximum delay among all stages plus the inter-stage latch delay ($d$):

Given stage delays are $180, 250, 150, 170,$ and $250$ ns, and the latch delay is $10$ ns:

2. Calculate Total Execution Time

The total time $T$ required to execute $N$ instructions in a $k$-stage pipeline (assuming no stalls) is given by:

Substituting the given values ($k = 5$ stages, $N = 1000$ instructions):

3. Convert to Microseconds ($\mu$s)

Since $1\ \mu\text{s} = 1000\text{ ns}$:

Thus, the time taken to process $1000$ instructions is $261.04$ microseconds.