GATE CS 2004 Q69 — Instruction Pipelining

To find the total time taken to process $1000$ data items on the pipeline, we first need to determine the clock cycle time ($t_p$) of the pipeline.

Step 1: Calculate the Clock Cycle Time ($t_p$)

The clock cycle time of a pipeline is determined by the delay of the slowest stage plus the overhead of the interface registers:

$$t_p = \max(\text{Stage Delays}) + \text{Register Delay}$$

Given stage delays are $150\text{ ns}$, $120\text{ ns}$, $160\text{ ns}$, and $140\text{ ns}$, and the register delay is $5\text{ ns}$:

$$t_p = \max(150, 120, 160, 140) + 5 = 160 + 5 = 165\text{ ns}$$

Step 2: Calculate the Total Execution Time ($T$)

The total time taken to process $N$ tasks in a $k$-stage pipeline is given by the formula:

$$T = (k + N - 1) \times t_p$$

Where:

• $k = 4$ (number of stages)
• $N = 1000$ (number of data items)
• $t_p = 165\text{ ns}$

Substituting these values into the formula:

$$T = (4 + 1000 - 1) \times 165\text{ ns}$$

$$T = 1003 \times 165\text{ ns} = 165,495\text{ ns}$$

Step 3: Convert to Microseconds

$$T = \frac{165,495}{1000}\ \mu\text{s} = 165.495\ \mu\text{s} \approx 165.5\ \mu\text{s}$$

Therefore, the total time taken is approximately $165.5\ \mu\text{s}$, which corresponds to Option C.