GATE CS 2016 Set 2 — Question 40
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Computer Organization & Architecture → Instruction Pipelining → Pipeline Stages & Throughput
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Question
Suppose the functions and can be computed in 5 and 3 nanoseconds by functional units and , respectively. Given two instances of and two instances of , it is required to implement the computation for . Ignoring all other delays, the minimum time required to complete this computation is ________ nanoseconds.
Correct answer
28 to 28
Solution
We have 10 tasks, where each task consists of computing (taking 3 ns) followed by (taking 5 ns). We have 2 units of and 2 units of .Step 1: Schedule G operations
Since there are 2 units, we can process 2 operations in parallel. Each batch of 2 takes 3 ns.
operations can only start after the corresponding operation is complete AND a unit is available. There are 2 units, taking 5 ns each.
Since there are 2 units, we can process 2 operations in parallel. Each batch of 2 takes 3 ns.
- : Start at 0, Finish at 3 ns
- : Start at 3, Finish at 6 ns
- : Start at 6, Finish at 9 ns
- : Start at 9, Finish at 12 ns
- : Start at 12, Finish at 15 ns
operations can only start after the corresponding operation is complete AND a unit is available. There are 2 units, taking 5 ns each.
- Batch 1 ():
- Ready at 3 ns. available at 0.
- Start at ns.
- Finish at ns.
- Batch 2 ():
- Ready at 6 ns. available at 8 ns (when Batch 1 finishes).
- Start at ns.
- Finish at ns.
- Batch 3 ():
- Ready at 9 ns. available at 13 ns.
- Start at ns.
- Finish at ns.
- Batch 4 ():
- Ready at 12 ns. available at 18 ns.
- Start at ns.
- Finish at ns.
- Batch 5 ():
- Ready at 15 ns. available at 23 ns.
- Start at ns.
- Finish at ns.
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