A processor takes 12 cycles to complete an instruction I. The corresponding pipelined processor uses 6 stages with the execution times of 3, 2, 5, 4, 6 and 2 cycles respectively. What is the asymptotic speedup assuming that a very large number of instructions are to be executed?
(A) 1.83
(B) 2
(C) 3
(D) 6
Answer: (B)
Explanation:
Let the large number of instructions be \'n\'.
Time required for sequential execution = number of cycles *n
= 12n
Time required in a pipelined processor = (k + n - 1)tp
where, k = number of stages in pipeline unit.
n = number of instructions
tp = execution time unit
NOTE: when variable time units are given for different pipeline stages, the largest time unit is taken.
Speedup = sequential time/ pipelining time
= 12n / (6 + n - 1)6
= 12n /(n + 5)6
= 12n /6n
= 2
Option (B) is correct.
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