ISRO | ISRO CS 2011 | Question 25

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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