This homework covers Chapter 6.
There two interpretations of the this problem.
A) 0.02% of the instructions are serial and what percentage of total
instructions are spent in 50 processors.
B) 0.02% of the multiprocessor time are in serial mode and what percentage of total multiprocessor time are spent in 50 processors.
I gave full credit to both interpretation.
T_single = Total execution time for single processor
T_multi = Total execution time for multi processor
A)
T_multi = [serial fraction + 50 fraction / 50 speedup + 100 fraction/
100 speedup] * T_single
= [0.0002 + 50 fraction / 50 speedup + (0.9998 - 50 fraction) / 100 speedup]
* T_single
= [0.0002 + 50 fraction / 50 + (0.9998 - 50 fraction) / 100 ] * T_single
T_single/T_multi = 1/ [0.0002 + 50 fraction / 50 + (0.9998 - 50 fraction)
/ 100 ]
80 = 1/ [0.0002 + 50 fraction / 50 + (0.9998 - 50 fraction)
/ 100 ]
1/80 -0.0002 - 0.009998 = 50 fraction / 100
50 fraction = 23%
B)
T_single = [serial fraction + 50 fraction * 50 speedup + 100 fraction
* 100 speedup] * T_multi
T_single = [0.0002 + 50 fraction * 50 + (.9998-50 fraction)*100] *
T_multi
T_single/T_multi = [0.0002 + 50 fraction * 50 + (.9998-50 fraction)*100]
80 = [0.0002 + 50 fraction * 50 + (.9998-50 fraction)*100]
50 fraction = 40%