CA 714CA - Homework #4

Homework 4 is due Wed, 3/6/02.

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%