A computer employed in arithmetic processing uses a software division routine. A program runs for two minutes on this machine, with division taking 60% of the total time. If we wish to add a dedicated division unit in order to increase the performance of the computer by a factor of two, how much faster do we have to make the hardware division unit than the existing division mechanism?
What will be an ideal response?
The program takes 2 minutes = 120 s. Division takes 60% of the time, so the program takes 48 s + 72 s (division). After modification, the division takes 72/m seconds. The total time is now 48 + 72/m seconds. If the system is to have a twofold overall increase, then 48 + 72/m = 60. Therefore, 72/m = 12 and m = 72/12 = 6. As a simple check, the new time will be 48s (unchanged) + 12s (division) = 60s (i.e., half the previous time).
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