benefits from the increasing number of processors (parallel part). Example. — A computer program that processes files from disk. A part of that program may scan the directory of the disk and create a list of files internally in memory. After that, another part of the program passes each file to a separate thread for processing. The part that scans the directory and creates the file list cannot be sped up on a parallel computer, but the part that processes the files can. Without loss of generality, let the total execution time on the parallel system be . Denote the serial time as and the parallel time as , where . Denote the number of processors as . Hypothetically, when running the program on a serial system (only one processor), the serial part still takes , while the parallel part now takes . The execution time on the serial system is: Using as the baseline, the speedup for the parallel system is: By substituting or , several forms in the previous section can be derived. Applications Application in research Amdahl's law presupposes that the computing requirements will stay the same, given increased processing power. In other words, an analysis of the same data will take less time given more computing power. Gustafson, on the other hand, argues that more computing power will cause the data to be more carefully and fully analyzed: pixel by pixel or unit by unit, rather than on a larger scale. Where it would not have been possible or practical to simulate the impact of nuclear detonation on every building, car, and their contents (including furniture, structure strength, etc.) because such a calculation would have taken more time than was available to provide an answer, the increase in computing power will prompt researchers to add more data to more fully simulate more variables, giving a more accurate result. Application in everyday computer systems Amdahl's Law reveals a limitation in, for example, the ability of multiple cores to reduce the time it takes for a computer to boot to its operating system and be ready for use. Assuming the boot process was mostly parallel, quadrupling computing power on a system that took one minute to load might reduce the boot time to just over fifteen seconds. But greater and greater parallelization would eventually fail to make bootup go any faster, if any part of the boot process