We have measured the ultra-high energy cosmic ray flux with the newer one of the two detectors of the High Resolution Fly's Eye experiment (HiRes) in monocular mode. An outline of the HiRes experiment is given here, followed by a description of the trigger and Flash ADC electronics of the HiRes-2 detector. The computer simulation of the experiment, which is needed for resolution studies and the calculation of the detector acceptance, is presented in detail. Different characteristics of the simulated events are compared to real data to test the performance of the Monte Carlo simulation. The calculation of the energy spectrum is described, together with studies of systematic uncertainties due to the cosmic ray composition and aerosol content of the atmosphere that are assumed in the simulation. Data collected with the HiRes-2 detector between December 1999 and September 2001 are included in the energy spectrum presented here. We compare our result with previous measurements by other experiments.
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