The High Resolution Spectrograph for the Hubble Space Telescope uses two pulse-counting Digicon detectors to record ultraviolet spectra in the wavelength range 1050 Å ( A< 3200 Å. One of the attractive features of the Digicon is the well behaved relationship between the measured count rate and the true photon arrival rate. At low rates the relationship is linear with unit slope and zero offset. At higher rates the intervals between photon arrivals become comparable to the response time of the electronics and not every pulse will be counted. This "paired-pulse" effect causes the relationship to depart from linearity at high count rates and must be corrected for during the reduction of raw data. In this paper we describe the characteristics of the pulse-counting circuits, and present two analytic equations which quantify the dead-time losses. During the ground-based calibration of the HRS observations of bright emission lines in the spectrum of an argon miniarc lamp were made to calibrate the non-linearity. By attenuating the light with neutral density filters the same spectrum could be recorded with input count rates ranging from 20 to 1.4 million counts per second per channel. The less attenuated spectra are severely distorted by the dead-time losses. Comparison with the undistorted low count rate data allows a detailed analysis to be made of the pulse counting characteristics over five decades of input event rates. The fitting formulas allow data with input rates up to 100000 counts per second to be linearized with no systematic errors. Our equations and calibration methods should be generally applicable to all kinds of multi-channel pulse counting detectors, which are becoming increasingly common in both ground and space based astronomical instruments.