The present paper points toward the possibility of reducing the proportion of analog processing in an apparatus employed to measure the neutron and photon energy spectra. The digitization of the detector output pulses makes it possible to process the information contained in the pulses either instantaneously or subsequently. The present paper deals with the method of digitizing the leading edge of the pulses generated by a stilbene organic scintillator or an NE-213 scintillator. The neutron versus gamma discrimination can be carried out on the basis of the pulse leading edge duration. Coping with this task requires a digitizer featuring quite a high sampling frequency, which must exceed 1 GHz. The requirements for the amplitude digitization frequency are less severe, however, the amplitude resolution must be better than 8 bits. Both of the above requirements can be met with present-day components. The digitization is expected to result in reducing the apparatus size and improving its functionality.