One of the goals of the Cryogenic Magnetic Detector at Budker Institute of Nuclear Physics SB RAS (Novosibirsk, Russia) is a study of hadron production in electron-positron collisions near threshold. The neutron-antineutron pair production events can be detected only by the calorimeters. In the barrel calorimeter the antineutron annihilation typically occurs about 5 ns or later after the beams crossing. For identification of such events it is necessary to measure the time of flight of particles to the LXe-calorimeter with an accuracy of about a few nanoseconds. The LXe-calorimeter consists of 14 layers of ionization chambers with two readout: anode and cathode. The duration of charge collection to the anodes is about 4.5 μs, while the required accuracy of measuring of the signal arrival time is less than 1/1000 of that (i.e. 4.5 ns). Besides, the signals' shapes differ substantially from event to event, so the signal arrival time is measured in two stages. In the paper we describ the development of the special electronics which performs waveform digitization and the on-line measurement of signals' arrival times and amplitudes.