This paper presents the Bismuth Germanate Oxide (BGO) front-end electronics design and signal processing in Modular X- and Gamma ray sensor (MXGS) instrument onboard the Atmosphere Space Interaction Monitor (ASIM) mission, funded by the European Space Agency. University of Bergen is responsible for the design and development of the detector layers and readout electronics for the MXGS instrument. The principal objective of the instrument is to detect Terrestrial Gamma ray Flashes (TGFs), which are related to thunderstorm activity. The digital pulse processing scheme used in the MXGS BGO detector gives it a significantly higher rate capability than what has been achieved in other instruments used in the study of terrestrial gamma flashes. The front-end electronics for the BGO detector layer in MXGS system also uses fewer components compared to conventional analog front-ends for BGO detectors, thereby increasing its reliability and projected lifetime in the harsh space environment. The MXGS instrument is expected to see about 1000 TGFs in a time period of one year.