The AEgIS experiment is an international collaboration with the main goal of performing the first direct measurement of the Earth's gravitational acceleration on antimatter. Critical to the success of AEgIS is the production of cold antihydrogen (Hmacr) atoms. The FACT detector is used to measure the production and temperature of the Hmacr atoms and for establishing the formation of a Hmacr beam. The operating requirements for this detector are very challenging: it must be able to identify each of the thousand or so annihilations in the 1 ms period of pulsed Hmacr production, operate at 4 K inside a 1 T solenoidal field and not produce more than 10 W of heat. The FACT detector consists of two concentric cylindrical layers of 400 scintillator fibres with a 1 mm diameter and a 0.6 mm pitch. The scintillating fibres are coupled to clear fibres which transport the scintillation light to 800 silicon photomultipliers. Each silicon photomultiplier signal is connected to a linear amplifier and a fast discriminator, the outputs of which are sampled continuously by Field Programmable Gate Arrays (FPGAs).