This paper investigates the differential binary modulation for decode-and-forward (DF) based relay-assisted free space optical (FSO) network under the effect of strong atmospheric turbulence together with misalignment error (ME). The atmospheric fading links experience K-distributed turbulence. First we derive novel closed form expression for average bit error rate (BER) and outage probability (OP) in terms of Meijer’s G function. Further, the OP of differential DF-FSO system with multiple relays is derived. We also analyze the asymptotic performance for the sake of getting the order of diversity and the coding gain. The power allotment term is utilized to examine the effect of different power allotment techniques on BER and OP. The simulation results have been used to validate the derived analytical results.