This letter investigates the one-bit consensus control of multi-agent systems (MASs) with independent and identically distributed and Markovian packet loss. To explore the impact of packet loss on one-bit communication, this letter first quantitatively characterizes the information loss of one-bit communications caused by packet loss, which provides the proportional relationship between one-bit data with and without packet loss in the sense of expectation. Based on quantitative characterizations, a one-bit packet loss consensus algorithm with a packet loss proportional coefficient is proposed to compensate for the information loss, where the coefficient is designed as the reciprocal of the information loss proportion. Furthermore, this letter demonstrates that the proposed algorithm enables the MAS to achieve one-bit consensus in the mean square sense at a rate of O(1/t) with packet loss. Two simulation examples are given to validate the algorithm.