This paper studies an average consensus problem for multi-agent systems (MAS) with binary-valued communications of relative state between neighbors. A two-scale algorithm consisting of 'estimation' stage and 'control' stage is proposed for discrete-time MAS over directed graph. In the 'estimation' stage, the relative states between agents and neighbors are estimated with and without considering measurement noise. In 'control' stage, a distributed control protocol is designed based on the estimations of relative states to achieve average consensus. Convergence and convergence speed of the algorithm are analyzed theoretically under mild conditions. Finally, a numerical simulation is given to validate the developed results of this paper.