Data replication can be used to improve the availability of data in a distributed database system. In such a system, a mechanism is required to maintain the consistency of the replicated data. Weighted voting is a popular solution for maintaining the consistency. The performance of a voting system is determined by the vote assignment. It was shown in previous studies that finding the optimal solution among nonnegative integer vote assignments requires O(2N(2)) time. So it is not suitable to find the optimal integer vote assignment (OIVA) for large systems. In this paper, we propose the optimal binary vote assignment (OBVA) considering only binary vote assignments. It is shown that OBVA can achieve nearly the same availability of OIVA. On the other hand, OBVA requires only O(N2) time, which is preferred for large systems.