This paper studies the finite-time leader-following tracking problems for a group of autonomous agents modeled by second-order nonlinear dynamics under a dynamic reference leader. First, based on distributed binary measurements, a class of finite-time leader-following tracking algorithms are only requiring a single-bit quantization error relative to each neighbor. Then, by using a topology-dependent Lyapunov function, the finite-time distributed tracking problem can be solved with a finite settling time estimation if the graph of all agents contains a directed spanning tree with the leader as the root and the subgraph among the followers is undirected. Finally, an example is shown to illustrate the effectiveness of the analytical results.