The algorithm gives you a tree and you need to truncate it at some level to get clusters. In case of those bit strings, you should just take first L characters.
For example, cutting at the second character gives you two clusters
10 chased
11 dog
11 mouse
11 cat
At the third character you get
110 dog
111 mouse
111 cat
The cutting strategy is a different subject though. If you want to know more about Brown Clustering, studying the Machine Learning Course is the best.