As I understand from your question, you want to analyse binary data and construct a dendrogram. There are a lot of free programs for it but I can suggest:
1. Phylip, it contains different programs for different analyses.
https://phylipweb.github.io/phylip/
2. PAUP, PAUP 5.0 is testing and free now.
https://paup.phylosolutions.com/
3. PAST 4, it is for paleontological and ecological studies, but it has a lot of functions.