I understand that a binomial heap can be represented as binary numbers according to the degree of each tree but what exactly is the relationship between inserting a new node into the binomial heap and incrementing the binomial number.

In addition to that, I assume that there is a relationship between performing union on two binomial heaps and adding the two binary numbers of the binomial heaps but what exactly is the relationship.

I’m looking for something like a formal / textbook definition or of the relationship (if possible)