This question comes up with TableForm and MatrixForm a lot. The solution is to do the assignment inside the *Form function.
In[1]:= BaseForm[theMin = 16^^1000, 10]
Out[1]//BaseForm=
4096
In[2]:= theMin
Out[2]= 4096
In[3]:= Head[theMin]
Out[3]= Integer
Usually, the content of the *Form wrapper can be extracted with First.
In[5]:= aMin = BaseForm[16^^1000, 10]
Out[5]//BaseForm=
4096
In[6]:= First[aMin]
Out[6]= 4096
