  Conner and Hurrelbrink established a method of determining the structure of
the 2-Sylow subgroup of the tame kernel $K_2(\mathcal{O})$ for certain
quadratic number fields. Specifically, the 4-rank for these fields was
characterized in terms of positive definite binary quadratic forms. Numerical
calculations led to questions concerning possible density results of the 4-rank
of tame kernels. In this paper, we succeed in giving affirmative answers to
these questions.
