  The stable mod 2 cohomologies of the spectra for connective real and complex
K-theories are well known and easy to work with. However, the known bases are
in terms of the anti-automorphism of Milnor basis elements. We offer simple
bases in terms of admissible sequences of Steenrod operations that come from
the Adem relations. In particular, the basis for the complex case is that you
don't use any Steenrod operations in degree one or $2^n+1$, $n > 0$.
