  Cosmic microwave background (CMB) determinations of the baryon-to-photon
ratio $\eta \propto \Omega_{\rm baryon} h^2$ will remove the last free
parameter from (standard) big bang nucleosynthesis (BBN) calculations. This
will make BBN a much sharper probe of early universe physics, for example,
greatly refining the BBN measurement of the effective number of light neutrino
species, $N_{\nu,eff}$. We show how the CMB can improve this limit, given
current light element data. Moreover, it will become possible to constrain
$N_{\nu,eff}$ independent of \he4, by using other elements, notably deuterium;
this will allow for sharper limits and tests of systematics. For example, a 3%
measurement of $\eta$, together with a 10% (3%) measurement of primordial D/H,
can measure $N_{\nu,eff}$ to a 95% confidence level of $\sigma_{95%}(N_\nu) =
1.8$ (1.0) if $\eta \sim 6.0\times 10^{-10}$. If instead, one adopts the
standard model value $N_{\nu,eff}=3$, then one can use $\eta$ (and its
uncertainty) from the CMB to make accurate predictions for the primordial
abundances. These determinations can in turn become key inputs in the
nucleosynthesis history (chemical evolution) of galaxies thereby placing
constraints on such models.
