Ionization is a problematic quantity in that it does not have a well-defined thermodynamic definition, yet it is a key parameter within plasma modelling. One therefore still aims to find a consistent and unambiguous definition for the ionization state. Within this context, we present finite-temperature density functional theory calculations of the ionization state of carbon in CH plasmas using two potential definitions: one based on counting the number of continuum electrons, and another based on the optical conductivity. Differences of up to 10\% are observed between the two methods. However, including ``Pauli forbidden'' transitions in the conductivity reproduces the counting definition, suggesting such transitions are important to evaluate the ionization state.
