Cronbach's alpha with weighted data


I have a test whose reliability I want to calculate, using Cronbach's alpha. The first 18 questions are scored 0 or 1 (right or wrong). The final 7 questions are scored 0, 1 or 2 (because they are not dichotomously right or wrong, there exists a 'half right' possibility).

Is it correct to calculate Cronbach's alpha over the whole test, despite the fact that the final section's questions are more heavily weighted? Or do I simply have to calculate it for each section separately?

Thanks for any advice you can give