Confuse about transit visa to china

Hello, I am travelling with Air China from singapore to xian with a layover in beijing PEK airport for 14 hours. I hold a singapore passport and I understand that Singaporeans are exempted from visa to china for 30 days. Please correct me if I'm wrong. If I want to exit pek aiport for a short day tour at great wall and then come back to airport for my domestic flight to xian, do I need to apply for a transit visa? Thanks.