change of terminal

Yes, you will have to cross the immigration and to formally enter China because the transfers between those two terminals are done by shuttle buses over the public area. However, if you layover is shorter than 24 hours, you are allowed to do that.

In order to perform your transfer the first thing upon landing is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit. Here you will present your itinerary. This application is free of any charge. After a short check you will be granted a permit and you will proceed to the immigration. After the exit, you will take a shuttle bus to the other terminal. Upon arrival in the other terminal, you will cross the immigration to reach the gate for your flight to Hong Kong.

As you can see, there are some formalities to be accomplished but nothing that will prevent you to perform your transfer in Beijing absolutely visa free. In any case, you are ready to go with the remark that your total transit time cannot exceed 24 hours even for a second based on the scheduled and not real time.