[15.13] How can I "reopen" std::cin and std::cout in binary mode?

This is implementation dependent. Check with your compiler's documentation.

For example, suppose you want to do binary I/O using std::cin and std::cout.

Unfortunately there is no standard way to cause std::cin, std::cout, and/or std::cerr to be opened in binary mode. Closing the streams and attempting to reopen them in binary mode might have unexpected or undesirable results.

On systems where it makes a difference, the implementation might provide a way to make them binary streams, but you would have to check the implementation specifics to find out.
Is it talking about using cin and cout like cin>>x, cout<<x so that it outputs in binary instead of ASCII text?
Because my understanding is that write() and read() can do the job.