Foggy Bottom is having more than its usual difficulty communicating these days.

But contrary to the impression that some callers have received, the State Department hasn't gone out of business. It is only changing the vast telephone system that connects it to the outside world.

Among the first to have their phones changed were Chief of Protocol Selwa Roosevelt and her staff -- smack in the middle of the visit here of Britain's Prince Charles and Princess Diana and the consequent deluge of calls with questions about the royal schedule.

If you tried to call the Office of Protocol at its listed 632-0685 yesterday, you got only a recorded message advising, "You have reached a disconnected federal number." For assistance, it added helpfully, you should call 655-4000.

At 655-4000, a cheerful federal information operator completed the circle and advised that the number listed for the protocol office is 632-0685.

The most visible feature of the new system involves a change of the 632 prefix that most department phones have had for years to 647. For example, Secretary of State George P. Shultz, whose number is 632-4910, will be answering at 647-4910 once the changeover is completed.

Last month, the department issued the new annual edition of its internal telephone directory listing the hundreds of new 647 numbers for officials of the department, the Agency for International Development and the Arms Control and Disarmament Agency. That was done on the assumption that the new system would be in operation by Nov. 9.

But the deadline was missed. Instead the change began last week in piecemeal fashion, and department officials have no idea how long it will take for all the phones to be switched to 647. So for a while, some offices will have the new number, some will operate on the old one, and outsiders may find that trying to get a call through resembles a game of roulette.

In the meantime, what will happen if some foreign leader has to get in touch with Shultz? Department officials say the secretary is still working from his 632 number so the question hasn't yet been put to the test.

But in any case, they say, there are other ways of getting through to the secretary. And if all else fails, he can probably be reached at the summit in Geneva next week.