Does fgets() always terminate the char buffer with \0?

Does fgets() always terminate the char buffer with \0 even if EOF is already reached? It looks like it does (it certainly does in the implementation presented in the ANSI K&R book), but I thought I would ask to be sure.

I guess this question applies to other similar functions such as gets().

EDIT: I know that \0 is appended during "normal" circumstances, my question is targeted at EOF or error conditions. For example:

FILE *fp;
char b[128];
/* ... */
if (feof(fp)) {
    /* is \0 appended after EACH of these calls? */
    fgets(b, 128, fp);
    fgets(b, 128, fp);
    fgets(b, 128, fp);
}