In reply to Postmanpat:
Here is an article on that very thing
http://phenomena.nationalgeographic.com/2013/05/07/charlemagnes-dna-and-our...
Basically you have two parents, then four grand parents, then 8 great grand parents, then 16 great-great grand parents and so on. As you go back to in time, forty generations or so (the time of Charlemagne), you should get to a generation of a trillion ancestors. That’s about two thousand times more people than existed on Earth when Charlemagne was alive.
To quote the article.
"As you go back further in time, more of those lines cross as you encounter more common ancestors of the living population. And then something really interesting happens. There comes a point at which, Chang wrote, “all individuals who have any descendants among the present-day individuals are actually ancestors of all present-day individuals.”
So you are related to William the conquerer as he was related to Charlemagne. There are 32 generations between Elizabeth and William so i am not sure how that works out