Let's compare this to the concept of the Schrödinger's Cat:
We have a cat and a sealable box which you cannot view the interior of when it is sealed. The box contains a special mechanism that will cause a container of poisonous gas to break open at any randomly given time. We will seal the cat inside the box, give it a steady supply of air and protect the mechanism from interference by it, and we will be unable to see the state of the cat or the mechanism again until we reopen the box.
While the box is closed, we have no way of knowing if the cat is alive or dead due to the random nature of the mechanism. However, once we open the box, we can finally measure the cat's state. Likewise, we don't know what the "both" digit is until we measure it. So, to answer your question, you don't actually "see" both digits at once, but rather, you see what it has been defined as when it is finally observed.