Suppose the X's had 0 entropy each - that is, they were states with no "internal moving parts," like an electron.

Now imagine that you introduced ignorance into the problem - now we don't know if the electron is in state 4 or state 7, so you assign each P=0.5. What is the entropy of this distribution?

Well, it turns out the entropy (amount of ignorance) is 1 bit. Which is 1 bit more than the 0 bits of entropy that states 4 and 7 had on their own.