The ADC stuff is useful if you want to describe the signal you receive. If you know you are receiving a numerical signal, and expect it to be 0 or 1, you have much more efficient ways to know if your signal is 0 or 1.
You probably know the logical 1 is often 5V, and the 0 0V. Those values depends on the technology you use (most parts on high-end microprocessors now use 1.2V as 1, and 0V as 0), but I will always say "5V" in my answer, for readability.
Were does it comes from ? From transistors. Digital electronics uses transistors as commutators. Transistors either let the current pass, or block it. If you put 5V on the gate of your transistor, it let the current pass, if you put 0V, it blocks the current (some transistors works just the opposite way, some are just different, but it does not matter here). By using 5V in your whole circuit, you become able to switch transistors ON and OFF using other transistors.
So, why precisely 5V ? In fact, we don't really need 5V. 4.5V works fine too, 5.5V works fines too, but 10V will probably make your transistor burn, while 2V will make your transistor let some current pass, but resist to it. On the first case, you destroy your circuit, it is obvious it won't work. On the second case, you just can't predict if your output will allow to put the following transistor to either 0 or 1. This lead to logical issues, such as your processor making a subtraction instead of an addition.
To sum up, we need binary logic, and we make electronics behave as logical systems. We have just chosen some parts of the analog characteristics that allow us to do logic, and avoid to make transistors be between passing and blocking state, as it makes no sense in binary logic.