How precise must the voltage of a bit pulse be?

From my last question, I learned that a computer registers bits (a "1" or a "0") by checking whether there is a ~3 volt pulse or no pulse during a certain (short) period of time. I now wonder what happens when there is a ~2 or a ~1 volt pulse. I guess that more or less is good enough for the computer, for instance a ~2.999 volt pulse. My question is: if we count down from ~3 volt, at what voltage does the computer not register a "1" anymore?