Assuming you define all your terms correctly, yes it does. On page 379 of Principia Mathematica by Alfred North Whitehead and Ludwig Wittgenstein, they finally getting round to proving this:
1 + 1 = 2 indeed, and here is the very roundabout way of proving it. Personally, I would rather hold up two fingers and count them, but to each his own.
And in Base2 (binary), 1 + 1 should be 10.
For all intents and purposes though, the vast majority of time for the overwhelming majority of people, 1 and 1 does indeed equal two, so the equation of pretty much like death and taxes in that sense.
