Wrong, anything digital uses base 2.  It's just the nature of digital,
   there is either electricity or there is not.  When you start measuring
   the level of the electricity, you enter the analog world.

Not at all: you can have digital things that use base 3, 4, or other
bases and, in fact, most modern signalling technology (56 k modems,
100 Mbps Ethernet, digital television) uses very large bases (e.g.,
256).

It's a trade-off: the larger the base, the more care you have to take
in recovering the signal and the less loss budget you have.

Think of the difference between a DC signal and one with a frequency
of, say, .00001 sec.

In any event, you're confusing "base 10" with BCD.  Calculators indeed
use base 2, but they do their math in base 10 using BCD.  So they
don't have the base 2 representation problems.

Craig

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