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MainFragger,

One reason why we use binary systems to perform mathematical operations is relative immunity to noise. Having a system that has only two states, high and low, means that there is a very large difference between the two states that allows noise to be ignored. To be more explicit, anything above a set threshold is high, and anything below is low. Thus, when noise, an inevitable intruder, is found on the signal, it can be amazingly high before it causes error. But, in a system that is trying to use multiple levels, such as your hexidecimal example, any noise that is greater than 1/32nd of the full scale will cause an error. The greater the precision required of a given signal, the smaller a given noise can be that will cause error. Thus, the system is very likely to be error prone.

Another reason binary systems are used is cost. It is far easier to make on/off switches than it is analog amplifiers with the accuracy needed for higher modulo math systems. Analog computers were developed before binary computers proved to be far more economical. (As a youngster, I build such a simple analog computer, just for kicks, after reading about them in an electronics hobby book from a few decades earlier.)

--Candice H. Brown Elliott