Dividing by Zero

Dear sci/math,

I have a problem i would like to understand. Everybody knows you can't divide by zero, like everybody knows that binary codes just consist of 0 and 1.
First question: Why do you take a variable that is not defined at
for such an important system?

Second question: Would there be any difference if zero was defined for the casual use of Computers?

Maybe someone can help me just imagining how zero could be defined a little, if my questions make too little sense.

Thanks anon.

>>4
It can simplify some things to use 0 and 1.  For example, logical AND can be defined as multiplication.

>>5
So try it.  I remember this guy Anderson invented the so-called transreal numbers where you could divide by zero.