Before turning to nonlinear dynamics proper, we need
some familiarity with the binary number system.
Consider the problem of converting a fraction between
0 and 1 
written in decimal (base 10) to a binary
number (base 2). The formal expansion for a binary fraction in powers
of 2 is
where 
. The goal is to find the 
's
for a given decimal fraction. For example, if 
then
The general procedure for converting a decimal fraction less than one to
binary is based on repeated doublings in which the ones or ``carry'' digit
is used
for the 's. This is illustrated in the following calculation for
:
so
