  We introduce new method for generating correlated or uncorrelated Bernoulli
random variables by using the binary expansion of a continuous random variable
with support on the unit interval. We show that when this variable has a
symmetric probability density function around 12 , its binary expansion
provides equiprobable bits over {0, 1}. In addition we prove that when the
random variable is uniformly distributed over [0, 1], its binary expansion
generates independent Bernoulli random variables. Moreover, we give examples
where, by choosing some parameterized nonuniform probability density functions
over [0, 1], samples of Bernoulli variables with specific correlation values
are generated.
