  We note with B2 the Boole algebra with two elements. We define for the R->B2
functions the limits, the derivatives, the differentiability, the test
functions, the integrals. We also define the distributions over the space of
these test functions, the regular and the singular distributions, the support
sets of the distributions. We also define for the RxR->{0,1} functions the test
functions and the distributions over them. The direct product of the
distributions is presented, as well as the convolution algebras of
distributions. Generalizations of the binary test functions and of the
distributions over them are given.
