Abstract
A three dimensional hypercube representing all of the 4,096
dyadic computations in a standard bivalent system has been
created. It has been constructed from the 16 functions arrayed
in a table of functional completeness that can compute a dyadic
relationship. Each component of the dyad is an operator as
well as a function, such as “implication” being a result, as well
as an operation. Every function in the hypercube has been
color keyed to enhance the display of emerging patterns. At
the minimum, the hypercube is a “multiplication table” of
dyadic computations and produces values in a way that
shortens the time to do operations that normally would take
longer using conventional truth table methods. It also can
serve as a theorem prover and creator. With the hypercube
comes a deductive system without the need for axioms. The
main significance of the 3-D hypercube at this point is that it is
the most fundamental way of displaying all dyadic
computations in binary space, thus serving as a way of
normalizing the rendition of uninterpreted, or raw, binary
space. The hypercube is a dimensionless entity, a standard by
which in binary spaces can be measured and classified,
analogous to a meter stick.