GTODE
"General Theory Of Digital Elements"

Planets,  Elements

GTODE (General Theory of Digital Elements) is a theory that classifies the binary operators of a z-radix digital system into a series of sub-classifications.  At the end, GTODE filters out the basic binary operators from a z-radix digital system which are called "elements".  These elements are the core operators digital system.  All other operators in the system are called degenerate operators.  That means, they can be generated from the main elements physically and functionally.   This also means that degenerate operators inherit all the properties of their ancestors (elements).

For example, we know that the ternary system has 19,683 binary operators.  The study of this large number of operators can be simplified by GTODE.  GTODE reduces this number to 139 elements.  All the ternary system binary operators can be degenerated from the "139" elements.  All the theorems that describe these elements can be  inherited by the degenerate operators using the degeneracy theory. See ternary system elements 

GTODE draws two models for the binary operators of a z-radix digital system.  The first model is called the "Planetary Model or Universal Model" the second model is called the "Atomic Model".  Both models classify the binary operators of a z-radix system.  The planetary model results is a macroscopic classifications.  On the other hand, the atomic model results in a microscopic classifications of binary operators.  For example, the quaternary system has about 4.3 billion binary operators. This large number of operators is partitioned into consecutive partitions that ends to the solutions of the "elements" of the quaternary system.