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General I will post all my papers on this site. The papers are ready on computer files. However, they need time to be rearranged and converted to HTML formats.
Like never before! AOP presents for MVL designers z! binary operators
for any z-radix digital system called prioritors
(priority operators). AOP presents 2 prioritors for the binary
systems, 6 prioritors for the ternary system, and 24 prioritors for the
quaternary system. No operators are added to the binary system by
AOP. However, AOP adds four additional operators to the classical operators
(MIN and MAX) of ternary system. It also adds 22 additional operators to
the classical operators (MIN and MAX) of the quaternary system. Prioritors
will be the modern operators for digital systems designs. Never under estimate
them. Who said in 1849 that the operators founded by Boole will take us to
the current age of computers? After 89 years, people realized the significance
of Boole's operators by a smart man "Claude Shannon" in 1938. See AOP
design for the ternary multiplication and think about
the various combinations that can be done with these operators in MVL
systems.
In addition to prioritors, AOP presents a complete mathematical tools to manipulate and work around these operators. AOP uses these new operators for circuits design and provides all the rules and procedures that lead to the design of any given digital circuit from this set of operators. The designs by the new operators, using AOP, are more simpler and much more efficient than the designs obtained by the classical operators (MIN, MAX) of MVL systems. Keep in touch with site to be updated on AOP news .
I will post all the papers on degeneracy theory after posting all papers on AOP. The degeneracy theory will replace the duality theory in Boolean and Post algebras. Degeneracy is a more generalized concept than duality. The degeneracy theory helps in classifying the binary operators of any z-radix digital system and it also helps in designing different digital circuits with the same functionality. R. K. Abu-Msameh 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 the basic binary operators from a z-radix digital system which are called "elements". These elements are the core operators of any z-radix digital system. All other elements 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 inherits 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. GTODE draws two models for the binary operators of any 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 serial partitions that ends to the solutions of the "elements" of the quaternary system. I will post all the papers on GTODE after posting all papers on Degeneracy.
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