What is AOP?

AOP is a mathematical tool that is aimed on providing a new algebraic system for the field of MVL. It introduces a new set of unary and binary operations that will make design more flexible than would be using just the traditional operators alone. This makes AOP the first multi-operational algebra to be introduced for this field. Also, since it works for any z-radix system, it is a multi-valued algebra. Hence, AOP  is a multi-valued multi-operational algebra. The unary operations are classified into two categories: conservative operators and orthogonal operators. The binary operations are called prioritors  The number of these operations depends on the system radix where AOP is to be used.  For a z-radix system it is z2(z-1) for its orthogonal operators, z! for its conservative operators, and z! for its prioritors. Thus, these are the basic operations of AOP that are used to design any digital circuit. The traditional operators we mentioned above are a subset of the new operators of AOP.

There are seven major papers on AOP, which cover about 90% of AOP theoretical and practical aspects.  These papers are:

1. A New Set of Unary and Binary Operators With a New  Algebraic System For Multiple-Valued Logic Systems: The Algebra of Priority (AOP).  Table of Content (TOC-1)  Major contributions:  

   • Priority Concept to replace current Logic Concepts 

   • Unary Set of Orthogonal and Conservative Operators similar to Post complementary functions

   • Prioritors similar to AND, OR, MIN, and MAX

   • Priority Rules (Essential, Basic, and advanced Theorems) to replace logic rules.

   • Absorption Theorem III to replace Kleene's Law

   • Z! representations for MVL functions to extend Post representations

   • Z! expansions for  MVL functions to extend Post expansions 

   • Uniform Image-Scaling Theorem to replace DeMorgan's Laws

   • Comments On AOP Theorems
     

2. An Introduction to the Advanced Theorems Of AOP Major contributions:

   • Comments

   • Uniform Degeneracy Theory to replace duality theory

   • Coprioritors similar to NAND and NOR
     

3. AOP Applications in Combinatorial Logic Design Major contributions: 

   • Comments

   • Use of prioritors and orthogonal operators in designing: gates, decoders, encoders, multiplexers, demultiplexers, ..etc

   • Design of MVL functions from their function tables using orthogonal theorems of AOP 
     

4. AOP Applications in Sequential Logic Design Major contributions: 

   • Comments

   • Basic cells for data storage.

   • Basic cells for latches similar to RS-latch

   • Basic cells for registers similar to D and JK flip-flops

   • Basic cells for counters similar to JK-flip flop

   • Design examples using the above basic cells such as:

   • Counters, registers, and latches

5. VBP transistors Major contributions

   • Four-terminal voltage-switched transistor (VBP transistor)

6. Electronic Implementation of Unary Operators of AOP Major contributions

   • Power-bus concept

   • Global circuits using VBP transistor for implementing unary operators

   • Comments

7. Electronic Implementations of Prioritors of AOP Major contributions

   • Global circuits for implementing all types of binary operators.

   • Global circuits for implementing prioritors
     

8. Devices Design Using AOP (under work)