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Ternarylogic LLC

Ternarylogic LLC

Advanced computing? No matter how complex a program or application, how large the memory or how fast the internal clock of a processor or digital circuit, in essence we are still dealing with a computer being a relatively simple switching machine. The buidling blocks of these switching machines are the simplest of simple switching devices: binary switches. This is curious, as virtually no process in the real world (including mathematics) is a binary process. Almost every concept we deal with has multiple possible states.

If you are one of those people who have an innate curiosity and wonder how things can be done differently, you have come to the right place. You probably have heard many times that current digital technology is binary. Why not ternary, you may wonder. Or why not a 256 state logic? What would non-binary logic mean or look like? Find out here and on related web sites.

Ternarylogic LLC is an R&D company that develops Intellectual Property (IP) in non-binary machine logic and switching technology.

Our inventions are related to novel ways of using non-binary switching functions.

Non-binary Switching and Machine Logic

What is this non-binary switching?

Non-binary switching relates directly to an apparatus or device that processes (or switches) signals. The signals are represented by non-binary symbols. The non-binary switching machine does not perform logic or any conceptual or abstract function, it merely processes signals. The logic, often called Boolean logic, associated with switching functions, is merely a description for humans to understand how the switching devices operate.

Humans have been searching for a long time for ways to automate mathematical and arithmetical expressions. It is evident from the history of computing that merely having an expression is not sufficient to have it implemented and executed by a machine. Even known numerical methods, such as 'regula falsi' for finding roots, or Taylor series approximation, could only be performed by humans, not by machines.

The trick, it turned out, was to express the steps of calculating methods in switching or logic functions which were effective descriptions of the switching performance of actual devices, such as electro-mechanical relays. This was an invention by Claude Elwood Shannon as part of his M.I.T. thesis in 1937. It is important to realize that even with the description, the devices such as relays do not perform logic. They merely switch. The switching devices also do not perform any symbol processing: they only change state and generate signals. Without any meaningful human interface, one would not be able to determine what a switching machine is actually doing, besides switching from one state to another state.

The 'logic' description of the circuitry was recognized by Dr. Blaauw and Dr. Brooks, co-architects of the System IBM/360, to be a design layer that describes the function of the physical realization, without having to specify the actual circuitry. It means that every expression used in an implementation description has a physical realization.

Non-binary switches are devices that provide on an output a signal that represents a non-binary symbol. The non-binary symbol is merely a human representation for the signal. The non-binary switch does not process symbols, it processes signals and it does not produce symbols, it produces signals.

Non-binary machine logic is the description of physical devices that operate in accordance with non-binary switching devices. Any symbol that describes a switching state is arbitrary. While often using the symbols 0 and 1 in binary switching, one may as well select A and B, or any other representation. The selection of 0 and 1 reflects the human need to 'see' signals as representing symbols in a finite field GF(2). Such a description is not required for a switch to work, it is only required for humans to understand its functionality.

Non-binary machine logic as applied by Ternarylogic is thus a reflection of realizable physical devices and switching tables and not a mere description of conceptual or abstract logic.

If you are new to the concept of non-binary switching, you should probably download and read this brief paper on the subject on why and how it is different from binary switching. And why switching is not human logic, but rather machine logic.

Cryptography is Non-binary: the Finite Lab-transform (FLT)

Almost all messages transmitted between machines contain non-binary data. Text messages are coded in bytes, image pixels are coded as 24-bitwords and sound samples are coded as 16-bit words. Still, computer cryptography uses standard and predictable switching techniques which are based either on XOR switches (such as 3DES and AES) or on modulo-n arithmetic, such as RSA key exchange and elliptic curve cryptography. They all have in common that i+0=i; i*0=0; and i*1=i for all allowable values of i. Herein 0 is called a zero-element and 1 a one-element.

It would be beneficial to the unpredictability of a cryptographic method if 0 is not the zero-element and 1 is not the one-element. It would seem that a simple substitution can achieve that. Unfortunately, a simple substituition would ruin arithmetical properties such as associativity and distributivity of operations such as addition and multiplication.

The Finite Lab-transform (FLT) preserves essential properties of operations (such as finite field properties) while modifying the zero and one-element.

The Lab-transform allows a modification of cryptographic operations, such as AES, SHA-2, SHA-3, RSA, elliptic curve cryptography, Diffie Hellman, etc. while leaving the basic process steps in place. A benefit of the Lab-transform is that there are n! (factorial of n) different n-state inverters that determine an n-state Lab-transform.

This paper explains details of the Finite Lab-transform.

The Patents

Ternarylogic LLC owns a portfolio of over 60 inventions of in non-binary switching. Copies of the issued patents are available for download here.

How difficult is it to work with non-binary machine logic?

If you are familiar with binary logic and related truth tables, working with non-binary machine logic is amazingly simple. As with many engineering problems, insight will come by first articulating a non-binary logic machine problem that is followed by solving the problem.

The article "Shift Register Based Applications with MVL Switching Functions" by Peter Lablans, uses issues around non-binary shift registers with feedback, to explain, find and apply non-binary switching functions to create shift register based devices. It does not replace the book, the presentations and Matlab programs. However, the article is probably easier to read than the related patents and will provide sufficient insight on a high level.

The shift register examples lend themselves to a relatively easy visualization that may be more difficult to achieve in other non-binaryapplications, such as non-binary machine arithmetic and non-binary switching latches.

Availability of the Book, Presentations and Programs

The Intellectual property (IP) of Ternarylogic LLC is described and illustrated in the book, presentations and programs, available for purchasing or licensing.

The IP may be acquired by a party that wishes not to make these documents publicly available. At that time, Ternarylogic LLC will remove all documents from being accessed. At that time only patents and published patent applications may remain as a descriptive public source.

The Logic of More - Applications in Non-binary Machine Logic:
The Programs and Presentations

The best way to learn about the concepts of non-binary machine logic is to run and play with programs that perform non-binary logic.

A set of Matlab®/Freemat programs is now available to become familiar with the concepts. A set of 24 presentations accompanies the programs, explaining in detail the purpose and the structure of the applications.

By following the flow of the presentations you will become rapidly familiar and comfortable with non-binary switching tables and inverters. In fact, you may start to consider binary machine logic to be extremely limiting.

It is well known that analysis of patents is not easy. Analysts are mainly focused on the claims of patents, to assess possible infringement. This is somewhat risky, as in general the wider ramifications of the underlying invention are not well understood by only analyzing claims. The Ternarylogic inventions may affect millions if not hundreds of millions of devices. The Ternarylogic Package is very helpful to quickly understand the role and use of non-binary switching functions in its portfolio. This may not be achieved in a reasonable time frame by only relying on 40 or more patent documents. The Ternarylogic Package may also point you to advantageously use non-binary machine logic.

The price of the Ternarylogic Package is $ 395 and the Package can be ordered on-line from the Ternarylogic Store. The content of the Ternarylogic Package is available here. The price is not refundable.

The programs are experimental in nature. Please read the Ternarylogic Package License Agreement before you buy the Package. By entering the password 'I accept the License Agreement' you accept the terms and conditions of the License Agreement.

Help to install is available at this Help page

Take a look here at the table of contents of the presentations.

You will be taken to the Ternarylogic Store by clicking on the below image or on the Buy Now button.

Nonbinary Machine Logic: The Video

A free introductory video on the subject of Nonbinary Machine Logic is here.

If you prefer an MP4 format (for Apple for instance) click here.

The Logic of More - Applications in Non-binary Machine Logic: The Book

An extensive description and explanation of the inventions with simple examples is provided in an eBook that is now available for purchase. The title of this unique book is "The Logic of More.  Applications in Non-binary Machine Logic."  The price is $ 9.95.

Take a look at the Table of Contents.

An unlimited copy license is available at significantly reduced cost for qualified schools, institutions and companies. Send a request for information to admin@ternarylogic.com.

Hardcopy of the Book

A nicely printed hardcopy of the book is now also available. The price is $ 185. Fulfillment of printing and delivery of the book is provided by The Bookpatch. The hardcopy has a 8 by 11 inch size format and is much easier to read than on a screen.

Please allow 2-3 weeks for delivery.

  TheBookPatch.com Buy Now style 1 button

Substantial discount rates are available for purchase of multiple copies. Contact us at admin@ternarylogic.com.

Review Copy

If you would like to review the book or the programs you should send an email for a review copy to admin@ternarylogic.com.

The Ternarylogic LLC IP Portfolio

The Ternarylogic portfolio has over 50 inventions and covers:
- building blocks, such as switches and memories;
- self-synchronizing LFSR based descramblers in Galois and Fibonacci configuration;
- n-state symbol sequence generators;
- sequence detectors;
- correlation methods;
- error-correcting coding (BCH, convolutional and product codes);
- encryption, including Feistel network based codes and ECC coding;
- radix-n arithmetical methods; and
- Galois Field arithmetic.

Access to Our Portfolio and Licensing Opportunities

This web site comprises a wealth of information, links, white papers and references to patents and patent applications. Feel free to download any of the documents.  Please be aware that none of the patented inventions disclosed are in the public domain. No license is provided to use any part of our Intellectual Property.  But you can certainly review it. Or invent something new, if you are inspired by it.

A list of Issued Patents and Published Patent Applications is provided in a document that can be downloaded for www.ternarylogic.com/portfolio.pdf. This document has live links to at least some of the disclosures. Please, visit the US Patent Office web site here for an up-to-date listing of all issued patents.

Contact us if you wish to apply any of our inventions or obtain a license. While we encourage you to review all the disclosed matter, we frown upon any infringement of our IP rights. What does this mean? It means that you cannot use, make, sell, offer to sell, or import any of our inventions that are protected by US Patents in the USA without our express and written permission. Please review the Infringement Statute to update your knowledge about patent infringement in the USA.

Immediate Applications

Non-binary concepts are currently used in error-correcting decoding such as in Reed Solomon (RS) codes. The n-state logic functions are generally implemented as additions and multiplications over Finite or Galois Fields (GF(n)).

By using a non-binary switching approach to RS-coders (rather than an implementation of the more complicated polynomial arithmetical approach) one can simplify the understanding of the RS-coder as well as some error correcting strategies.

In a similar way one can address convolutional coders, including non-binary ones.

The eBook explains the above approaches and examples are provided in the Freemat/Matlab programs.

Youtube Ternarylogic Video Channel

Non-binary machine logic is not trivial. However, it is not difficult either, but it takes some exposure to get used to.

A series of Youtube videos related to different aspects of non-binary switching devices is posted and expanded on a regular basis. Examples programmed under Matlab Guide are provided to visualize the aspects of non-binary switching devices. A free copy of the Matlab programs can be obtained by sending a request to admin@ternarylogic.com.

The following videos (most recent ones listed first) are currently available.
 16) Non-Binary Feedback Shift Registers
 15) Binary Feedback Shift Registers
 14) Reduction of non-binary switching function with inverter
 13) Non-binary text encryption with reversible inverters
 12) Non-binary circulating memories from reversible inverters
 11) Non-binary reversible inverters
 10) Non-binary (3-state and 4-state) feedback memory latch
  9) Visualization of unstable states binary feedback latches
  8) Non-binary logic gates with numerical logic values
  7) Non-binary logic gate states in color
  6) Binary Gate States in Color
  5) Binary Inverting Gates
  4) Non-binary Inverters (3-state and 4-state)
  3) Ripple Adder in Binary and Ternary Logic 
  2) Modified OR/AND memory latch
  1) Novel Binary Feedback Latches

Novel Binay Latches

In order to design non-binary latches, a switching model has been developed that enables the simulation and design of binary and non-binary feedback latches. A presentation has been posted on Youtube that explains and applies the model for the binary case. Novel latches such as the "a greater than b" and the "OR/AND latch" are explained by the way of novel switching tables, simulation and in actual circuitry.

The presentation can be viewed at Youtube here.

A zipped file, including Matlab files, Multimedia Logic files and the Powerpoint presentation can be downloaded here.