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
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.
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.
Availability of the Book, Presentations and
The Intellectual property (IP) of Ternarylogic LLC
is described and illustrated in the book, presentations and programs,
available for purchasing or licensing.
The Logic of More - Applications in Non-binary
The best way to learn about the concepts of non-binary
machine logic is to run and play with programs that perform non-binary
Nonbinary Machine Logic: The Video
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.
An unlimited copy license is available at significantly reduced cost for qualified schools, institutions and companies. Send a request for information to firstname.lastname@example.org.
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.
Substantial discount rates are available for purchase of multiple copies. Contact us at email@example.com.
If you would like to review the book or the programs you should send an email for a review copy to firstname.lastname@example.org.
The Ternarylogic LLC IP Portfolio
The Ternarylogic portfolio has over 50 inventions and
Access to Our Portfolio and Licensing
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.
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)).
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.
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.