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
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
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
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
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.
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
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
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
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
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
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
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 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
- 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
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
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
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 email@example.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
of unstable states binary feedback latches
logic gates with numerical logic values
logic gate states in color
Gate States in Color
Inverters (3-state and 4-state)
Adder in Binary and Ternary Logic
OR/AND memory latch
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
The presentation can be viewed at Youtube
A zipped file, including Matlab files, Multimedia Logic
files and the Powerpoint presentation can be downloaded