0 1 to -1 0 1

[hlreed]

0 1 are the symbols of a binary digit. A binary digit is on off, happy, sad... ,always binary.
The only arithmetic you can do with binary is Boolean. (AND, OR, NOT)
-1 0 1 are symbols of a trinary digit. A trinary digit is left center right, off left on off right... always trinary. (I just made up trinary.)
I expect it has been used before but I don't remember seeing it.
With trinary digits, in addition to three states you have phase. -1 0 0 1 is 0 1 2 3 - 1
With trinary you can do regular arithmetic. (+, -)
which also encompass Boolean arithmetic. In other words, you do not lose anything by moving up.

[billdar]

I've been lurking through your posts for a while
now, and must say you come up with some unique
ideas...<p>This 'trinary' idea is something I've thought
a lot about before, mostly because of the increase
in computing.<p>But what I could not wrap my mind around, and
what I see as a primary draw-back to using a
trinary system, is that our brains work in binary.<p>It might be a conditioned attribute, but when
you add any string of numbers (say 12+6+38) you
always break it into binary operaters <p> (12+6) + 38
or for me
((( (2+6) + 8 ) + 10) + 30 )<p>Other than some parralel operations, or some
look ahead prediction, I can't see how a
trinary system would work.<p>But it is fun to think about

[hlreed]

Thanks for the comment.
Binary goes back to Aristotle and is ingrained in everthing since then. It made computers and switches neatly and a binary digit is one wire.
Fuzzy logic tried to go multiple, but they screwed it up. Trinary logic takes two wires for each digit and is a base four number. Of course we go beyond this with multiple digits, but one must start at the bottom first. The logic is trinary because it takes three tests to examine a digit. One must ask if it is 0, plus or minus.
The difference in binary and trinary is qualitative.
Again, thanks for talking. I am sailing against the wind here.

[Ron H]

At the risk of being called a nitpicker...<p>Trinary (ternary seems to be the preferred term) numbers are base 3 numbers, not base four. Or did you mean that with 2 wires, you can potentially have a base four number?<p>A Google search for "ternary arithmetic" and "trinary arithmetic" yields some interesting web sites.<p>Cheers, Harold -<p>Ron<p>[ November 13, 2002: Message edited by: RonH ]<p>[ November 13, 2002: Message edited by: RonH ]</p>

[hlreed]

Ron,
Nitpicking is fine with me.
Yes, 1 wire is base 2 0 1
2 wires are base 4 00 01 10 11
You can, of course have a base in any positive number. Base 3 is 00 01 10 or 0 1 2
Note that base is also symbol count for the digit.
When you get above base 2 there are no good names.
Best to use the symbol count. Personally I like base 256 digits. They use up eight wires.

[Dean Huster]

Maybe I'm nitpicky, too, Harold. I would think that base 4 would be 0, 1, 2 and 3, not 00, 01, 10, 11. The former would be the digits in base 4, the latter would be the conversion from base 4 to binary -- not the same thing. Similar observation for base 3, etc. In other words, the 00, 01, 10, 11 representation would be analogous to counting in English like this: uno, dos, tres, quatro ...<p>I'm starting to think, Ron, that the bulk of your 401K must be tied up in Google.com -- you never suggest Mamma.com or Dogpile.com!<p>Dean

[josmith]

How are you going to represent the minus sign? In binary they use a sign bit which is really just another binary digit.

[hlreed]

Dean,
Thanks but 00 01 10 11 and 0 1 2 3 are the same digit. Write them side by side like:
count binary base 4
0 00 0
1 01 1
2 10 2
3 11 3
Note that a symbol can have more than one character. 11 is one symbol here. 15 and F are both one symbol, one value, one number.
Josmith,
The minus sign bit is arbitrary and by convention.
Let the most significant bit be the minus sign.
0 = plus 1 = minus : Of course we use up a bit.
count binary base 4
0 00 0
1 01 1
2 10 0 ;note that 00 and 10 are both 0
3 11 -1 ;by convention
Having two zeroes does not mean much in base 256
and above.
Base is always the digit symbol count.
You can call a decimal integer base 3 by writing
count base 3
0 -1
1 0
2 1
What is the base of a decimal number? (12.54)<p>[ November 25, 2002: Message edited by: Harold ]</p>

[Ron H]

Hogwash, Harold. 15 is made up of two symbols: 1 and 5. Sure, you can redefine it as one symbol if you want, but you'll wind up having to explain yourself every time you do it - just like you did here.<p>Dean, I used Dogpile as my search engine of choice until I discovered Google. I had never even heard of Mamma. You probably think I live under a rock, huh?<p>Ron

[greg123]

I thought a base was defined, in DECIMAL, as the number of different digits.<p>e.g. Binary, 0-1, Base 2. Octal 0-7 base 8. Decimal 0-9 base 10.<p>So wouldn't that make base 4 0-3?<p>11 isn't one symbol...it's 2. 3 is one symbol.....like F in hex is one symbol (in that base) but the corresponding binary equivalent 1111 is 4 and the decimal 15 is 2.<p>Am I off on the topic??

[hlreed]

To all,
You can define a symbol to be whatever you say it is. Conventional math is stuck with one symbol per character because it has no multiply symbol. Go to computer science. Use symbol separaters, space or operator symbol. Columns don't line up here so you might not see what I am saying.
123 is one symbol if it has one meaning and one value. It could be a base 124 or a base 1000.
Symbols are not numbers.
Free base from decimal and let it roam.
Free symbols from one character.
Free math from mathematicians.
Let 0 1 go to -127 to 128. Go from lumpy to smooth.
This long variable = this thing - that thing
(Three properly delimited variables.)
Excuse the mixture of statements and proclamations.
The arguments are:
1. Symbols are not numbers and are arbitrary
2. Digit base is a count of the symbols required to specify its values plus the zero symbol.
3. Every number can be transformed into a digit by changing its base. (Removing infinities.)
Thanks guys. I am enjoying this.

[Dean Huster]

Ron, Mamma.com is just another metasearch engine, but it has one interesting capability: you can e-mail the results to yourself for off-line viewing. I don't know if any other other can do that.<p>Harold, you may be right. Touch typists consider words like "the", "and", "other" and other commonly-used words as a single character. That's why so often, I accidentally type "and" when I meant "an" since my fingers insist upon automatically finishing out the word.<p>Still, semantics aside, I agree that the use of 00, 01, 10, 11, etc. is not the use of single symbols, but multiple symbols. Actually, I would think that the defining measure would be to use your individual symbols together to form a larger number. "33012" is a heck of a lot easier to decipher as thirty-three thousand twelve than is "1111000110" which most would read as one-billion, one-hundered eleven million, one-hundered ten (since base 10 is assumed with no other qualifier).<p>Dean<p>[ November 27, 2002: Message edited by: Dean Huster ]</p>

[hlreed]

Dean,
May I send you a paper on number wheels. What it does is change the number line into a circle which is turned into a drum which allows you to write all the symbols side by side. The drum clicks from one number to the next. The click is the number. The symbols are arbitrary.
You have probably seen decimal click wheels on old equipment. That is where the click comes from.
Mathematics should have been redone after the computer.
Give me an email address and I will send you the paper. It is MSWord.

[greg123]

Someone tell me what we are aruging about again?

[bwts]

Hi H
I agree that one base's symbol is another base's symbols, but I do not agree with "Symbols are not numbers and are arbitrary". Symbols may well be arbitrary (differances in languages is a good example of this) but numbers ARE symbols!!! Try and express any number without the use of symbols reguardless of your symbolic system it is impossible!!!!!!
Numbers are a symbolic system used to represent quantity.<p>On another note Ive always thought that 3 state logic is an excellent idea <p>B