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MCD



Joined: 21 Aug 2004
Posts: 604
Location: Germany
MCD
As I went on to a chase for unusual number systems, I encountered the balanced ternary system - a positional system using 3 different figures: -1 0 and 1, and the best of it is that numbers don't need a separate sign symbol to denote negative numbers!
Wikipedia has something more about it, and it says that even some experimental computers were built with it.

I want a working ternary computer!

On the other hand, I wonder how this can be built using digital electronic components, especially CMOS-type circuits, since in CMOS, signals may be either high or low, but NOT in between (only for an intermediate short burst time). Pulling the input of a CMOS-type circuit to a level in between high and low basically either short the circuit or sets the output on high impedance, depending on what kind of field effect transistors one uses(depletion or enhancement).

I think a balanced ternary digital computer would have to employ a completely different kind of circuit topology than CMOS if it were to be made run efficiently.

What do you think? Are there other weird number systems that can be practically employed to build computers? Negative binary or even complex binary being other examples.

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Post 15 Dec 2011, 01:42
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
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revolution
I think that before you start designing the hardware and selecting the transistors you will need to define the set of functions you need to support. Boolean functions are only good for binary, what is the ternary equivalent? Once you can answer that then you can decide whether or not CMOS (or another) topology is suitable.


Last edited by revolution on 15 Dec 2011, 15:12; edited 1 time in total
Post 15 Dec 2011, 02:12
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shoorick



Joined: 25 Feb 2005
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shoorick
Post 15 Dec 2011, 10:34
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Matrix



Joined: 04 Sep 2004
Posts: 1171
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Matrix
MCD wrote:
As I went on to a chase for unusual number systems, I encountered the balanced ternary system - a positional system using 3 different figures: -1 0 and 1, and the best of it is that numbers don't need a separate sign symbol to denote negative numbers!...


ok, so how is that superior to a binary system?

btw.: i'd like to have a "16384 level primitive 3d storage matrix", so i can store 128 TB of data on my micro SDXWC type keychain pendrive (size = 15x11x1mm)



haha, that triangle PCB reminds me of a fluxcapacitor Smile
Post 15 Dec 2011, 14:58
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cod3b453



Joined: 25 Aug 2004
Posts: 619
cod3b453
I think {-1,0,1} probably could be implemented in CMOS using polarity and gates similar to bidirectional thyristors; though my guess is this is more silicon than the two bits you could have to represent the sign bit Laughing I have no idea how such a system would work but it's likely there'd be as many tricks you could use.
Post 17 Dec 2011, 20:53
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edfed



Joined: 20 Feb 2006
Posts: 4237
Location: 2018
edfed
build the -1,0,1 logic is not a problem at all. it is exactlly the same as the 0/5V and -12/+12V binary logic, mixed with full and halves bridge gates. it is easy, and very powerfull.

then, how to encode numbers with trinary? what would be the result of -1 and +1, etc, etc... first, define the arithmetic, second, define a way to use it in our real world (decimal domain, using multiplications, additions, divisions, pi, sinus, etc...), and then, we wlll design and print the circuit. Smile
Post 18 Dec 2011, 02:12
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malpolud



Joined: 18 Jul 2011
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malpolud
Yeah, revolution is right, the most important thing is the logic. Encoding numbers with potentials under and over 0 is easy, -1 is low, 0 is middle, 1 is high
SHL1 = multiplying by 2
00010001 *2 = 00100010

but what happens when we SHL trenary? The same thing but the SHLed number tripples
-1 -1 -1 -1 0 0 1 1 = 0d44 will become -1 -1 -1 0 0 1 1 -1 =0d132

About boolean logic:
maybe some simple bit logic could be converted into a comparison logic?

-1 = -1 - true 0
-1 = 0 - false 1 (more)
0 = -1 - false -1 (less)

Of course a single byte will contain much more information than a binary byte, but the question is if trenary logic can be used more efficiently than binary by electronic circuits?
Post 18 Dec 2011, 23:43
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Matrix



Joined: 04 Sep 2004
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Matrix
You might be better off defining a trinary system with values [0-2]
(octal is [0-7])
A trinary bit can contain zero=0, half/floating=1, hi=2
Advantage is: it uses space more efficiently
Disadvantage is: floating level is slower to handle, and noise immunity is lower.

Same logic can be extended to any amount of data in a single bit, 16 bit information stored in an analog way needs to have 2^16 levels with good signal to noise ratio.
Post 19 Dec 2011, 15:26
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