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Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits.

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On 8/16/2011 1:53 PM, Ian Martin Ajzenszmidt wrote:
> On Aug 17, 5:13 am, MitchAlsup<MitchAl...@aol.com>  wrote:
>> The reason that binary "took over" in logic design is that it has the largest signal to noise tollerance of any logic family. This translates into vanishingly low error rates and highest possible speed/power product.
>>
>> 1-bit inverter 60 GHz
>> 4-bit flash converter 7 GHz
>> 8-bit A/D 200 MHz
>> 14-bit A/D 16 MHz
>> 20-bit A/D 2 MHz  (only reaches 18.3 bits of precision)
>>
>> Notice a pattern?
>
> Based on the following Wikipedia article, and its Literature
> citations, use 2 to n possible value logic, where n is a number from 1
> to infinity. Lower electricity consumption.
>
> http://en.wikipedia.org/wiki/Ternary_computer

Yeah?  So?

It's still an issue of noise.

If you have a circuit technology that is extremely low noise, go for 
multilevel.

Note that flash uses multiple signal levels per bitcell - although it is 
quickly converted into binary.



>
> Main article: Balanced ternary
> Ternary computing is commonly implemented in terms of balanced
> ternary, which uses the three digits -1, 0, and +1. The negative value
> of any balanced ternary digit can be obtained by replacing every +
> with a – and vice versa. It is easy to subtract a number by inverting
> the + and – digits and then using normal addition. Balanced ternary
> can express negative values as easily as positive ones, without the
> need for a leading negative sign as with decimal numbers. These
> advantages make some calculations more efficient in ternary than
> binary.

By the way: I suspect that what you (and wikipedia) call ternary is, in 
the computer arithmetic community[*], usually called "signed binary".

The distinction binary versus ternary is made according to the base.

E.g. if you have a number whose digits are
     {d_i} = {dn, d_n-1, ... d2, d1, d0}

then it is a binary notation if the value is

D = sum d_i * 2**i

and it is a ternary notation if the value is

D = sum d_i * 3**i


There is no restriction that the digit set be only two values, {0,1}, in 
binary.

It is quite common to have digit sets of {-1,0,1} in binary,  also 
{-1,0,1,2}, etc.   Sometimes {-1,1}, with no zero, for specialized 
applications.

---

[*] At least, this is what I was taught to call it, by Robertson, the R 
in SRT division.   And I am fairly certain that it is current in most.

I am surprised that Knuth calls it ternary.  I will ask him about that 
in November.

---

I suppose that we could say that the digit set is binary or ternary, 
while the base is 2.

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Thread

Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. Ian Martin Ajzenszmidt <iajzenszmi@gmail.com> - 2011-08-16 11:38 -0700
  Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. MitchAlsup <MitchAlsup@aol.com> - 2011-08-16 12:13 -0700
    Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. Ian Martin Ajzenszmidt <iajzenszmi@gmail.com> - 2011-08-16 13:53 -0700
      Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-16 18:11 -0700
        Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. Robert Wessel <robertwessel2@yahoo.com> - 2011-08-16 20:38 -0500
          Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-08-16 20:50 -0700
            Re: Binary switching logic circuits versus rotary switching 1 to n position switching logic circuits. Robert Wessel <robertwessel2@yahoo.com> - 2011-08-16 23:43 -0500

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