Re: Negabinary Number System

I agree with everyone else I think. Instead of racking your brains to figure out how to do that with gates, figure out what naturally uses this system and map numbers to that system. We use binary two's compliment because that's what gates really like.

But "grey code" is kind of wierd, similar to your negbinary system, and it's not good for gates. But, it's very good for positional encoding of a shaft, since only one bit changes at a time.

So, think about what really works that way. It sounds like something swinging back and forth and getting higher each swing, like an amplifier sinewave, with + being left and - being right.

So think about a spring-driven system. The restoring force is proportional to the displacement, and this produces nice sine waves. If force is constantly being added (or the restoring force constantly weakening) what power curve would be needed to give each turn-around point twice as far away as the previous?

IAC, keep us posted.

—John

Comment on Re: Negabinary Number System

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Re: Re: Negabinary Number System by Cirollo (Friar) on Sep 06, 2001 at 03:44 UTC
Of course, this only corresponds to an idealized driven-spring system, because the restoring force-displacement proportionality is only linear for small displacements, and it isn't 100% accurate (in a real physical system), because the return force is also proportional to the displacement squared, and cubed, and so on. The effect of the higher order proportionalities is just negligible for small displacement. My point is that you could conceptualize the system as a system of springs, or a driven LC circuit, but if you were to try to actually build some sort of device to do calculations using the idea, it would quickly become inaccurate.	[reply]
Re: Re: Re: Negabinary Number System by John M. Dlugosz (Monsignor) on Sep 06, 2001 at 07:40 UTC
Which is exactly why analog computers fell out of favor, except for really specialized applications that can't be approached in any way other than modeling the system. What else naturally alternates in two directions? And is digital in nature, no less? Natural positional systems are like car odometers.	[reply]