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Optical Bench REDUX: Digital Switching can have Analog Functions!

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RJSV:
Diagram helps to illustrate my point, showing packaging for 9 parts and 10 parts types.

RJSV:
As seen in previous diagram, options can be for a typical 9-part plus zero, for conventional looking decimal words (10 columns total).  Also, you could, optionally, do some proportional stuff...requiring that you have 'parts or portions' of tenths or 10 % each, and having 10 columns.
Very confusing, in some settings, but usually get things right, after careful checking.  Tried placing a tenth 'zero' column, but then have a decision to make, and gets into ridiculous when pondering; Do I need a One' s flag, or digital 'ON', flag to indicate the (digital off) 'zero' state is present ? Gets ridiculous, partly due to the passive nature, of doing a data transfer of 'nothing', which is generally a format needing some kind of active clocking, while that 'ZERO' is present, or, err, 'not present'.

On the encoded OCTAL here, I've coded in a bias, of '2', to avoid that 'zero passive' case handling

RJSV:
In this enclosed diagram, is using the Golden Ratio related factor, of 6/7 or '0.833'.

RJSV:
...You can see the real number count-down are anything but linear, but still can be useful, doing a distorted decrement.
Reminds me of Piano, music theory, where each note or piano key, has a frequency that is a set constant ratio, each to the next.  In that case, each next piano note frequency is higher by the '12th root' of '2', for a total 'octave' that doubles in frequency, across it's range.  Somewhat by analogy, here, could be the 'notes' or OCTAL range values, within the decimal WORD, each seeming to be using the Golden Ratio, term to term, as the constant multiplier.  By exception, it was needed to try using two shifts, for reduction of incoming value, to the multiplier stack.  That way, in case of the lowest number needing a decrement, (3 as code for a '1'), that value '3' can be reduced by 2/3, in the very first multiply step, to, actually, a 'perfect' 2.0 !

RJSV:
Photo shows a fairly accurate multiplier stack, after much adjusting / fudging, for best compromise action.