Optical Illusion Teaser, at end, (see photo also).

Putting out this summary, progress and problems so far. THEN,...it will be Wednesday,

PLANES, TRAINS and AUTOMOBILES.

Fun friends, and famulilly !

The Dividing and multiplying, with various mixing of analog with digital formats, makes interesting tool set, but it was the 'DECREMENT' or integer counting that had surprising results, or partial realizations.

So, in cases of single digit, a multiply, (by 0.8 or by 0.85), serves as substitute for (blind) subtraction, as ratio to 56-1 vs 98-1 as 1 to 50 vs 1 to 100 change.

But a consistent multiply factor (applied blindly to a single digit, 0 thru 9, ) can be optimized for best 'curve' match.

Using ratiometric (multiply by number between 00 and 99) has a 'residue' that persists, going smaller and smaller. Another, similar option, uses similar looking operation, but ends up, discrete shifting, completely shifting all empty, due to the physical right shift, of the ten partitioned BUS defined lines.

But the 'integer' subtraction method gets interesting; instead of usual, roll-over with higher digits that occurs once each ten times, the method, blindly without clue where/when rollover should precisely occur, routine will do, constantly, a '1/10th' rollover, and that is literally done by 'rolling' a one value, every repetition. That way you still get 10 every 10 times you (decrement).

And while you must 'borrow' from the 'tens' column, a one, and then subtract that, it makes sense to 'JUST DO NOTHING', with low digit, and work on the rest of the task, which is to complete a subtract, of 'one' from the high digit, which represents '10' being moved over, in traditional paper-pencil subtraction protocol.

The error, however, or mean random error, for a ratio related subtraction, is about in order of one of those (low digit) decrement (virtual decrement).

That's what I've termed an 'Eye for an Eye' type of one for one subtract, by decrement in turn, usually with a zero test for 'j= 0'. Still not sure about that test, speed wise.

An alternate way, if For-Next repetitions use a parameter that becomes ineffective, I.E. goes to zero (by discrete shifting), even while the 'loop' continues on, unchecked but also not doing harm...

A mess, but have to admit; there is enough progress, to be presenting some real snags, areas of frustration (integer-like decrementing), and even an OPTICAL ILLUSION QUESTION:

(PLEASE SEE PHOTO, ENCLOSED).

Why, when moving head, are those after-images tracked out, from the little light ? At 232 khz those images, when eyeball 'flicks' around rapidly, those images aren't spaced right, for the speed they supposedly oscillate.