from the silver platter department ...
in the picture attached below, we've manually stored the values 0, 1, 2, 3, 4, 5, etc. in locations B3:0, B3:1, B3:2, B3:3, B3:4, B3:5, etc. ...
now look DOWN the "0" column of bits on the table and notice the 0, 1, 0, 1, 0, 1, etc. pattern ...
now look DOWN the "1" column of bits on the table and notice the 0, 0, 1, 1, 0, 0, etc. pattern ...
so - FINALLY - something useful for all of that "binary numbering" theory that they make us learn in school ...
note to Bernie ... I can remember how stunned I was when I first noticed that pattern for myself ... NONE of my instructors EVER pointed out the very simple pattern to me - I just noticed it one day ...
here's another simple pattern that I noticed just a few years ago ... learning the NINE's multiplication table is EASY to remember ... suppose you need to multiply NINE times SEVEN ... the answer will start with ONE LESS THAN the "question" number ... so since we're multiplying by SEVEN, our answer must start with SIX ... and the two numbers in the answer always add up to NINE ... so since we've already got SIX for the first number, the second number must be THREE ... so - NINE times SEVEN equals SIXTY-THREE ... I've helped about a dozen neighborhood school kids with that little trick ...
now then - can you image just how many little "math" patterns are rattling around in the noggin of our distinguished colleague Peter Nachtwey? ... I hate to even think about it ...