Quick Tutorial on De Morgan's Laws


It's not a "theory", it's "the Law"!! ;-> It's MATH. It works or it
doesn't!! No testing required after it works right. ;-) DeMorgan's Laws.

They are written as /(AB)=(/A)+(/B)  and,  /(A+B)=(/A)(/B)  and that's
why they are plural, "..Laws".

But the graphic principles with using the over-bar for "NOT"-ing
equationally, and with GATES are:
                                      __   _ _       ___    _  _
1) "Break the line/Change the Sign",  AB = A+B  and  A+B = (A)(B)

2) The gate "sense" changes from OR to AND or from AND to OR
when you PUT "balls" (inverters) where they weren't,
and take them from where they were,
on ALL inputs and output!
    ___                ___                  ___                 ___
A--|    \          A-O\    \            A--\    \           A-O|    \
   | AND )O-C <==>     ) OR )--C  :AND:     ) OR )O--C <==>    | AND )--C
B--|___ /          B-O/___ /            B--/___ /           B-O|___ /

P.S., It ALSO works with any inputs or output mixed as well, too!!
      Not JUST Both/All inputs vs output as shown here!! Example:
    ___                ___                  ___                 ___
A-O|    \          A--\    \            A--\    \           A-O|    \
   | AND )O-C <==>     ) OR )--C  :AND:     ) OR )O--C <==>    | AND )--C
B--|___ /          B-O/___ /            B-O/___ /           B--|___ /

Told you it was Quick!!
-Steve
--
-Steve Walz  rstevew@armory.com  ftp://ftp.armory.com:/pub/user/rstevew
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