Active-HI and Active-LO?

by Richard Steven Walz


>I'm trying to learn a bit about electronics at the moment and have no
>great problems understanding terminology such as AND, NAND, OR, NOR,
>truth tables, etc, etc - however, Active Hi and Active Lo only seem to
>make sense SOME of the time!
-----------------------
Okay, here we introduce the concept of a variable label for the output of
any gate or array of gates. If I call some wire "RESET", does it mean that
it will reset when it is HI or when it is LO?? If I say it is active-HI,
then you know that it will perform its named function when it is HI and not
when it is LO, in other words it is "active-WHEN-HI", thus, "active-HI". And
the same for active-LO. Another way to say it is that it "does its name"!

When a proposition is active-LO we call it "inverted logic" or such, but 
that's just a confusing way to say you can swap "0" and "1" and see the
core proposition of the logical gate switch, and that it that relates to 
DeMorgan's Laws, which we'll get to in a couple paragraphs. I don't use the
term "inverted logic" because it just confuses people, and this below
covers all exigencies anyway:

If RESET is "active-HI" we know what we're doing, but is there a way to
know by the label itself? Yes! The labels are usually NEGATED for anything
that is "active-LO", that is, the label itself contains a  negative sign or
a slash in front of it, or it has a bar over it (made with the underline
char of the character positions on the line above it), thus -RESET or
           _____
/RESET or: RESET depending on how much room you have and what your editor
permits.

Now:

The reason we use a NEGATED symbol for that signal label is that it is part
of the way we write things in Boolen Algebra. Now don't let this confuse or
scare you, I taught Boolean to my son when he was age 5 in a half-hour. If
you know AND and OR and NAND and NOR and NOT and XOR and XNOR, then just
use the new symbols with variables: A AND B is written AB or A(dot)B or
A*B, and this is done since 1 * 1 = 1 in arithmetic, which is just like it
does in the AND proposition. Likewise A OR B = A+B, since 1+0=1 in plain 
arithmetic just as it does in Boolean. We even use the -, the slash "/" or
the bar over a symbol to mean that it does its named function when it is 
LO(Active-LO).

The reason this is so handy is that (-A) NAND (-B) = A OR B, or another way
to write it is -((-A)(-B))=A+B , and also, (-A) NOR (-B) = A*B which is
written as -((-A)+(-B))=A*B . Now this is the same as saying that if you
put "inverter balls" on all the inputs and outputs of an OR gate that you
get an AND gate, and vice versa. That's Demorgan's Laws!! And you can add
more or less balls as well, as you can see in this old file of mine:

http://www.armory.com/~rstevew/Public/Boolean/DeMorganTut.txt

Another good file to read is:

http://www.armory.com/~rstevew/Public/Boolean/BooleanTut.txt

 (excerpt)
-----------------------------*****-------------------------------
DeMorgan's Laws in Gate form:
( <==> = "Is Equivalent To", and in both directions! )
     ___                   ___
A---|    \            A--O\    \      
    | AND )---  <==>       ) OR )O-- <-- A true AND Gate at left!
B---|___ /            B--O/___ /     (Yes, it looks like an NOR, but just
     ___                   ___       think of "BALLs" as discrete "NOTs"!)
A--O|    \            A---\    \
    | AND )---  <==>       ) OR )O-- 
B---|___ /            B--O/___ /
     ___                   ___
A---|    \            A--O\    \
    | AND )---  <==>       ) OR )O-- 
B--O|___ /            B---/___ /
     ___                   ___
A--O|    \            A---\    \
    | AND )---  <==>       ) OR )O-- <-- A true NOR Gate!
B--O|___ /            B---/___ /
     ___                   ___
A---|    \            A--O\    \
    | AND )O--  <==>       ) OR )--- <-- A true NAND Gate at left!
B---|___ /            B--O/___ /
     ___                   ___
A--O|    \            A---\    \
    | AND )O--  <==>       ) OR )--- 
B---|___ /            B--O/___ /
     ___                   ___
A---|    \            A--O\    \
    | AND )O--  <==>       ) OR )--- 
B--O|___ /            B---/___ /
     ___                   ___
A--O|    \            A---\    \
    | AND )O--  <==>       ) OR )--- <-- A true OR Gate
B--O|___ /            B---/___ /

In OTHER words, swap OR core for AND, and put "BALLs" where there weren't
and take them away where they were, and you have converted an OR to AND
core proposition, or the reverse. These above are EQUALITIES, which have
the SAME TRUTH TABLE as the Gate Array!! For further fun, use DeMorgan and
"slide" the "BALLs" along a wire to where two meet and cancel and see what
results, or introduce two at opposite ends of a wire and see what DeMorgan
Law conversions can be accomplished to use up hex gate and quad gate chips
most efficiently!! Look at our first XOR made of an OR, 2 ANDs, and 2 NOTs
above and see if you can make it ONLY with either NAND or NOR gates. These
are the only two Gates which each have the property that ALL other Gates
can be made from them alone, all NANDs or all NORs, even any computer
architecture, functionally speaking!!
 
And even though DeMorgan's Laws don't cover the XOR and XNOR Gates:
There ARE even SOME interesting DeMorgan-esque features like this to the
XOR and XNOR Gates, but I'll leave that exploration to you out there with
idle time and a lot of napkins at some restaurant tonight!!
-------------------------****-----------------------------------

Enjoy!
-Steve
--
-Steve Walz  rstevew@armory.com   ftp://ftp.armory.com/pub/user/rstevew
Electronics Site!! 1000's of Files and Dirs!!  With Schematics Galore!!
http://www.armory.com/~rstevew or http://www.armory.com/~rstevew/Public