When dealing in and implementing Boolean Equations, we are forced to reduce
NAND and
NOR into regular
AND and
OR statements. To do this, we follow
Demorgan's Laws:
_____ _ _
A * B == A + B A NAND B == Not A OR Not B
_____ _ _
A + B == A * B A NOR B == Not A AND Not B
-----
A * B == A + B A AND B == Not A NOR Not B
-----
A + B == A * B A AND B == Not A NOR Not B
This, of course, expands to equations of several terms, such as
A NOR B NOR C == Not A AND Not B AND Not C.
A simple example:
----------
A * (B * C)
_ -----
A + (B * C)
_
A + (B * C) (the two negations cancel)
Yet Another:
- -
(A + B) * (C + E)
_____ - -
(A + B) + (C + E)
_ _
(A * B) + (C * E)