two-valued logic
digital logic

    (Commonly known as "Boolean algebra") A mathematical
   system concerning the two truth values, TRUE and FALSE and
   the functions AND, OR, NOT.  Two-valued logic is one of
   the cornerstones of logic and is also fundamental in the
   design of digital electronics and programming languages.

   The term "Boolean" is used here with its common meaning -
   two-valued, though strictly Boolean algebra is more general
   than this.

   Boolean functions are usually represented by truth tables
   where "0" represents "false" and "1" represents "true".  E.g.:

   	A | B | A AND B
   	--+---+--------
   	0 | 0 |    0
   	0 | 1 |    0
   	1 | 0 |    0
   	1 | 1 |    1

   This can be given more compactly using "x" to mean "don't
   care" (either true or false):

   	A | B | A AND B
   	--+---+--------
   	0 | x |    0
   	x | 0 |    0
   	1 | 1 |    1

   Similarly:

           A | NOT A       A | B | A OR B
           --+------       --+---+--------
           0 |  1          0 | 0 |   0
           1 |  0          x | 1 |   1
                           1 | x |   1

   Other functions such as XOR, NAND, NOR or functions of
   more than two inputs can be constructed using combinations of
   AND, OR, and NOT.  AND and OR can be constructed from each
   other using DeMorgan's Theorem:

   	A OR B   =  NOT ((NOT A) AND (NOT B))
   	A AND B	 =  NOT ((NOT A) OR (NOT B))

   In fact any Boolean function can be constructed using just NOR
   or just NAND using the identities:

   	NOT A  =  A NOR A
   	A OR B  =  NOT (A NOR B)

   and DeMorgan's Theorem.

   (2003-06-18)