Source : Free On-Line Dictionary of Computing

two-valued 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)