(really about xor)

[Frank Adams]

In article <7220 at brl-smoke.ARPA> gwyn at brl.arpa (Doug Gwyn (VLD/VMB) <gwyn>) writes:
|In article <2701 at mmintl.UUCP> franka at mmintl.UUCP (Frank Adams) writes:
|>In article <131 at puivax.UUCP> ian at puivax.UUCP (Ian Wilson) writes:
|>>exclusive or being the only information-preserving logical operation.
|>Equivalence also has this property.
|
|What in the world are you two talking about?? ... As I think I
|pointed out, you could also use
|differencing in a similar fashion, and I'm sure there are other
|operators that would serve.  The important thing is not to lose
|dimensionality of the combined set of data (such as would happen
|if one variable were copied onto the other).

This is another way of saying what we were saying.  The pairs A^B,A and
A^B,B must each contain the same information as the pair A,B.  Exclusive or
and its complement, equivalence, are the only *logical* (i.e., Boolean)
operations with this property.  There are, of course, many other operations
on words of more than one bit which would serve.

Strictly speaking, of course, the information preserving operation is not
A,B -> A^B, but A,B -> A^B,B.  Another way of looking at it is to note that
A -> A^K and B -> K^B are both information preserving operations for any
constant K.
-- 

Frank Adams                           ihnp4!philabs!pwa-b!mmintl!franka
Ashton-Tate          52 Oakland Ave North         E. Hartford, CT 06108