I was looking for a way to do a BITOR() with an Oracle database and came across a suggestion to just use BITAND() instead, replacing BITOR(a,b) with a + b - BITAND(a,b).
I tested it by hand a few times and verified it seems to work for all binary numbers I could think of, but I can't think out quick mathematical proof of why this is correct.
Could somebody enlighten me?
A & B is the set of bits that are on in both A and B. A - (A & B) leaves you with all those bits that are only on in A. Add B to that, and you get all the bits that are on in A or those that are on in B.
Simple addition of A and B won't work because of carrying where both have a 1 bit. By removing the bits common to A and B first, we know that (A-(A&B)) will have no bits in common with B, so adding them together is guaranteed not to produce a carry.