## Simultaneous equations with XOR [closed]

The scope of what I'm looking at is much broader, but I've simplified it down to this form:

Where A/A1 and B/B1 are known initial conditions, and C1/C2 are constants to solve for, I have these equations to solve simultaneously. The other forms I work with I fit into matrices to solve no problem, and I'm looking at the best way to solve this form.

A + C1 + (A XOR C2) = A1

B + C1 + (B XOR C2) = B1

Please note that these all represent real integers, in range 0 - 0xFFFF.

A practical real example is below (example only, not necessarily solveable):

0x32A3 + C1 + (0x32A3 XOR C2) = 0xF82B

0x873C + C1 + (0x873C XOR C2) = 0xD18A

Most troubling for me is if its possible to algebraically solve the bitwise XOR operation like this. Is there a NON-substitution approach to take?

Thanks!

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 Am I correct that you are trying to solve a system of equations where you use both addition-with-carry (+), and addition-without-carry (as XOR)? It seems that you can iteratively solve for the bits, starting from the least significant. At any rate, your question seems more suitable for Stackoverflow, or math.stackexchange.com than this site. – S. Carnahan♦ Nov 9 2011 at 23:30