Convert (x + y = z) to propositional logic formula for 8-bit numbers

Question

(Note: this was asked in the cstheory stackexchange, but I was told this is a more appropriate place for it.)

I have three 8-bit 2's-complement numbers (X, Y, and Z). I want to find a propositional logic formula using only the variables (x₁, x₂... x₈, y₁... y₈, z₁... z₈), where x_i is the i^th bit of x which expresses the concept that X + Y = Z. How would I go about doing this?