Adder circuit with sign bit (not twos complement)

I've found and implemented a full adder to be able to do unsigned or two's complement addition on wikipedia: https://en.wikipedia.org/wiki/Adder_(electronics)#Full_adder

However, in my particular case, I'd like to use a sign bit instead of twos complement, due to there being a variable (unbounded) number of bits involved.

How can i do addition and subtraction with binary numbers using a sign bit? (say, it's a separate bit, not one of the binary digits per se).

I also only have access to AND and XOR.

Edit: Potatoswatter suggested that twos complement is still able to be done with an unbounded number of bits. What do you do when you want to add 6 bits and 8 bits together? Also, is multiply, divide and modulo easily done in twos complement? Keep in mind i have only AND and XOR, so don't have the ability to do if statements, the logic needs to be "branchless".

Thanks!!

• You can have two's-complement with an unbounded number of bits. Just let the most-significant bit be the sign. Alternately, say that the sign bit "isn't one of the digits," let the digits be a number less than $2^N$ where $N$ is given in a length prefix or whatever, and let the sign bit be something else which subtracts $2^{N+1}$ from that number. Two's-complement almost always saves headaches. (Floating point is the big exception.) – Potatoswatter Oct 4 '15 at 8:31