I made a hat game in a very high level language I AM HELPFUL but not really. :<

I can never hope to be as prolific a programming artist as you with that game under your belt ;3;

You only need addition to do all the math stuff. Subtraction would be special case of addition where one of the operands gets two's complemented.
As far as carry goes, simple addition parts have 3 inputs and 2 outputs - data1, data2, carry in, carry out and result. The different bits are stackued together so the carry out of one element goes to carry in of other, allowing larger numbers to be added together with more and more elements.
Z is zero, and the other bits sound awfully similar to CPU flags register which is used to act decide whether or not to branch code somewhere else in most cases. Z you'll get by checking if all output bits are zero, job for simple logic. Carry flag is the final Carry out of the adding elements chain. Overflow happens when carry bit changes after math operation, True Sign is last bit of the data, when that bit is set you always have a negative number.

Thank you so much!
Okay, after studying a zillion Powerpoint slides, I think I've got most of it down, you can let me know if I have this all right:
http://tinyurl.com/psl4k9v
C is 0 = No final Carry
V is 0 = No overflow, sign bit stayed the same
S is 0 = Sign is positive
Z: I'm still not too sure about this one, it has 4 inputs? 0+1+0+0 outputs a 0 with an NOR gate, right? How do you account for 4 inputs?
Sign of the true result: 0 because you XOR gate V and S, which means the sign of the true result is positive

NOR gives 1 only when all inputs are zero, and that's clearly not the case.
All seems good to me.