3-Bit 2's Complement Circuit
The best way if you want to do this in the older conventional design flow follows these steps. 


Write down a full truth table of input states and corresponding output states. 
For each bit output column in the truth table craft a Karnough map of the output '1's within the matrix of the input state bit values. 
Use the Karnough map minimization technique to find groups of output '1's that basically show what inputs are don't-care for certain of the output groups. 
Write the logic equations in AND/OR format for the minimal set of output groups that cover all the '1' positions. 


There are plenty of web site resources that will describe each step of this process.