One of my final exam questions in digital design was to design a circuit that converts an 8-bit Sign/Magnitude number to Two's Complement number using only inverters, XOR gates, half adders and full adders. The simplest approach to this problem, I thought, was to use a multiplexer. However, I couldn't design one using the allowed components. Is it even possible to make a MUX out of these components or does this problem require a different approach?
If I could make a multiplexer, my solution would be to multiplex the input number and a version of it that is inverted and added 1 using the sign bit as select.