Full adder using DEC 2/4
If you are constrained to use decoders and NOR gates, the logic is a whole lot simpler if you redefine the carry inputs and outputs to be active-low instead of active-high. I'll present a solution based on this, and maybe it will provide some insight to your original problem.







simulate this circuit &ndash; Schematic created using CircuitLab

Actually, it only requires one additional gate to make them active-high, but I'll leave that as an exercise for the reader.