Transistor full adder circuit
With the exception of your &quot;NOT&quot; gates, none of your gates have any voltage gain. They all use transistors wired as emitter followers, which means that the voltage offsets from base to emitter accumulate until your signal levels are useless.
See my answer to Why are NAND gates used to make AND gates in computers? for a more thorough discussion of this issue.
See also Can you make a CPU out of electronic components drawn by hand on paper? and Will this schematic work as a four-bit shift register?
And your question is essentially an exact duplicate of Building a full adder with NPN BJT transistors