2001 question

When I was a child in the early 80s, I read a science fiction book handed down to me by my father, so I suspect that it was written in the 40s or 50s. I cannot recall the title but distinctly remember that it was about a boy who lived in a city surrounded by inescapable walls. Reproduction was no longer possible, and people lived thousands of years, so every few thousand years, the machines generated a new person. People had once been able to communicate telepathically but had lost that ability and could now only communicate with machines that way. They boy escapes the city to discover the world accompanied by his guardian robot that is egg-shaped and floats. He discovers people still exist outside his city. They still have full telepathic abilities but live only normal-length lives. He eventually finds a machine that can duplicate other machines, so he has it duplicate his robot which he eventually uses to board a spaceship and fly off to discover the galaxy which is how the book ends. Any help with this would be greatly appreciated.