IME 84 (1963) World's First Electronic Transistor Desk Calculator by Industria Macchine Elettroniche
This video shows a functioning specimen of the world's first fully electronic desk calculator: The 1963/1964 IME 84 calculator by Industria Macchine Elettroniche S.p.A. The first "Transistorrechner" or "Der erste elektronische ganz transistorierte Tischrechenautomat".
After the 1961 Sumlock Anita Mark VII & VIII, which used a variety of tubes for calculations, this was the first modern, transistor based calculator. I have not seen any other working machines in recent years, so let me know if you want to see more.