Black and white sci-fi film. US and USSR build supercomputers to run missiles, computers link up become sentient and take over the world by threat of nukes. A designer tries to disable them, fails and is made to watch his friends executed as he is needed.
This is Colossus: The Forbin Project.
[A]n advanced American defense system, named Colossus, becom[es] sentient. After being handed full control, Colossus' draconian logic expands on its original nuclear defense directives to assume total control of the world and end all warfare for the good of mankind despite its creators' orders to stop.