The year is 1970, and the setting is a radio telescope on the North Yorkshire moors in England. While doing routine work on the telescope Fleming picks up a signal from the Andromeda Galaxy. His interest aroused, Fleming trains the telescope in the direction of the signal, which is a series of long and short beeps, like a morse code message. Fleming continues to listen to the signal, and its repetitive pattern eventually convinces him that it must be from an intelligent source. Fleming informs his colleagues, who are equally convinced, and then his employers, the ministry of defense, who compel him to secrecy on pain of losing his job.
Fleming has decoded the message, which he thinks is a set of mathematical instructions for constructing a computer of complexity beyond anything in existence. The authorities give the go-ahead for the building of the computer at Thorness, in Scotland. the military, politicians and scientific community all prepare in their own way for what the construction of the computer will mean. meanwhile, knowledge of the message becomes public and Britain is thrown into panic.
The construction of the computer is completed, and immediately it becomes apparent that it is under control of an alien intelligence. Fleming and his colleagues engage in a bizarre question and and answer session with the computer: the computer asks the questions, and Fleming and his colleagues do the answering. It transpires that one of Flemings colleagues, Bridger, is passing information about the discovery to a mysterious organization called Intel. A government agent monitoring Bridger is killed. Meanwhile the computer has been spelling out the molecular structure of a living cell. Fleming now begins to fear the computer,and considers that the project should be brought to a close. in this he finds himself in conflict with one of his colleagues, Madeline Dawnay.
After having caught passing information about the project to Intel, Bridger is chased by security agents and falls down a cliff to his death. Following instructions from the computer, Dawnay and her colleagues create a living organism in a tank. Fleming suggests connecting an electric current between it and the computer. In an attempt to find out more about the humans, the computer compels Dawnay's assistant, Christine to touch an exposed terminal, killing her.
Intel agent Kaufman becomes interested in the project, and despite Fleming's warnings, Dawnay follows the computers instruction and begin to create living cells. The result is a human baby christened Andromeda. The baby grows rapidly and Fleming and Dawnay are astonished to see that the emerging creature resembles their dead colleague Christine. The international political situation deteriorates, and in desperation the Prime minister turns to Andromeda and the computer for help.
Together Andromeda and the computer provide plans to the government to construct a missile capable of intercepting and destroying any foreign rockets which are fired upon Britain. Everyone is delighted with this except Fleming, who sees the teaming up of Andromeda and the computer as a menace. Fleming tries to destroy the computer, which retaliates, but it's blow falls on Dawnay.
As Dawnay hovers between life and death. Andromeda tells Fleming that he can use the computer to find an antidote to the serum the computer has used against Dawnay. Fleming has fallen in love with Andromeda, and tries to talk her into distancing herself from the computer.