A mother computer is a term used in various Sonic games to refer to supercomputers. The most of the time during the series, many of mother computers are created and controlled by Dr. Eggman in order to make progress on taking over the world of Sonic the Hedgehog, but there have been few exceptions. Frequently, the hero characters will be required to hack into one (or simply blow it up) in an effort to bring down Eggman's created robot battalions.
The mother computer created by Eggman is located at hidden Gimme Shelter in Sonic Battle. In the game, Cream the Rabbit and Emerl have to interact with it in order to escape the base; Rouge also attempts to hack it to get access to the Doctor's data.
Shadow the Hedgehog
In Shadow the Hedgehog, there are three mother computers located inside of GUN Fortress and being built by the Guardian Units of Nations. The organization sees Shadow assigned to attack the humans' three mother computers by Black Doom, who thinks that, as their computers disabled, the human army will be easy pickings for his Black Arms.
Sonic Riders: Zero Gravity
Before the events of Sonic Riders: Zero Gravity, Doctor Eggman builds another mother computer, this time for his shell company, MeteorTech, which is located out in the desert of Monopole. It is powered by one of the Babylonians' Ark of the Cosmos, which Eggman found and researched on. However, during the game's storyline, Eggman notices that the mother computer was not following his remote commands and later finds that SCR-HD took over MeteorTech and the company's robot models under its command upon obtaining another one of the Arks of the Cosmos.