Marvin is the servant to the crew aboard the Heart of Gold. He is incredibly smart, having a "brain the size of a planet," with the capabilities of computing extremely complex mathematics, as well as solving difficult problems and operating high-tech devices. Although he is capable of these things, he usually performs duties such as opening doors and other less intelligent tasks which causes him to be depressed,
Eddie is an A.I. computer system that controls the Heart of Gold. He can manipulate navigation, defense, weapons, shielding, the Improbability Drive, escape pods, airlocks, and various other systems. He is capable of carrying on conversations with the crew, as well as talking with other computers aboard the ship.
This is a propulsion system that allows the Heart of Gold to travel through all points in the galaxy in less than a second by passing through every possible point in every universe simultaneously. When traveling from one point to another, you need exact coordinates. When you reach the destination, you will change species but change back once normality is restored.
The starship Heart of Gold was the first spacecraft to make use of the Infinite Improbability Drive, that is located at the heart of the ship. The ship is powered by the drive, and houses Marvin and Eddie.
Deep Thought, according to the movie, is the most powerful computer ever built. It was designed to derive the answer to Life, the Universe, and Everything. After 7.3 million years, this answer was 42, the question which was asked had not been determined.
The supercomputer, Deep Thought, created a computer to calculate the greatest question of life, the universe, and everything. This computer was the planet Earth.