Minor detail, but the undecidability Halting Problem strictly requires an infinite tape (infinite storage space).
In "practice", if you could call it such, a computer with limited memory becomes a "linear bounded automaton" and the Halting Problem is decidable; cf. http://cs.stackexchange.com/q/22925
Of course, big enough memory can mean that it can be impossible to detect termination before the heat death of the universe - we are talking theory here.
In "practice", if you could call it such, a computer with limited memory becomes a "linear bounded automaton" and the Halting Problem is decidable; cf. http://cs.stackexchange.com/q/22925
Of course, big enough memory can mean that it can be impossible to detect termination before the heat death of the universe - we are talking theory here.