Regarding Turing Machine Halting Problem All problems solved by standard today's general purpose computer can be solved by standard Turing machine.As general purpose computer can't do more than Turing machine so The Turing machine halting problem must also be  unsolved by today's general purpose computer.How can I realize the fact that halting problem can't be solved by todays general purpose computers.
The halting problem is the question of whether a program $B$ halts on and some given input $x$. It is impossible to create a program that decides the halting problem, so the effect is that, whatever program $A$ you create, there will exist some program $B$ and input $x$ such that $A$ will not tell correctly whether $B$ halts on input $x$.