To claim something is impossible, we have to have a great reason to show the happening of that thing is against scientific laws. But we know or at least we assume human is intelligent. So intelligence is not something against science law! So what I want to show there should be a point which technology reaches that point which it has intelligence as human-being. I do not have any idea about that technology will be used same computers we are using now or it could be reachable with quantum computers or with development of neural science, but I presume the singularity will be happening.
Programming is one of greatest skills everybody could be learn, skill of dividing problem to smaller problems and solving each of them in few simple steps, skill of not trying to be using your mental power to solve a single problem but to solve a problem in general form, and skill of connecting with abstract mathematical logic and language. Our living style are changing after development of internet and access to computers as PC, laptop, smart phones, etc. All of this devices from supercomputers or severs or a single smart phone are based on same architecture and same logic, hardware which is running a program. So what make each of them responsible for certain task additional than their hardware (like any other machine) is their software, which only material for creating them is not any physical substance but it is idea and thinking right about its implementation.
This question is difficult to answer, first because the meaning and structure of mind is not scientifically obvious. Technologically we do not find how is exact relation of brain functions and mental states. Secondary when we ask the question about possibility of computer with a mind, it is not clear what we expect from our computers. But in order to neglect this incommensurability, I try to figure out what should be mind if it is possible to have a computer with a mind.