This reminds me of a similar question I answered a few weeks ago. Not exactly the same situation, but the leading theory is that it comes down to complexity.
I'll start out by saying that we don't know for sure what animals are conscious or even what consciousness is, exactly. In fact, it's not even possible to prove without a doubt that you or I are conscious.
We do mostly seem to have a general intuition of what consciousness is, and which things are or are not conscious. Probably most people would say that an ant does not possess consciousness, and the complexity argument would back that up. While ants do have brains, the structure of their brains is very different from the brain of a mammal. Most people would say that a human has consciousness; from experience for one thing. How about a killer whale, a monkey, or even a human infant? There might be less of a consensus in these cases. In my opinion, we should err on the side of consciousness whenever possible.
Lastly, I get what you're saying with the computer analogy, but the human brain is so much more complex than a computer and it definitely works differently than any kind of man made computer. Even some of the new chips that are built to mimic networks of neurons are missing a lot of what is going on in vivo. There are interactions occurring between living neurons that aren't fully understood yet. A more accurate analogy would be that the human brain is like a high-end future computer-like object and an ant nervous system is like a very low-end future computer-like object. One difference between high-end and low-end future computer-like objects might be the ability to experience consciousness.