"as well" instead of "and"

As well has a different meaning from and.

As well is used mostly in spoken English. In written English, people usually prefer to use also:

Parents are also welcome.

And apart from that, as well as is also slightly different from as well:

as well as something/somebody: in addition to something or someone else

Your final sentence won't turn into a false meaning if you replace as well as with and; however that sentence wants to imply that "not only this algorithm is capable of processing text, but also it can process binary files, [too]."

Reference from Subscription-Only LDOCE

"as well" in an enumeration makes the first mentioned item more important than the second, whereas "and" normally does not.

I agree with the other answers, but I believe that there should have been more focus on the in addition to alternative.  And I agree that “A as well as B” emphasizes A.  It seems to me that this would apply to situations where the audience would expect the statement to be true about B, but might be surprised to hear it about A.  For example,

The shareholders’ meeting will be attended by men and women.
The shareholders’ meeting will be attended by children as well as adults.

So, in your example, I’d think

The algorithm can process binary files as well as text files.

might actually be more appropriate.