It's not binary searches and merge sorts that are broken, it's the INT data type that is "broken" (and I put "broken" in scare quotes because they aren't really broken, they just don't do what you want in most cases). People tacitly assume that INTs model the integers, but they don't. They model the integers modulo 2^N for some value of N. If you code as if INTs were integers and you hit the 2^N limit you will lose.

The algorithm as given would work perfectly well on a straightforward translation into a language with a real integer data type like Python or Lisp.

And you can lose in the other direction too: if you're doing crypto, for example, the algorithms are often designed to use arithmetic operations modulo 2^N, so INTs (and NOT integers) can be just what you need.

But this has nothing do do with binary search or mergesort.