  We analyze different ways of constructing binary extended formulations of
mixed-integer problems with bounded integer variables and compare their
relative strength with respect to split cuts. We show that among all binary
extended formulations where each bounded integer variable is represented by a
distinct collection of binary variables, what we call "unimodular" extended
formulations are the strongest. We also compare the strength of some binary
extended formulations from the literature. Finally, we study the behavior of
branch-and-bound on such extended formulations and show that branching on the
new binary variables leads to significantly smaller enumeration trees in some
cases.
