The binary compound formed by barium (Ba) and iodine (I) is called barium iodide. The chemical formula for this compound is BaI2.
To explain further, barium is an alkaline earth metal with a +2 oxidation state, while iodine is a halogen with a -1 oxidation state. In order to form a neutral compound, two iodine atoms are needed to balance the charge of one barium atom. Thus, the formula reflects that there are two iodine ions for every barium ion, resulting in BaI2.