**Explanation:**
Hydrogen bonding occurs when a hydrogen atom is bonded to a highly electronegative atom such as oxygen, nitrogen, or fluorine. In this case, we are comparing the strength of hydrogen bonding in the compounds HI, HCl, HF, and HBr.

**Hydrogen Bonding Strength:**
The strength of a hydrogen bond is determined by the electronegativity and size of the atom to which the hydrogen atom is bonded. The greater the electronegativity and smaller the size of the atom, the stronger the hydrogen bond.

**Comparing the Electronegativities:**
To determine the strength of hydrogen bonding, we first compare the electronegativities of the atoms to which the hydrogen atoms are bonded.

- HI: hydrogen is bonded to iodine (electronegativity = 2.66)
- HCl: hydrogen is bonded to chlorine (electronegativity = 3.16)
- HF: hydrogen is bonded to fluorine (electronegativity = 3.98)
- HBr: hydrogen is bonded to bromine (electronegativity = 2.96)

**Comparison Results:**
Based on the electronegativities, we can see that fluorine (in HF) has the highest electronegativity, followed by chlorine (in HCl), bromine (in HBr), and iodine (in HI). Therefore, HF has the strongest hydrogen bonding because fluorine is the most electronegative atom in this group.

**Explanation of the Correct Answer:**
The correct answer is option C, HF. This is because fluorine (in HF) has the highest electronegativity among the given compounds, making it the most electronegative atom to which the hydrogen atom is bonded. As a result, HF forms the strongest hydrogen bond compared to the other compounds.

**Conclusion:**
In summary, the compound HF has the strongest hydrogen bond among the given options because fluorine, with the highest electronegativity, is bonded to hydrogen in HF.