Given $8$ coins, at most one of them is counterfeit. A counterfeit coin is lighter than a real coin. You have a free weight balance. What is the minimum number of weighings necessary to determine the identity of the counterfeit coin if it exists
1. **Divide the 8 coins into groups:**
   - Group 1: 3 coins
   - Group 2: 3 coins
   - Group 3: 2 coins

2. **First Weighing:**
   - Weigh Group 1 (3 coins) against Group 2 (3 coins).

3. **Case 1: The scale balances out:**
   - If the scale balances, then all 6 coins in Group 1 and Group 2 are real.
   - The counterfeit coin, if it exists, must be in Group 3 (2 coins).
   - Weigh the 2 coins in Group 3 against each other.
     - If one coin is lighter, it is the counterfeit.
     - If they balance, there is no counterfeit coin.

4. **Case 2: One group weighs less than the other:**
   - Suppose Group 1 weighs less than Group 2.
   - The counterfeit coin is in Group 1 (3 coins).
   - Take 2 coins from Group 1 and weigh them against each other.
     - If one coin is lighter, it is the counterfeit.
     - If they balance, the third coin (not weighed) is the counterfeit.

Therefore, we only need 2 weighings to determine the counterfeit coin if it exists.

The final answer is $\boxed{2}$ weighings.