Start by understanding how base -2 works: each digit represents a power of -2, and digits can only be 0 or 1. How would you represent a number like 1 in base -2?

When adding 1 to a base -2 number, consider the carry-over rules. Unlike base 10 or base 2, the carry-over in base -2 depends on the current digit and the sign of the base. How does the carry propagate when the digit is 1?

To handle the carry correctly, you may need to adjust the number iteratively. Think about how to loop through the digits, apply the carry, and ensure the final result adheres to the base -2 representation. What happens if the carry propagates all the way to the most significant bit?