A computer program uses $4$ bits to represent nonnegative integers. Which of the following statements describe a possible result when the program uses this number representation?

I. The operation $4+8$ will result in an overflow error.

II$.$ The operation $7+10$ will result in an overflow error.

III. The operation $12+3$ will result in an overflow error.

II only

II and III only

I, II$,$ and III

I only