The formula for the surface area \( A \) of a sphere is:
\[ A = 4\pi r^2 \]
where \( r \) is the radius. We know the surface area \( A \) is 1256 and we will use \( \pi \) as 3.14.
First, we can rearrange the formula to solve for the radius \( r \):
\[ r^2 = \frac{A}{4\pi} \] \[ r^2 = \frac{1256}{4 \times 3.14} \]
Calculating the denominator:
\[ 4 \times 3.14 = 12.56 \]
Now substituting that back into the equation:
\[ r^2 = \frac{1256}{12.56} \] \[ r^2 = 100 \]
Now, taking the square root to find the radius:
\[ r = \sqrt{100} = 10 \]
The diameter \( d \) of the sphere is twice the radius:
\[ d = 2r = 2 \times 10 = 20 \]
So the diameter of the exercise ball is \( \boxed{20} \).