In a geometric sequence, each term after the first is found by multiplying the previous one by a constant called the common ratio (r).
To find the common ratio, we can take the second term and divide it by the first term:
\[ r = \frac{\text{second term}}{\text{first term}} = \frac{1/2}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
We can also verify it by calculating the ratio of the third term to the second term:
\[ r = \frac{\text{third term}}{\text{second term}} = \frac{1/8}{1/2} = \frac{1}{8} \div \frac{1}{2} = \frac{1}{8} \times \frac{2}{1} = \frac{2}{8} = \frac{1}{4} \]
And once more with the fourth term and the third term:
\[ r = \frac{\text{fourth term}}{\text{third term}} = \frac{1/32}{1/8} = \frac{1}{32} \div \frac{1}{8} = \frac{1}{32} \times 8 = \frac{8}{32} = \frac{1}{4} \]
Thus, the common ratio for the given geometric series is:
\[ \boxed{\frac{1}{4}} \]