To find out how much sugar Ms. Johnson used, we need to calculate \( \frac{1}{2} \) of \( \frac{7}{8} \).
We can do this by multiplying the two fractions:
\[ \frac{1}{2} \times \frac{7}{8} = \frac{1 \times 7}{2 \times 8} = \frac{7}{16} \]
So, Ms. Johnson used \( \frac{7}{16} \) cups of sugar for the dessert.