Number of zeroes between decimal point and first significant digit of $\left(\dfrac{1}{2}\right)^{20}$ ($\log 2 = 0.30103$):

$\log\left(\tfrac12\right)^{20} = -20 \times 0.30103 = -6.0206 = \bar7 + 0.9794$, so the characteristic is $\bar7$. The number of zeros after the decimal point before the first significant figure is $|\text{characteristic}| - 1 = 7 - 1 = 6$.