We show that a missing q-ary digit set F ⊆ [0,1] has a corresponding naturally associated countable binary q-automatic sequence f. Using this correspondence, we show that the Hausdorff dimension of F is equal to the base-q logarithm of the Mahler eigenvalue of f. In addition, we demonstrate that the standard mass distribution ν_F supported on F is equal to the ghost measure μ_f of f.