We study the set Γ consisting of univoque sequences, the set Λ consisting of sequences in which the lengths of consecutive zeros and consecutive ones are bounded, and their frequency subsets Γ a , Γ a , Γ a and Λ a , Λ a , Λ a consisting of sequences respectively in Γ and Λ with frequency, lower frequency and upper frequency of zeros equal to some a ∈ [0, 1]. The Hausdorff dimension of all these sets are obtained by studying the dynamical system (Λ (m) , σ) where σ is the shift map and Λ (m) = w ∈ {0, 1} N : w does not contain 0 m or 1 m for integer m ≥ 3, studying the Bernoulli-type measures on Λ (m) and finding out the unique equivalent σ-invariant ergodic probability measure.