This paper investigates infinite Bernoulli convolutions governed by a negabinary expansion: $\frac{2}{3} + \sum_{n=1}^{\infty}\frac{1}{2^{-n}}$, namely the distributions of random variables of the form $\displaystyle \xi=\frac{2}{3}+\sum_{n=1}^{\infty}\frac{\xi_n}{(-2)^n}=\Delta^{-2}_{\xi_1\xi_2\dots\xi_n\dots}$, where $(\xi_n)$ -- is a sequence of independent random variables taking values 0 and 1 with probabilities $p_{0n}$ and $p_{1n}$ respectively.

 Using the transformation formulas linking the negabinary expansion with the classical binary representation, we establish necessary and sufficient conditions for the distribution of $\xi$ to be discrete, singular, continuous, uniform, or exponential.

 The Lebesgue structure of the distribution of the random variable $\tau = \Delta^{-2}_{\tau_1 \tau_2 \dots \tau_n \dots}$  under the assumption that the digits $\tau_n$ of its negabinary expansion form a homogeneous Markov chain has been determined.

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