  The generalized cyclotomic binary sequences $S=S(a, b, c)$ with period $n=pq$
have good autocorrelation property where $(a, b, c)\in \{0, 1\}^3$ and $p, q$
are distinct odd primes. For some cases, the sequences $S$ have ideal or
optimal autocorrelation. In this paper we determine the autocorrelation
distribution and 2-adic complexity of the sequences $S=S(a, b, c)$ for all $(a,
b, c)\in \{0, 1\}^3$ in a unified way by using group ring language and a
version of quadratic Gauss sums valued in group ring $R=\mathbb{Z}[\Gamma]$
where $\Gamma$ is a cyclic group of order $n$.
