  We consider homogeneous binomial ideals $I=(f_1,\ldots,f_n)$ in $K[x_1,
\ldots, x_n]$, where $f_i = a_i x_i^{d_i} - b_i m_i$ and $a_i \neq 0$. When
such an ideal is a complete intersection, we show that the monomials which are
not divisible by $x_i^{d_i}$ for $i=1,\ldots,n$ form a vector space basis for
the corresponding quotient, and we describe the Macaulay dual generator in
terms of a directed graph that we associate to $I$. These two properties can be
seen as a natural generalization of well-known properties for monomial complete
intersections. Moreover, we give a description of the radical of the resultant
of $I$ in terms of the directed graph.
