  We study arithmetical aspects of Ito-Sadahiro number systems with negative
base. We show that the bases $-\beta<-1$, where $\beta$ is zero of
$x^3-mx^2-mx-m,\ m\in\mathbb N,$ possess the so-called finiteness property. For
the Tribonacci base $-\gamma,$ zero of $x^3-x^2-x-1$, we present an effective
algorithm for addition and subtraction. In particular, we present a finite
state transducer performing these operations. As a consequence of the structure
of the transducer, we determine the maximal number of fractional digits arising
from addition or subtraction of two $(-\gamma)$-integers.
