We describe a technique to calculate partial virial coefficients up to seventh order in a binary mixture of hard spheres, using hit-and-miss Monte-Carlo (MC) numerical integration. The algorithm makes use of look-up tables of all the blocks contributing to each partial virial coefficient. All topologically equivalent graphs are listed in this table so as to improve the statistical efficiency of the calculation. For the case of additive hard spheres, we report the partial contributions to the sixth and seventh virial coefficients, for size ratios ranging from 0.1 to 0.9. For the non-additive mixture we truncated the expansion at sixth order and only considered one set of potential parameters: size ratio 0.1 and non-additivity factor +0.1. In line with previous work, our results indicate that for additive spheres with a size ratio in the region of 0.1, there would appear to be a liquid-liquid de-mixing transition but at an overall packing fraction that would imply that this is meta-stable with respect to a fluid-solid transition. A positive non-additivity serves to increase the tendency for liquid-liquid de-mixing, but appears to have an adverse effect on the rate of convergence of the virial series. (C) 2003 Elsevier B.V.. All rights reserved.