One method for developing an accurate, global equation of state (EOS) for real fluids involves use of a hard-convex body EOS as a reference function, with additional terms to compensate for deviations between real fluid and hard-convex body behavior. If the hard-convex body expression accurately reflects reference behavior, it appears that fewer and simpler compensation terms suffice. This paper describes a hard-convex body EOS which describe hard spheres within 0.1% up to the fusion density. In addition, they possess poles at the random close-packed density. The hard-convex representations are few and simple, and only one constant results from a fit of the "data". The expressions produce exact virial coefficients through the fourth virial coefficient.