A. V. Marchuk, F. Muratore, A. P. Milone, M. V. Legnardi, F. D'Antona, G. Cordoni, A. Mastrobuono-Battisti, E. Bortolan, F. Dell'Agli, E. Dondoglio, E. P. Lagioia, A. F. Marino, M. Tailo, C. Ventura, P. Ventura, T. Ziliotto

A significant fraction of stars in both the Galactic field and stellar clusters are members of binary systems. Understanding their properties is therefore essential for a comprehensive view of stellar structure, evolution, and cluster dynamics. Despite extensive studies of cluster binaries, key issues remain unresolved, particularly for photometric binaries among low-mass stars. While the binary fraction in the field strongly depends on stellar mass, cluster studies have generally suggested an approximately constant fraction over the limited mass ranges explored. In addition, the mass function (MF) of very low-mass stars is still poorly constrained in clusters older than a few hundred Myr. We use deep Hubble Space Telescope imaging of the intermediate-age open cluster NGC 2158 to investigate its binary population and derive the luminosity and MFs down to ~0.14 solar masses, enabling the first detailed analysis of binaries in this cluster. We measure a global binary fraction of 38%, consistent with other open clusters, and find a clear mass dependence: it decreases from ~52% at 1.0 solar masses to ~11% at 0.2 solar masses. This trend mirrors that of Galactic field stars, suggesting similar binary properties. The MF is characterized by three regimes: high-mass stars (alpha= -2.49 +- 0.19), low-mass stars (alpha= -1.11 +- 0.09), and very low-mass stars (alpha= -0.08 +- 0.07). The slope change near 1.0 solar mass agrees with recent surveys, though we find a deficit below ~0.3 solar masses. We also detect a main-sequence discontinuity around ~0.3 solar masses, possibly linked to the 3He-driven instability predicted by stellar models and analogous to the Jao Gap seen in nearby field stars.