To cope with the challenges posed by the High-Luminosity LHC, the CMS experiment will feature a new silicon tracker. The modules of the upgraded inner tracker are hybrid silicon pixel modules based on a new readout chip, developed by the RD53 collaboration. Compared to the readout chip of the current pixel detector, the RD53 chip is capable of sustaining higher hit rates and radiation levels, as well as enabling the use of serial-powering chains. The qualification of the latest version of this chip (RD53B) is underway, and it will lead to the final version of the readout chip to be used in the CMS inner tracker during the HL-LHC. First digital modules featuring the RD53B-CMS chip have been assembled in 2022 (the term digital module denotes a module assembly with readout chips, but without sensors bonded to them). This contribution presents results of tests on these first prototype modules.