Electronic readout of markers of disease provides compelling simplicity, sensitivity and specificity in the detection of small panels of biomarkers in clinical samples; however, the most important emerging tests for disease, such as infectious disease speciation and antibiotic-resistance profiling, will need to interrogate samples for many dozens of biomarkers. Electronic readout of large panels of markers has been hampered by the difficulty of addressing large arrays of electrode-based sensors on inexpensive platforms. Here we report a new concept--solution-based circuits formed on chip--that makes highly multiplexed electrochemical sensing feasible on passive chips. The solution-based circuits switch the information-carrying signal readout channels and eliminate all measurable crosstalk from adjacent, biomolecule-specific microsensors. We build chips that feature this advance and prove that they analyse unpurified samples successfully, and accurately classify pathogens at clinically relevant concentrations. We also show that signature molecules can be accurately read 2 minutes after sample introduction.