Synthetic biology has advanced the design of standardized control devices that program cellular functions and metabolic activities in living organisms. Rational interconnection of these synthetic switches resulted in increasingly complex designer networks that execute input-triggered genetic instructions with precision, robustness and computational logic reminiscent of electronic circuits. Using trigger-controlled transcription factors, which independently control gene expression, and RNA-binding proteins that inhibit the translation of transcripts harbouring specific RNA target motifs, we have designed a set of synthetic transcription–translation control devices that could be rewired in a plug-and-play manner. Here we show that these combinatorial circuits integrated a two-molecule input and performed digital computations with NOT, AND, NAND and N-IMPLY expression logic in single mammalian cells. Functional interconnection of two N-IMPLY variants resulted in bitwise intracellular XOR operations, and a combinatorial arrangement of three logic gates enabled independent cells to perform programmable half-subtractor and half-adder calculations. Individual mammalian cells capable of executing basic molecular arithmetic functions isolated or coordinated to metabolic activities in a predictable, precise and robust manner may provide new treatment strategies and bio-electronic interfaces in future gene-based and cell-based therapies.