Efforts to construct synthetic biological circuits with more complex functions have often been hindered by the idiosyncratic behavior, limited dynamic range and crosstalk of commonly utilized parts. Here, we employ de novo RNA design to develop two high-performance translational repressors with sensing and logic capabilities. These synthetic riboregulators, termed toehold repressors and three-way junction (3WJ) repressors, detect transcripts with nearly arbitrary sequences, repress gene expression by up to 300-fold and yield orthogonal sets of up to 15 devices. Automated forward engineering is used to improve toehold repressor dynamic range and SHAPE-Seq is applied to confirm the designed switching mechanism of 3WJ repressors in living cells. We integrate the modular repressors into biological circuits that execute universal NAND and NOR logic and evaluate the four-input expression NOT ((A1 AND A2) OR (B1 AND B2)) in Escherichia coli. These capabilities make toehold and 3WJ repressors valuable new tools for biotechnological applications.