Synthetic biology promises the ability to program cells with new functions. Simple oscillators, switches, logic functions, cell-cell communication and pattern-forming circuits have been created by the connection of a small set of natural transcription factors and their binding sites in different ways to produce different networks of molecular interactions. However, the controlled synthesis of more complex synthetic networks and functions will require an expanded set of functional molecules with known molecular specificities. Here, we tailored the molecular specificity of duplicated Escherichia coli ribosome x mRNA pairs with respect to the wild-type ribosome and mRNAs to produce multiple orthogonal ribosome x orthogonal mRNA pairs that can process information in parallel with, but independent of, their wild-type progenitors. In these pairs, the ribosome exclusively translates the orthogonal mRNA, and the orthogonal mRNA is not a substrate for cellular ribosomes. We predicted and measured the network of interactions between orthogonal ribosomes and orthogonal mRNAs, and showed that they can be used to post-transcriptionally program the cell with Boolean logic.