Asymmetric selection of single-stranded guide RNAs from double-stranded RNA precursors is crucial in RNA silencing-mediated gene regulation. However, the precise mechanisms of small-RNA asymmetry are unclear, especially because asymmetric selection can still occur when the putative asymmetry sensors Drosophila R2D2 and mammalian Dicer are depleted. Here we report a direct contribution of mammalian Argonaute 2 (Ago2) to microRNA (miRNA) asymmetry. Ago2 selects strands with 5'-uridine or 5'-adenosine and thermodynamically unstable 5' ends in parallel through its two sensor regions, which contact the 5' nucleobases and 5'-phosphates of prospective guide strands. Hence, miRNA asymmetry shows superposed patterns reflecting 5'-end nucleotide identity ('digital' pattern) and thermodynamic stability ('analog' pattern). Furthermore, we demonstrate that cancer-associated miRNA variations reprogram asymmetric selection. Finally, our study presents a model of this universal principle, to aid in comprehensive understanding of miRNA function and development of new RNA-silencing therapies in precision medicine.