The discovery of the DNA double helix has revolutionized our understanding of data processing in living systems, with the complementarity of the two DNA strands providing a reliable mechanism for the storage of hereditary information. Here I reveal the 'strand commutation' phenomenon-a fundamentally different mechanism of information storage and processing by DNA/RNA based on the reversible low-affinity interactions of essentially non-complementary nucleic acids. I demonstrate this mechanism by constructing a memory circuit, a 5-min square-root circuit for 4-bit inputs comprising only nine processing ssDNAs, simulating a 572-input AND gate (surpassing the bitness of current electronic computers), and elementary algebra systems with continuously changing variables. Most importantly, I show potential pathways of gene regulation with strands of maximum non-complementarity to the gene sequence that may be key to the reduction of off-target therapeutic effects. This Article uncovers the information-processing power of the low-affinity interactions that may underlie major processes in an organism-from short-term memory to cancer, ageing and evolution.