We have created novel engineered genetic counter designs and methods of use thereof that utilize DNA recombinases to provide modular systems, termed single invertase memory modules (SIMMs), for encoding memory in cells and cellular systems. Our designs are easily extended to compute to high numbers, by utilizing the >100 known recombinases to create subsequent modules. Flexibility in our engineered genetic counter designs is provided by daisy-chaining individual modular components, i.e., SIMMs together. These modular components of the engineered genetic counters can be combined in other network topologies to create circuits that perform, amongst other things, logic and memory. Our novel engineered genetic counter designs allow for the maintenance of memory and provide the ability to count between discrete states by expressing the recombinases between their cognate recognition sites.