Boolean Memories

Conditions for equilibrium states in Boolean nets by delay-free feedback are investigated. The result is a new class of circuits called memories, the simplest member of which is the ordinary set-reset flip-flop. A memory is defined as an asynchronous sequential machine with specific properties. The need for gain in feedback loops and the assumption that each amplifier is a NOT operator make it possible to state two theorems on the equilibrium codes. In algebraic treatment it is shown how to design a memory from a given state assignment. Symmetric Boolean memories include multistable flip-flops but also, for instance, a decadic memory utilizing only five inverters.