RST Flip-Flop Input Equations

There are several different usable combinations of the inputs of an RST flip-flop. It is shown how all of the possible combinations can be displayed simultaneously on three Karnaugh maps, facilitating the choice of the simplest input equations. The application equation for flip-flop Q characterized by a sequential problem is plotted on a map designated Qⁿ⁺¹. Additional maps, (Qⁿ⁺¹)^* and (Qⁿ⁺¹)' are derived from Qⁿ⁺¹. Cells corresponding to prime implicants not containing the variable Q are identified on these maps, and are used to enter the properly designated arbitrary elements on the R, S, and T maps of flip-flop Q. The method is based on the following theorem: ``If Qⁿ⁺¹ = (g₁Q + g₂Q')ⁿ, and if F is the set of all prime implicants that do not contain the literals Q or Q', then the Boolean function g₁g₂ is the union of all the prime implicants of Qⁿ⁺¹ that belong to the set F.'' A simple illustrative example is included.