# Flip-Flop Input Equation **A Boolean equation describing the inputs of a [[flip-flop]].** Flip-flop input equations are derived from [[State Table|state tables]] and [[Excitation Table|excitation tables]] and used to form the output combinational circuit. > [!Example] > For a [[Flip-Flop#T flip-flip|T flip-flop]] circuit, the extended state table derived from an excitation table is: > >| Present<br>state | | Inputs | | Next<br>state | | Flip-flop<br>inputs | | |:--------------------:|:---:|:--------:|:--------:|:-----------------:|:--------:|:-----------------------:|:-----:| | $A$ | $B$ | $S$ | $F$ | $A(t+1)$ | $B(t+1)$ | $T_A$ | $T_B$ | | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ | | $0$ | $0$ | $\times$ | $1$ | $0$ | $1$ | $0$ | $1$ | | $0$ | $0$ | $1$ | $\times$ | $1$ | $0$ | $1$ | $0$ | | | | | | | | | | | $0$ | $1$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | | $0$ | $1$ | $\times$ | $1$ | $1$ | $0$ | $1$ | $1$ | | $0$ | $1$ | $1$ | $\times$ | $1$ | $1$ | $1$ | $0$ | | | | | | | | | | | $1$ | $1$ | $0$ | $0$ | $1$ | $1$ | $0$ | $0$ | | $1$ | $1$ | $\times$ | $1$ | $0$ | $0$ | $1$ | $1$ | | $1$ | $1$ | $1$ | $\times$ | $0$ | $1$ | $1$ | $0$ | | | | | | | | | | | $1$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | $0$ | | $1$ | $0$ | $\times$ | $1$ | $1$ | $1$ | $0$ | $1$ | | $1$ | $0$ | $1$ | $\times$ | $0$ | $0$ | $1$ | $0$ | > > Note that for this particular circuit, $S=F=1$ is not a possible combination. To derive the flip-flop input equations, [[Karnaugh Map|K-maps]] can be used. > > ![[LightControllerTAKMap.svg|400]] > *** > ![[LightControllerTBKMap.svg|400]] > > Thus, the flip-flop input equations are >$\begin{align*} T_{A}&=BF+S \\ T_{B}&=F \\ \end{align*}$