# State Equation **A Boolean function describing the next state of a [[sequential circuit]] in terms of the present state and inputs.** A **state equation**, also known as a **transition equation**, is a [[Boolean function]] describing the relationship between the *next state* of a [[sequential circuit]] and the *present state and inputs*. > [!Example] > [[Flip-Flop#D flip-flop|D flip-flops]] have a characteristic equation where its output is equal to its input. > > ![[DFlipFlopSequentialExample.svg]] Thus, the state equations for the circuit are: > $\begin{align*} A(t+1)&=AX+BX \\ &=X(A+B) \\ B(t+1)&=\bar{A}X \\ Y(t+1)&=\bar{X}(A+B) \end{align*}$