# 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:
> $\begin{align*}
A(t+1)&=AX+BX \\
&=X(A+B) \\
B(t+1)&=\bar{A}X \\
Y(t+1)&=\bar{X}(A+B)
\end{align*}$