# State Table **A table showing the inputs, present and next state, and outputs of a [[sequential circuit]].** A **state table**, also known as a **transition table**, is a table that displays *all possible* binary combinations of *present and next states, inputs, and outputs* of a [[sequential circuit]]. A state table can be filled using logic diagrams, [[State Equation|state equations]], or [[Excitation Table|excitation tables]]. State tables are often used as the first step of [[state reduction]]. > [!Example] For the following state equations, >$\begin{align*} A(t+1)&=AX+BX \\ &=X(A+B) \\ B(t+1)&=\bar{A}X \\ Y(t+1)&=\bar{X}(A+B) \end{align*}$ the state table is: > | Present state | | Next state | | | | Output | | |:--------------------:|:---:|:-----------------:|:---:|:-----:|:---:|:------:|:-----:| | | | $X=0$ | | $X=1$ | | $X=0$ | $X=1$ | | $A$ | $B$ | $A$ | $B$ | $A$ | $B$ | | | | $0$ | $0$ | $0$ | $0$ | $0$ | $1$ | $0$ | $0$ | | $0$ | $1$ | $0$ | $0$ | $1$ | $1$ | $1$ | $0$ | | $1$ | $0$ | $0$ | $0$ | $1$ | $0$ | $1$ | $0$ | | $1$ | $1$ | $0$ | $0$ | $1$ | $0$ | $1$ | $0$ |