State table

Also called: next-state table, state transition table, transition table

A table form of a state machine: one row per present state, giving the next state, and the output, for every input value.

A state table holds exactly the same information as a state diagram, laid out in rows and columns.

Each row is a present state.
There is a column of next states for each input value.
Outputs: a moore machine has one output column (one output per row); a mealy machine writes next state / output in every cell.

Why bother when you have the diagram? A table makes it impossible to forget an arrow, because every row has a cell for every input. And it's the bridge to hardware: once the states are given codes (state encoding), the table becomes a truth table whose inputs are the present-state bits and the machine inputs, and whose outputs are the next-state bits. From there you write next-state equations with K-maps.

Counters use a simpler version, the next-state table: with no inputs except the clock, each present state has just one next state.

Tables also make it easy to spot equivalent states: rows with the same outputs and the same next states can be merged.

Worked examples

Example

The Mealy 110 detector as a table

Write the diagram above as a state table. Each cell is next state / output.

1.
Row A: X = 0 → A / 0. X = 1 → B / 0.
2.
Row B: X = 0 → A / 0. X = 1 → C / 0.
3.
Row C: X = 0 → A / 1. X = 1 → C / 0.
4.
Three rows, two cells each: six cells, matching the six arrows in the diagram.

Example

A Moore table

The Moore 110 detector has states S0 to S3, with output 1 only in S3.

1.
S0: X = 0 → S0, X = 1 → S1. Output 0.
2.
S1: X = 0 → S0, X = 1 → S2. Output 0.
3.
S2: X = 0 → S3, X = 1 → S2. Output 0.
4.
S3: X = 0 → S0, X = 1 → S1. Output 1.
5.
One output per row, because the output depends on the state alone.

Common mistakes

Mixing up the present-state column and the next-state columns.
Writing one output per row for a Mealy machine. Its output can differ between inputs in the same row.
Leaving cells empty. Every present state needs a next state for every input (or an explicit don't-care for unused codes).

Practice State table

Interactive questions with instant feedback and a worked solution for every wrong answer.

Counters lesson full course

Finite State Machines lesson full course

Practice exams

Learn it step by step

State table is taught in Finite State Machines and Counters.

Finite State Machines →Counters →

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