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# Design a Moore machine to generate 1's complement of a binary number.

Moore machine has 6 tuples, which are as follows −

**(Q, q0, Σ, O, δ, λ)**

Where,

- Q: Finite set of states
- q0: Initial state of machine
- Σ: Finite set of input symbols
- O: Output alphabet
- δ: Transition function where Q × Σ → Q
- λ: Output function where Q → O

The transition diagram is as follows −

## Explanation

**Step 1**− q0 is the start state on input ‘0’ goes to q1 state and on ‘1’ goes to state q2 generating output 0.**Step 2**− q1 on input ‘0’ goes to q1 itself and on ‘1’ goes to q2 generating output ‘1’.**Step 3**− q2 on input ‘0’ goes to q1 and on ‘1’ goes to q2 generating output ‘0’.

**For instance,**

Take one binary number: **1011**.

Input

Input | 1 | 0 | 1 | 1 | |
---|---|---|---|---|---|

State | q0 | q2 | q1 | q2 | q2 |

Output | 0 | 0 | 1 | 0 | 0 |

Let’s construct the transition table for the given language. The table is as follows −

Current State | Next State | Output | |
---|---|---|---|

0 | 0 | ||

->q0 | q1 | q2 | 0 |

q1 | q1 | q2 | 1 |

q2 | q1 | q2 | 0 |

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