Kernaugh map is the technique to reduce the design of an electronic circuit . Any electronic circuit is made of different different small circuits like Multiplexers . Multiplexers uses binary values as inputs and produce the output in the binary format also and then converts these digital values into analog signal to perform the desired output .

Let , we take a Truth table of a 2-input Multiplexer as below with A,B , S as Inputs and Y as output -

S | A | B | Y |

0 | 0 | 0 | 0 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 1 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 0 |

1 | 1 | 1 | 1 |

So the output function in the terms of minterms as -

Y = Σ(2, 3, 5, 7)

Here we can reduce electronic circuit , using the boolean algebra rules but it becomes very hard to reduce the size of circuit , when circuit is too big and have Large number of inputs and then the Technique of Kernaugh Map comes into the picture to solve the circuit reducing problems .

Basically We use kernaugh map for 2 , 3 and 4 inputs and for more larger designs other techniques are also available .

**Rules to draw and reduce the circuit design as -**

1. Design the basic cells for the number of inputs like -

K-Map for 2-Input Circuits |

K-Map for 3-Input Circuits |

K-Map for 4-Input Circuits |

2. Each cell with a 1 must be included in at least one group.

3. Try to make the largest possible groups.

4. Try to end up with as few groups as possible.

5. We can create groups of only 2 elements or 4 elements or 8 elements or in the power of 2 ,

elements and may be square or rectangular only .

6. We can include wrap around elements of multiple groups at the grid edges .

7. Do not include diagonals or zig-zags to form a group.

To Reduce above Multiplexer using Kernaugh map is like below -

Steps and Groups making in K-Map |

Reduced circuit generated by K-Map |