The sum-of-products (SOP) form is a method (or form) of simplifying the Boolean expressions of logic gates. In this SOP form of Boolean function representation, the variables are operated by AND (product) to form a product term and all these product terms are ORed (summed or added) together to get the final function.

SOP form can be obtained by

- Writing an AND term for each input combination, which produces HIGH output.
- Writing the input variables if the value is 1, and write the complement of the variable if its value is 0.
- OR the AND terms to obtain the output function.

Ex: Boolean expression for majority function F = A’BC + AB’C + ABC ‘ + ABC

A | B | C | F |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 1 |

1 | 1 | 1 | 1 |

The product of sums form is a method (or form) of simplifying the Boolean expressions of logic gates. In this POS form, all the variables are ORed, i.e. written as sums to form sum terms.

All these sum terms are ANDed (multiplied) together to get the product-of-sum form. This form is exactly opposite to the SOP form. So this can also be said as “Dual of SOP form”.

POS form can be obtained by

- Writing an OR term for each input combination, which produces LOW output.
- Writing the input variables if the value is 0, and write the complement of the variable if its value is 1.
- AND the OR terms to obtain the output function.

Ex: Boolean expression for majority function F = (A + B + C) (A + B + C ‘) (A + B’ + C) (A’ + B + C)

A | B | C | F |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 1 |

1 | 1 | 1 | 1 |

Source : http://www.electronics-tutorials.ws/boolean/bool_6.html