## Sum of products (SOP) and Product of sum (POS):

Boolean expression can be simplified and expressed in two ways they are

1) Sum of products (SOP)

2) Product of sum (POS)

### Sum of products (SOP):

As the name says, it is adding the product terms. In other words we can say that product terms (AND operation) is added (OR operation). The product term is called as the Minterm and it is represented as ‘m’.

#### Example:

Let us implement the following function in SOP

F= ABC+ DEF+GHI

Where F is the output and A, B, C, D, E and F are the input variables.

Implementation of SOP |

### Construction of SOP from truth table:

- We have to consider the rows which have the output ‘1’ and write the expression only for that row.
- In that row if the input is ‘0’, it has to be inverted. For example in the second row the output is 1, A=0 and B=0. So the inputs have to be inverted as A' and B'.
- All the AND terms or connected to the OR gate. The output of OR gate gives the output function F.

Statements are converted into Boolean expression. So if we have a condition that when the C input is 1 the output should be 1, we get the below truth table.

Truth table of SOP |

Implementation of the truth table |

### Product of sum (POS):

In the product of sum, the inputs are given to the OR gate and the output of the OR gate are summed up by the AND gate. It is represented by ‘M’. The sum and the product are not the arithmetic operation but it is logical operation.

F= (A+B+C).(D+E+F).(G+H+I).(J+K+L)

Implementation of POS |

### Construction of POS from truth table:

- We have to consider the rows which have the output ‘0’ and write the expression only for that row.
- In that row if the input is ‘1’, it has to be inverted. For example in the third row the output is 0, A=0 and B=1. So the input A is inverted.
- All the OR terms or connected to the AND gate. The output of AND gate gives the output function F.

Implementation of the truth table |

Difference between SOP and POS:

Difference between SOP and POS |

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