## Sum of Product (SOP)

Sum of Product abbreviated as SOP is a form of expression in Boolean algebra in which different product terms of inputs are being summed together. This product is not arithmetically multiply but it is Boolean logical AND and the Sum is Boolean logical OR.

Minterm is product of Boolean variable either in normal form or complemented form. Minterm means the term that is true for a minimum number of combinations of inputs. That is true for only one combination of inputs. Since AND gate also gives true only when all its input are true so we can say minterms are AND of input combinations.

**Types of Sum Of
Product Forms **

- Canonical SOP form
- Non-Canonical SOP form
- Minimal SOP Form

### What You Need To Know About SOP

- SOP is a method of describing a Boolean expression using a set of Minterms or product terms. Minterm is product of Boolean variable either in normal form or complemented form.
- SOP generates expression in which all the variables in a domain are first multiplied then added.
- Minterms or product terms are mainly used in the SOP which associates with the high (1) value.
- While writing minterms for SOP, input with value 1 is considered as the variable itself and input with value 0 is considered as complement of the input.
- Minterms are represented as ‘m’.
- In the last step of the process, all terms are added with each other.

## Product Of Sum (POS)

Product of Sum abbreviated as POS is a form of expression in Boolean algebra in which products sum terms of inputs are taken. These are not arithmetic product and sum but they are logical Boolean AND and OR respectively.

Maxterm is sum of Boolean variables either in normal form or complemented form. Maxterm means the term or expression that is true for a maximum number of input combinations or that is false for only one combination of inputs. Since OR gate also gives false for only one input combination. So Maxterm is OR of either complemented or non-complemented inputs.

**Types of Product Of
Sum Forms**

- Canonical POS form
- Non-Canonical form
- Minimal POS form

### What You Need To Know About POS

- POS is a method of describing a Boolean expression using a set of maxterms or sum terms. Maxterm is sum of Boolean variables either in normal form or complemented form.
- The POS represents the Boolean expression having variables summed then multiplied with each other.
- In POS, Maxterms or Sum terms are employed, which produces a low (0) value.
- While writing maxterms for POS, input with value 1 is considered as the complement and input with value 0 is considered as the variable itself.
- Maxterms are represented as ‘M’.
- In the last step of the process, all the terms are multiplied with each other.

**Also Read:** *Difference Between Open And Closed Loop *

## Difference Between SOP And POS In Tabular Form

BASIS OF COMPARISON |
SOP |
POS |

Description | SOP is a method of describing a Boolean expression using a set of Minterms or product terms. | POS is a method of describing a Boolean expression using a set of maxterms or sum terms. |

Expression | SOP generates the expression in which all the variables in a domain are first multiplied then added. | The POS represents the Boolean expression having variables summed then multiplied with each other. |

Use Of Minterms & Maxterms
| Minterms or product terms are mainly used in the SOP which associates with the high (1) value. | In POS, Maxterms or Sum terms are employed, which produces a low (0) value. |

Writing Maxterms &
Minterms | While writing minterms for SOP, input with value 1 is considered as the variable itself and input with value 0 is considered as complement of the input. | While writing maxterms for POS, input with value 1 is considered as the complement and input with value 0 is considered as the variable itself. |

Representation Of Maxterms
& Minterms | Minterms are represented as ‘m’. | Maxterms are represented as ‘M’. |

Final Expression | In the last step of the process, all terms are added with each other. | In the last step of the process, all the terms are multiplied with each other. |