Product of Sums (POS)

Overview

Product of Sums (POS) is a standard form where Boolean functions are expressed as a product (AND) of sum terms (OR). Each sum term contains variables or their complements ORed together. POS form provides an alternative to SOP, often preferred when implementing functions with OR-AND logic gates.

Detailed Explanation

Formation Rules

1. Standard Form:
   F = S₁ • S₂ • S₃ • ... • Sₙ
   where each S is a sum term

2. Maxterm Form:
   F = M₀ • M₁ • M₂ • ... • Mₙ
   where M represents complete sum terms

Implementation Steps

1. Truth Table → Maxterms
   Row with F=0: Convert to sum term

2. Example:
   A B | F
   ----|--
   0 0 | 1
   0 1 | 0  → (A+B')
   1 0 | 1
   1 1 | 0  → (A'+B')

   F = (A+B')(A'+B')

Circuit Design

Two-Level Implementation:
Level 1: OR gates for sums
Level 2: AND gate for product

A --|OR |
B'--|   |
         |
A'--|OR |-|AND|--F
B'--|   | |

Practice Problems

1. Create POS from truth table
2. Minimize given POS expressions
3. Convert between POS and SOP

References

• Digital Design by Morris Mano
• POS Implementation Guide

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