Sum of product(SOP):
The sum of product (SOP) is a Boolean expression that is formed by summing together a number of product terms.
A product term is a Boolean expression that is formed by ANDing together a number of variables or their complements.
The SOP form of a Boolean function is a convenient way to represent the function, as it can be easily implemented in hardware using AND and OR gates.
Some examples are:
AND/OR implemention of an SOP expression:
NAND/NAND implementation of an SOP expression:
The Standard SOP form:
A standard SOP expression is one in which all the variables in the domain appear in each product term in the expression.
Example:
Converting Product term to Standard SOP:
Product of sum(POS):
The product of sum (POS) is a Boolean expression that is formed by multiplying together a number of sum terms.
A sum term is a Boolean expression that is formed by ORing together a number of variables or their complements.
The POS form of a Boolean function is another convenient way to represent the function, as it can also be easily implemented in hardware using AND and OR gates.
Some examples are:
Implementation of POS expression:
The Standard POS Form:
A standard POS expression is one in which all the variables in the domain appear in each sum term in the expression.
Example:
