# What is sum of products AND product of sums?

## What is sum of products AND product of sums?

Sum of Products and Product of Sums. The different forms of canonical expression which includes the sum of products (SOP) and products of the sum (POS), The canonical expression can be defined as a Boolean expression which has either min term otherwise max term.

### What is sum of product definition?

The Sum of Product (SOP) expression comes from the fact that two or more products (AND) are summed (OR) together. That is the outputs from two or more AND gates are connected to the input of an OR gate so that they are effectively OR’ed together to create the final AND-OR logical output.

What do you mean by POS expression?

Then we have seen in this tutorial that the Product-of-Sum (POS) expression is a standard boolean expression that takes the “Product” of two or more “Sums”. For a digital logic circuit the POS expression takes the output of two or more logic OR gates and AND’s them together to create the final OR-AND logic output.

What is the sum product rule?

The product rule states that the probability of two or more independent events taking place is equal to the product of their individual probabilities. On the other hand, the sum rule states that the probability of two or more mutually exclusive events occurring is equal to the sum of their individual probabilities.

## What is the product of a sum AND a difference?

The product of the sum and difference of the same two terms is always the difference of two squares; it is the first term squared minus the second term squared. Thus, this resulting binomial is called a difference of squares.

### What is meant by Prime Implicant?

A prime implicant of a function is an implicant (in the above particular sense) that cannot be covered by a more general, (more reduced, meaning with fewer literals) implicant.

What is SOP AND POS definition?

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 max terms or sum terms.

Does product and sum mean the same?

The product means that you need to multiply the three numbers together. The sum means that you need to add the three numbers together. Question: What do you get if you double 15? Answer: Just multiply the number by 2 to give 30. Question: Can you find two numbers which have a product of 12 and a sum of 7? Answer: 4 and 3 are a the answers.

## How is a product and a sum alike?

We can also derive the sum-to-product identities from the product-to-sum identities using substitution. We can use the sum-to-product formulas to rewrite sum or difference of sines, cosines, or products sine and cosine as products of sines and cosines. See Example (PageIndex{4}).

### What is the formula for the sum of products?

Canonical Expression. A boolean expression consisting entirely either of minterm or maxterm is called canonical expression.

• Different Forms of Canonical Expression. There are two forms of canonical expression.
• Sum of Products (SOP) A boolean expression consisting purely of Minterms (product terms) is said to be in canonical sum of products form.
• Can We express sum of products as product of sums?

The sum-to-product formulas allow us to express sums of sine or cosine as products. These formulas can be derived from the product-to-sum identities. For example, with a few substitutions, we can derive the sum-to-product identity for sine.