Convert the following expressions into their sumofproducts f

Convert the following expressions into their sum-of-products form. (A + B)\'((D)\' (A(B + C))\' + D\' (S\" + B) (B C)\' Simplify F = A\' BC\' + BC\' D\' + A\'CD + B\' CD + A\' BD using only the consensus theorem

Solution

The Sum-of-Products (SOP) form is a form of simplifying the
boolean expressions of logic gates and is also called as Disjunctive
Normal Form as the product terms are ORed together and Disjunction
operation is logical OR. Sum-of-products form is also called as Standard SOP.
In this SOP form of Boolean function representation, the variables are operated
by AND (product) to form a product term and all these product terms are summed
or added together to get the final function.

The product of sums form is a form of simplifying the
Boolean expressions of logic gates. In this POS form,
all the variables can be written as sums to form sum terms and
is also called as Conjunctive Normal Form as the sum terms
are ANDed together and Conjunction operation
is logical AND. Product-of-sums form is also called as Standard POS.

How to calculate:

Sum-Of-Products and Product-Of-Sums calculation:

SOP (Sum of Product)
1. Find out the correct truth table.
2. Find out the rows which lead to result 1.
3. If the input = 1, then write the input; if the input = 0, write the input’s
complement. (i.e. input is x and y, if x= 0, y = 1, then we write x’y). Each row
should be written in a form of product.
4. Add all the products.

POS(Product of Sums)
1. Find out the correct truth txble.
2. Find out rows which lexd to result 0.
3. If the input = 0, then write the input; if the input = 1, write the input’s
complement. (i.e. input is x and y, if x = 1, y = 0, then we write xy’)and each row
should be written in a form of addition.
4. Multiply all the sums.