DIGITAL LOGIC : Sum Of Products

DIGITAL  LOGIC

Subtopic  : Sum of Products (SOP)

What is Sum of Products?

Sum of products is any mathematical expressions in which addition operator is applied to two or  more subexpressions each of which is an application of a multiplication operator. The most common case would be scalar addition and multiplication.

e.g . : ab+cd

But the terms is also used for other kinds of operators with similar properties  such as AND or OR in Boolean Algebra.

e.g.  : (a AND b) or ( c AND d)

All Boolean equation can be represented in two forms :  Sum of Products and Product of Sums. But we will be focusing only on Sum of Products because it is easier.

Sum of Products(SOP)

→ Combination of input values that produced 1s is converted into equivalent variables, ANDed together then ORed with other combination variables with the same output.

 Now I will show you guys an example on how to find SOP  from truth table.

The  equation for the truth table is  F = A’B’+ABC’D

The truth table :

A	B	C	D	F
0	0	0	0	1
0	0	0	1	1
0	0	1	0	1
0	0	1	1	1
0	1	0	0	0
0	1	0	1	0
0	1	1	0	0
0	1	1	1	0
1	0	0	0	0
1	0	0	1	0
1	0	1	0	0
1	0	1	1	0
1	1	0	0	0
1	1	0	1	1
1	1	1	0	0
1	1	1	1	0

Now, based on the equation,what you should do is to choose those equations which has the  value 1 as the product and convert it into equation.

note : A = 1   A’=0

first row :

A=0 B=0 C=0 D=0 when converted into equation would be ,

A’B’C’D’

Second row :

A=0  B=0  C=0  D=1  when converted into equations would be,

A’B’C’D

Third row :

A=0  B=0  C=1  D=0 when converted into equations would be,

A’B’CD’

Fourth row :

A=0  B=0  C=1  D=1 when converted into equations would be,

A’B’CD

Fourteenth row :

A=1  B=1  C=0  D=1 when converted into equations would be,

ABC’D

Next, what you do is you combine all of them into one equation.

SOP Equation :

F = (A’B’C’D’)+( A’B’C’D)+( A’B’CD’)+( A’B’CD)+( ABC’D)

*The equation can also be used to build truth table*

Incase you guys dont understand, I've inserted a good tutorial video from Youtube. I do not own the video. It is for academic purpose only. I hope you guys find this post helpful.

By NURUL HIDAYAH BINTI ISMAIL  (B031310124) J