What is SOP?
It is one of the ways of writing a Boolean expression. As the name suggests, it is formed by adding (OR operation) the product terms. These product terms are also called as ‘min-terms’. Min-terms are represented with ‘m’, they are the product(AND operation) of Boolean variables either in normal form or complemented form.
Therefore, SOP is sum of minterms and is represented as:
F in SOP = [Tex]\Sigma [/Tex]m(0, 3)
Here, F is sum of minterm0 and minterm3.
Example of SOP
For Example:
A=0, B=0, C=0 Minterm is A'.B'.C' A=1, B=0, C=1 Minterm is A.B'.C
SOP Truth Table
Consider a function X, whose truth table is as follows:
A | B | C | X |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
The function X can be written in SOP form by adding all the min-terms when X is HIGH(1).
While writing SOP, the following convention is to be followed:
If variable A is Low(0) - A' A is High(1) - A
X (SOP) = [Tex]\Sigma [/Tex]m(1, 3, 6)
= A’.B’.C + A’.B.C + A.B.C’
Difference between SOP and POS in Digital Logic
In digital logic, the inputs and output of a function are in the form of binary numbers (Boolean values) i.e., the values are either zero (0) or one (1). Therefore, digital logic is also known as ‘Boolean logic’. These inputs and output can be termed as ‘Boolean Variables’. The output Boolean variable of a digital signal can be expressed in terms of input Boolean variables which forms the ‘Boolean Expression’.
Table of Content
- SOP Vs POS
- What is SOP?
- What is POS?
- Differences