What is POS?
As the name suggests, it is formed by multiplying(AND operation) the sum terms. These sum terms are also called as ‘max-terms’. Maxterms are represented with ‘M’, they are the sum (OR operation) of Boolean variables either in normal form or complemented form.
Therefore, POS is product of maxterms and is represented as:
F in POS = [Tex]\Pi [/Tex]M(1, 2) Here, F is product of maxterm1 and maxterm2.
Example of POS
For Example:
A=0, B=1, C=0 Maxterm is A+B'+C A=1, B=1, C=1 Maxterm is A'+B'+C'
POS 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 POS form by multiplying all the max-terms when X is LOW(0).
While writing POS, the following convention is to be followed:
If variable A is Low(0) - A A is High(1) - A' X (POS) = [Tex]\Pi[/Tex]M(0, 2, 4, 5, 7) = (A+B+C).(A+B'+C).(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
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