Applied Physics CSIE II: UNIT II: Logic Gates
Product of sums (POS)
A product of sums (POS) is a Boolean expression where several sum terms (OR terms) are AND‒ed (multiplied) together.
PRODUCT OF SUMS (POS)
Definition
A
product of sums (POS) is a Boolean expression where several sum terms (OR
terms) are AND‒ed (multiplied) together.
In
short, POS=AND of OR terms
Each
OR term is called a Maxterm
Example
Y
= (A + 
) (B +C) (
+ 
)
Here,
(A+),
(B+C) (+) are sum (OR) terms.
All
these terms are AND‒ed → Therefore it is called Product of Sums (POS).
OBTAINING A POS from a Truth Table
Let
us consider a Truth table as shown below
Step 1:
Identify rows where output Y = 0
These
rows represent the Max‒terms,
From
the Truth Table (gray shaded rows), we can observe that the output Y = 0 at the
following rows viz.,
(0,0,1),
(0,1,1), (1,0,1), (1,1,0)
Step 2:
For
each Max‒term, write
•
Variable without complement if the value = 0
•
Variable with Complement if the value = 1
The
Maxterms for the above is:
Row
with 0,0,1 → A+B+
Row
with 0,1,1 → A++
Row
with 1,0,1 → +B+
Row
with 1,1,0 → ++C
Step 3:
∴ The POS expression shall be written as
Applied Physics CSIE II: UNIT II: Logic Gates : Tag: Applied Physics : - Product of sums (POS)
Applied Physics CSIE II: UNIT II: Logic Gates
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