This preview shows pages 1–2. Sign up to view the full content.
Deriving sumofproducts (SOP) and productofsums (POS) forms
Every
group you make on a Karnaugh map is a product term.
When the product terms are unified, you've
formed a sumofproducts expression.
What makes the various SOP expressions different is if they're formed
by grouping ones on a map – that is, if they're prime
implicants
– or if they're formed by grouping zeros on a
map – that is, if they're prime
implicates
.
If you group ones on a map, you've obtained an SOP expression for the uncomplemented form of a function.
Let's call the function
f
.
With
f
determined in SOP form, the story is basically over.
We can implement the
SOP form of
f
with a set of firstlevel AND gates unified by a secondlevel OR gate.
Using bubble propagation,
all of the AND gates and OR gates can be turned into NAND gates.
If you group zeros on a map, you've implemented an SOP expression for the
complemented
form of
f
.
We'll
call this form
f
'.
We seldom care about
f
'.
We could implement
f
' in SOP form using AND gates on the first
level and a unifying OR gate on the second level, but then we'd have to invert the output to obtain
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 01/17/2011 for the course ECE 3504 at Virginia Tech.
 '06
 JSThweatt

Click to edit the document details