i want to know that PRODUCT OF SUMS is the complement of SUM OF PRODUCTS......I am giving u a problem to solve:
X=A+A'BC+B'C

 

product of sums must be the complement of the sum of products!!!!!!but it isn't!!!how????

 

Hi,

i want to know that PRODUCT OF SUMS is the complement of SUM OF PRODUCTS......I am giving u a problem to solve:
X=A+A'BC+B'C

How do you define "complement"?

You need to shorten your expression - fill your terms into a Karnaugh map like this.

A/BC | 00 01 11 10
-----+------------
 0   |  0  1  1  0
 1   |  1  1  1  1

Then I trust you to make the two circles and read out the answer yourself.

 

i want to know that PRODUCT OF SUMS is the complement of SUM OF PRODUCTS......I am giving u a problem to solve:
X=A+A'BC+B'C

Simple DeMorgans:

X = A+A'BC+B'C <- Sum of products

Double NOT:

X = (A+A'BC+B'C)''

Apply DeMorgans to whole expression:

X = ((A)'(A'BC)'(B'C)')'

Apply DeMorgans to each product term:

X = ((A)'(A + B' + C)(B + C'))' <- Complement of product of sums

It works the other way also.

Dave (4000)

 

thnks for giving me the suggestions