This one has also cause me hell....
simplification

Y= ABCD(not) multiplied by (AB+CD)
y= ( A[not])B[not] ) + (C[not]+D[not] )+ABCD

 

yea, thats a tough one

 

by

Y= ABCD(not) multiplied by (AB+CD)

do you mean

y = (!(A.B.C.D)) + ((A.B)+(C.D))

where

! is NOT
+ is OR
. is AND

Here are all the rules that should be used to simplify boolean expressions:
http://www.allaboutcircuits.com/vol_4/chpt_7/5.html

 

Y= ABCD(not) multiplied by (AB+CD)

What do you mean by "multiplied"?

y= ( A[not])B[not] ) + (C[not]+D[not] )+ABCD

Look at using DeMorgan's theorems. Check http://www.allaboutcircuits.com/vol_4/chpt_7/index.html and in particular http://www.allaboutcircuits.com/vol_4/chpt_7/8.html

Dave