What is exactly ur problem?
I mean do u need help understanding Karnaugh maps, or expressions reductions???
Karnaugh Maps for O/P one:
u draw a table for the i/p values say $AB$ for the rows and $CD$ for the columns, but remember that $11$ precedes $10$ to simplify the reduction. $d$ means $Don't$ $Care$ to use the non existing values to simplify the reduction.
C'D' C'D CD CD'
A'B' 1 0 1 1
A'B 0 1 1 1
AB d d d d
AB' 1 1 d d
To simplify the F1 we take as large squares as we can (circulation is allowed)
-We take the 2 last columns together making $D$
+The 2 last rows making $A$
Then we have 2 remaining 1s, for the 1st of them we take the middle square:
We have the 1st corner remaining 1, trying to largen any square or rectangle, we use the $circular$ reduction and take the 4corners. i.e.,
Now, example of the expression reduction method on the last O/P... say F7
We write down the expression for the each 1 in F7, then add them together (add here represents OR) and try to simplify normally.
F7 has 1s at: 2,3,4,5,6,8,9
F7= A'B'CD'+ A'B'CD + A'BC'D' + A'BC'D+ A'BCD' + AB'C'D' + AB'C'D
F7=(A'B'CD'+ A'B'CD) + (A'BC'D' + A'BC'D) + A'BCD' + (AB'C'D' + AB'C'D)
F7= A'B'C(D'+D) + A'BC'(D'+D) + A'BCD' + AB'C'(D' +D)
= A'B'C+ (A'BC'+ A'BCD') + AB'C'
= A'B'C+ A'B(C'+CD') + AB'C'
and so on,...
(u see, the karnaugh map is usually easier)