CBSE Guess > Papers > Important Questions > Class XII > 2012 > Computer Science > Computer Science Mr. Pradumna Singh
Computer Science- CBSE CLASS XII
Q. 21. State and verify Absorption law in Boolean algebra. For - 2 Marks
Ans.: Absorption law states that :
a) x+xy=x b) x(x+y)=x
Verification:
x+xy=x
LHS=x+xy by distributive law
=x(1+y) since 1+y=1
=x.1 since 1.x=x
=x = RHS, hence verified
OR (using truth table)
x |
y |
xy |
x+xy |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
Here column x and x+xy are identical, hence proved.
Q. 22. Write the SOP form of a Boolean function G, which is represented in a truth table as follows : For - 2 Marks
A |
B |
C |
G |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
1 |
Ans. Add extra column for min term and write min terms for the rows which have output (G) as 1:-
A |
B |
C |
G |
Min Term |
0 |
0 |
0 |
1 |
A’B’C’ |
0 |
0 |
1 |
1 |
A’B’C |
0 |
1 |
0 |
0 |
|
0 |
1 |
1 |
0 |
|
1 |
0 |
0 |
1 |
AB’C’ |
1 |
0 |
1 |
0 |
|
1 |
1 |
0 |
0 |
|
1 |
1 |
1 |
1 |
ABC |
Now sum all the min terms to get the SOP as:
Therefore SOP of F(A,B,C)= A’B’C’+A’B’C+AB’C’+ABC
Q. 23. Write the equivalent Boolean Expression R for the following circuit diagram : For - 1 Marks
Ans. : (A+B) (A+B’) (A’+B)
Q. 24. If F(P,Q,R,S) = π (0,2,4,5,6,7,8,10,11,12,14) , obtain the simplified form using K-Map. For - 4 Marks
Ans. Draw the 4 variable K-Map, plot & group the 0s starting from bigger to smaller group:
Reducing:
Octet = M0.M2.M4.M6.M8.M10.M12.M14
= S
Quad = M4.M5.M6.M7
= P+Q’
Pair = M10.M11
= P’+Q+R’
Therefore POS of F(P,Q,R,S)= S.(P+Q’).(P’+Q+R’)
Prepared By: Mr. Pradumna Singh
mail to: [email protected]
