Class XII D (Assignment on Boolean Algebra)
1. Write the equivalent expression for the following logical circuit:
a
b
c
e
2. Express P’ + QR’ in canonical SOP form.
F(P,Q,R,S)=∑(l,3,5,8,11,12,15)
3. Reduce the following Boolean expression using K-Map:
4. State and verify De Morgan’s theorem. Prove the theorem also.
5. State and prove the Distributive law algebraically and also with truth table.
F (x,y,z)= ∑ (0,2,4,6)
6. Write the equivalent POS expression of following SOP form
7. Draw the Logical circuit of the following expression with the help of NAND gate only x+yz
8. Obtain the simplified form of a Boolean expression using K-Map.
F(a,b,c,d)=∑(0,1,2,3,4,7,11,12,14)
9. State Involution Law and verify the same using truth table.
10. Write the Product of Sum and SOP form of the function F(x , y , z), truth table representation of F is given
below:
X
Y
Z
F
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
A
AND
C
O
R
AND
11. Write the equivalent Boolean Expression for the following Logic Circuit.
12. Reduce the following Boolean Expression using K-Map
F(A,B,C,D) = ∏ ( 0 , 2, 4, 5, 6, 7, 8, 10, 13, 15)
13. Write the equivalent Boolean Expression for the following Logic
Circuit.
1
X
AND
OR
Y
14. Reduce the following Boolean Expression using K-Map
15. Define the following terms giving examples?
16. Show algebraically:
i) Minterm
F(A,B,C,D) = ∏ ( 0 , 3 , 4 , 5 , 7 , 11 , 13 , 15)
ii) Tautology iii) maxterm
(A.(BC)) +BC+AC=1)
17. Convert the following expression into canonical SOP form.
( x y).( x
z )
18. Simplify using K-map and draw circuit diagram.
F(a,b,c,d)=(0,1,3,4,5,7,8,9,11,12,13,15)
19. Prove algebraically XY + YZ + Y’Z = XY + Z
20. Design a circuit for the Boolean expression (A’ + B’ + C’) (A + B’ + C’) (A + B + C’) using NOR to NOR
logic.
21. Write the POS & SOP form of a Boolean function F(X, Y, Z), and the truth table of which is given below:
X
0
0
0
0
1
1
1
1
Y
0
0
1
1
0
0
1
1
Z
0
1
0
1
0
1
0
1
F
1
0
1
0
1
0
1
1
22. Reduce the following Boolean expression using K-map: F(W, X, Y, Z) = ∏(0, 1, 3, 5, 6, 7, 10, 14, 15)
23. Simplify the following Boolean expression using K-map :
F(A, B, C, D)=m0 + m1 + m4 + m5 + m7 + m8
24. Prove XY+YZ+YZ’=Y, algebraically.
25.
Draw the circuit diagram for F = AB’C + C’B using NAND to NAND logic only.
26. Write the Products of sum and SOP form of the function G(U,V,W). Truth table representation of G is as
follows:
U
V
W
G
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
27.Reduce the following Boolean expression using K - Map :
F (P,Q,R,S) =
(1,2,3,5,6,7,9,11,12,13,15) and ∑ (0,2,3,4,6,7,8,10,12)
F (W,X,Y,Z) =
(0, 6, 8, 9, 10, 11, 13, 15)
28.Write short note on principles of Duality.
29.Prove algebraically (X + YZ) =(X+Y) (X+Z)
30.A Boolean function F defined on three input variables A, B, C and is 1(one) if and if only if number of 0(zero)
inputs is odd (e.g. F is 1(one) if A=0, B=1, C=1). Draw the truth table for the above function and express it in
canonical sum of product form.
31.Simplify the following Boolean expression using K-map :
F(A, B, C, D)=M0 . M1 .M4 . M 5 . M 7 . M 8
32.Draw the diagram of digital circuit for the function F(X,Y,Z)=(X+Y) . (X+Y) .(Y+Z)
33.Reduce the following Boolean expression using K-map. F(A, B, C, D)= (0, 1, 2, 4, 5, 7, 8, 9, 10, 11, 14)
34. Prove that XY+YZ+YZ’=Y
35.Convert the following expression into Canonical SOP form
36. Write the dual of the Boolean Expression 1)A+B’C=1
x+yx+xz
2) (AB`+A`B`C+AC)
37. Obtain the simplified form of a Boolean expression using K-Map.
38. Draw the logic diagram of expression AB`C`+B`C+ABC,
F(x,y,z)=∑(2,3,4,7)
using NAND Gates.
39.Write the SOP form of the function H(a,b,c,d)=(m0, m2,m3,m6,m7,m8,m10)Simplify the expression by using the
k-map.
40.Simplify the following 4-var K-map and write down the simplified maxterms expression.
AB CD
0 1
0
1
0 1
0
1
0 1
0
0
0 1
0
1
41.Draw a logical circuit diagram for the following Boolean expression: X’ . (Y’ + Z)
42. Convert the following Boolean expression into its equivalent Canonical SOP
(X’+Y+Z’).(X’+Y+Z).(X’+Y’+Z).(X’+Y’+Z’)
43. What are Universal gates and why are they so called?
3
44. Verify X’Y+X.Y’+X’Y’=(X’+Y’) using truth table.
45. State Absorption Law. Verify one of the laws using a truth table.
46. State and verify Associative Law.
47. Write the equivalent Canonical SOP for the following POS Expression: F(X,Y,Z)= ∏(1,3,6,7)
48. Convert the following Boolean expression into its equivalent Canonical POS form: AB’C+A’BC+A’BC
49. Draw logic diagram using NAND gates to implement the three function F = (0,1,2,5)
4