Class XII D (Assignment on Boolean Algebra)
1. Write the equivalent expression for the following logical circuit:
2. Express P’ + QR’ in canonical SOP form.
3. Reduce the following Boolean expression using K-Map: F(P,Q,R,S)=∑(l,3,5,8,11,12,15)
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.
6. Write the equivalent POS expression of following SOP form F (x,y,z)= ∑ (0,2,4,6)
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.
X / Y / Z / F0 / 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
10. Write the Product of Sum and SOP form of the function F(x , y , z), truth table representation of F is given below:
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.
14. Reduce the following Boolean Expression using K-Map F(A,B,C,D) = ∏ ( 0 , 3 , 4 , 5 , 7 , 11 , 13 , 15)
15. Define the following terms giving examples? i) Minterm ii) Tautology iii) maxterm
16. Show algebraically: (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)=S(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 / Y / Z / F0 / 0 / 0 / 1
0 / 0 / 1 / 0
0 / 1 / 0 / 1
0 / 1 / 1 / 0
1 / 0 / 0 / 1
1 / 0 / 1 / 0
1 / 1 / 0 / 1
1 / 1 / 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 / G0 / 0 / 0 / 0
0 / 0 / 1 / 0
0 / 1 / 0 / 1
0 / 1 / 1 / 1
1 / 0 / 0 / 1
1 / 0 / 1 / 0
1 / 1 / 0 / 0
1 / 1 / 1 / 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)= S(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 x+yx+xz
36. Write the dual of the Boolean Expression 1)A+B’C=1 2) (AB`+A`B`C+AC)
37. Obtain the simplified form of a Boolean expression using K-Map. F(x,y,z)=∑(2,3,4,7)
38. Draw the logic diagram of expression AB`C`+B`C+ABC, using NAND Gates.
39.Write the SOP form of the function H(a,b,c,d)=å(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 / 10 / 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?
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 =S (0,1,2,5)
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