Class XII Sample Questions
of Boolean Algebra

1. What are logical statements? 

2. What is tautologies and fallacies? 

3. State some laws of boolean algebra. 

4. State and prove Demorgan's law. 

5. What is duality principle? 

6. What is the difference between minterm and maxterm ? 

7. Define Kamaugh map. What do you und~rstand by map rolling? 8. Prove the following algebraically: 

(i) ab' + ab + abc 
(il) ab'c + a'bc + a'b'c + ab'c' 
(iil) ab + bc +. a'c 
(iv) (a + b)(a' + b') 
(v) xy+(x+y)(x'y'z') 

9. Prove the following by truth table: 

(i) x(y' + z) + z' 
(il) a.(b + c) + a.c' 
(iii) (x + y)(y + z)(z + x) 
(iv) xy + x'y' + xz 
10. Find the dual offollowing : 
(I) (a+b)(b+c)(a+c) 
(il) (1 + a)(ac) 
(iii) (a +O)(b + l)(c+ 1 +0) 
(iv) a'c + b'a 

11. Find the minterm designation of following : (I) xyz (ii) x'yz' 

12. Find the maxterm designation of following : (I) (u+v+w) (ii) (u'+w'+w) 

13. Find the complement of the following boolean function: 

Fl = (a + b)(c' + a')(b + d) 

14. Construct a boolean function of three variables p, q and r that has an output 1 when exactly two ofp, q, r are having values 0, and output 0 in all other cases. 

15. A boolean function F defined on three input variables X, Y and Z is 1, ifand only if number of I input is odd (e.g. F is 1 if X == 1, Y =0, Z =0). Draw the truth table for the above function and express it in canonical sum-of-product form. 

16. Given the truth table of a function F(x, y, z). Write the s-o-p and p-o-s expression and canonical form from the following truth table: 

17. Convert xy' + y'z + zx' into canonical sum-of-product form. 

18. Convert (x + z)(z + y) into canonical p-o-s form.

19. Simplify the following boolean expression: 
(i) ab'c' + a'bc + a'b'c' + abc'
(ii) xyz + x'y'z' + x'yz' + x'y'z 

20. Minimize the following using Karnaugh map: 

(I) F(x, y, Z, w) = wxyz + wx'y'z' + w'xyz + wxyz 

(ii) F(x, y, z) = xx' + x'y 

(iii) F(a, b, c) = abc + a'bc' + ab'c + ab'c' + a'bc 




21. Using the Karnaugh map technique obtain the simplified expression as sum of product for the following map. 

22. Draw and simplify the Karnaugh map ofx, y, z for (x +y+ z)(x' +y+ z)(x +y+z) 

23. Draw the logic circuit for 

(i) ab' + bc' (ii) (a + b')(b' + C + a) 

24. Draw the logic circuit for a'b'cd + abc'd + ab'cd using only NAND gates. 

25. Draw the logic circuit for (a'+ b'+ c + d)(a+ b+ c'+ d)(a+ b'+ c +d) using only NOR gates. 

26. Draw logic circuits for the following: 
(I) F(A, B, C, D) = L (1, 3, 5, 8, 10,12) (ii) F(W, X, Y) = L (0, 2, 4, 6, 7) 

27. Given a Boolean function F(a, b, c, d) = L(O, 1, 2, 3, 4, 10, 11) obtain the simplified expression using Karnaugh map in sum of product form. [CBSE Quan Book] 

28. Minimize the Boolean expression XYZ + XYZ' + XY'Z' + X'Y'Z + X'YZ' + X'YZ using Karnaugh map

29. Simplify using Karnaugh map where mj is a minterm F(A, B, C)= ml + m) + ms + m4' [CBSE Quan Book] 

30. Simplify using Karnaugh map where m; is a minterm F(A, B, C) = mo + ms + m7' [CBSE Quan Book] 

31. Simplify using Kamaugh map where mj is a minterm 
F(A, B, C, D) = m2 + m3+ m5 + m6 + m7 + m9 + m11 + m13 

32. Simplify using Kamaugh map where mj is a minterm 
F(A,B, C, D)=mo +m5 +m7 +m8 +m11 +ml3+m15 

33. Minimize F(a, b, c, d) = Σ(1, 4,5,8,9,12, 13) using Kamaugh map. 

34. Minimize F(a, b, c, d) = Σ (O, 1,2,4,5,7,8, 10, 13, 15) using Kamaugh map. 

35. Minimize F(a, b, c, d) = Σ (1, 2, 3,11,12,14, 15) using Kamaugh map. 

36. Prove that (a' + b')( a' + b)( a + b') = a'b' 

37. Prove that ac + ab' + bc' = abc + ab'c + abc' + acb' + a'bc' + ab'c'. 

38. Check the validity of the following Boolean expression: 

(y + z)(z + x) = (x' + y')(x' + z')(y' + z'). 

39. Simplify abc + a'bc + ab'c + abc' + ab'c' + a'bc' + a'b'c'. 

40. Find the complement of (a + c + d)(a + c + d')(a + c' + d)(a + b'). 

41. Simplify F(a,b, c, d) = a'b'c'd + a'bc'd + a'bcd' + a'bcd + abcd' + abcd using Kamaugh map. 

42. A combinational circuit has 4 inputs and one output. Output is I if: 

(i) All the inputs are equal to 1. 
(ii) None of the inputs are equal to 1. 
(iii) An odd number of inputs are equal to I. 

(a) Obtain the truth table 
(b) Find the simplified output function in SOP form 
(c) Find the simplified output function in POS form 
(d) Draw the logic diagram. 

43. Simplify F(x, y, z, w) = xy + wz + wx + y'z'w + x'yz + wy using Kamaugh map.