V+ TEAM

WWW.VIDYARTHIPLUS.COM 26. Convert Y= A+BC'+AB+A'BC into canonical form 27. What is meant by ‘essential prime-implicant’? 28.Obtain the complement of f=wx’y+xy’=wxz using de morgan’s theorem 29.Show that A+A’B=A+B using the theorems of Boolean algebra 30.What is the advantage of gray codes over the binary number sequence 31.Simplify the following Boolean function i)x(x’+y) ii)xy+x’z+yz 32.Convert the following function into sum of product form (AB+C)(B+C’D) 33.What is the significance of high impedance state in tri-state gates

I6 Marks questions 1.State and prove the postulates, theorems of Boolean algebra. 2.Use QM method to simply the Boolean expression(x1,x2,x3,x4,x5)= ∑(0,1,4,5,16,17,21,25,29) (NOV’2010) 3.Use Quine McClusky method to obtain the minimal sum for the following function. F(X1X2X3X4) = ∑ (0, 1, 3, 6, 7, 14, 15) (April 2003) 4.Simplify the function using Karnaugh map. (i) F (ABCD) = ∑ (0, 1, 2, 4, 5, 7, 11, 15) (8mark) (ii) F (WXYZ) = ∑ (2, 3, 10, 11, 12, 13, 14, 15)

(8mark) (April 2003)

4. (i) State and prove demorgan’s theorem and expand the function F = ( (( A B )C C D )

(6 mark)

(ii) Simplify the following switching function using karnaugh map, F(A,B,C,D) = ∑ (0,5,7,8,9,10,11,14,15) + Φ (1,4,13)

(10 mark)

5..i) Simplify the following Boolean function using 4 variable map F(w,x,y,z)= ∑(2,3,10,11,12,13,14,15)

(NOV’2010)

(8mark)

ii)Draw a NAND logic diagram that implements the complement of the following function F(A,B,C,D)= ∑(0,1,2,3,4,8,9,12)

(8mark)

6.Simplify the Boolean function using K-map and tabular methods. Compare the methods. F (A, B, C, D) =∑m(4,5,6,7,8)

d (A, B, C, D) = ∑m(11,12,13,14,15).

7.Implement using only NAND gates (i) Express the function f(x, y, z) = XY X Z as a product of sum WWW.VIDYARTHIPLUS.COM

terms form.

(4 marks) V+ TEAM

WWW.VIDYARTHIPLUS.COM (ii) Express the following function as the minimal sum of products, using a K-map

F (a,b,c,d) =∑m(0,2,4,5,6,8,10,15) + ∑Φ(7,13,14)

(12 marks)

8.Implement the following with either NAND gate or NOR gate gates. Use only 4 gates. Only the normal inputs are available. (i) d = WYZ

(8mark)

(ii) F = W XZ WYZ X WX Y Z (8mark) 9. Using tabulation method simplify the Boolean function F(w,x,y,z)=Σ(1,2,3,5,9,12,14,15) which has the don’t care conditions d(4,8,11). 10.Reduce the Boolean function using