Convert the following function into sum of product form. (AB+C)(B+C'D) ... (ii) Simplify the following switching function using karnaugh map,. F(A,B,C,D) = ∑ (0,5 ...
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WWW.VIDYARTHIPLUS.COM DIGITAL ELECTRONICS QUESTION BANK UNIT – 1 MINIMIZATION TECHNIQUES AND LOGIC GATES 2 marks 1. What happens when all the gates in a two level AND-OR gate network is replaced by NOR gates? 2. Implement Y  AB  A  ( B  C ) using NAND gates only. 3. If A and B are Boolean variables and if A=1 and A  B  0 , find B. 4. Express the switching function fAB = A in terms of minterms. 5. Apply Demorgan’s theorems to simplify A  BC . 6. Express x  yz as the sum of minterms. 7. What is prime implicant? 8. What are ‘minterms’ and ‘maxterms’? 9. Why binary number system is used in digital system? 10. Define the laws of Boolean algebra. 11. For a switching function of ‘n’ variables, how many distinct minterms and maxterms are possible? 12. State two absorption properties of Boolean algebra. 13. State Demorgan’s theorem 14.Draw an active tri-state buffer and write its truth table14. 15. Define canonical form. Express F  BC  AC in a canonical SOP form. 16. Write down Fan in & Fan out of a standard TTL IC 17. What is Propagation Delay of a gate? 18.List out the major categories of logic circuits 19.Express F= A+B’C as sum of minterms 20.Implement F= (AB’+ A’B)(C+D’) with only NOR gates. 21. Find the complement of x + yz 22. State and prove consensus theorem. 23.Implement AND and OR gate using NAND gate. 24. . Find the binary representation of decimal 125. 25. Complement the expression X(Y'+Z'). WWW.VIDYARTHIPLUS.COM


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)



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)


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


(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