Question Bank Digital Electronics

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  10EC33: DIGITAL ELECTRONICS Faculty: Dr.Bajarangbali QUESTION BANK E –  Examination QuestionS 1. Discuss canonical & standard forms of Boolean functions with an example. 2. Convert the following Boolean function F=xy+x 1 z to product of Maxterm. 3. Bring out the difference between Canonical & Standard forms. 4. Minimize the following using Kmaps: i) SOP expression given by f(A,B,C,D) = Σ  m(0,1,2,3,5,9,14,15) + Σ   Φ(4,8,11,12)  ii) POS expression given by f(A,B,C,D) =  M(0,1,2,5,8,9,10) Implement the minimal expressions thus obtained using basic gates (both normal and inverted inputs can be used) 5. List out the difference between combinational and sequential logic circuits 6. Convert the following to other canonical form. i) F(x,y,z) =  (1,3,7) ii) F(A,B,C,D)=  (0,2,6,11,13,14) iii) F(x,y,z) =  (0,1,2,3,4,6,12) 7. Expand the following function into canonical SOP form f(x1,x2,x3) = x 1 x 3 + x 2 x 3  + x 1 x 2 x 3  8. Expand the following function into canonical POS form F(W,X,Q) =(Q+W 1 ) (X+Q 1 ) (W+X+Q) (W 1 +X 1 ) 9. Mention different methods of simplifying Boolean functions. 10. Place the following equations into the proper canonical form a) P = f(a,b,c) = ab 1 +ac 1 +bc b) G = f(w,x,y,z) = wx 1  + yz 1 c) T = f(a,b,c) = (a+b 1 )(b 1 +c 1 ) 11. Express the following SOP equations in a minterm list (Short hand decimal notation) form: a) H = f(A,B,C) = A 1 BC + A 1 B 1 C + ABC b) G = f(W,X,Y,Z) = WXYZ 1  + WX 1 YZ 1  + W 1 XYZ 1  + W 1 X 1 YZ 1 12. Express the following POS equations in a maxterm list (decimal notation)   form:   a) T = f(a,b,c) = (a+b 1 +c) (a+b 1 +c 1 ) (a 1 +b 1 +c) 13. Simplify the following a) J = f(x,y,z) = ∑(0,2,3,4,5,7)   b) K = f(w,x,y,z) = ∑(0,1,4,5,9,11,13,15)   c) R = f(v,w,x,y,z) = ∑(5,7,13,15,21,23,29,31)  14. Draw a model representing combinational circuits. Label the input and output variables. Write a general expression showing the input and output relationship. 15. How does a “truth table” express a combinational circuit.  16. Convert the following equations into their requested canonical forms: a) (SOP) X = a 1 b+bc b) (POS) P = (w 1 +x)(y+z 1 ) c) (SOP) T = p(q 1 +s) d) (SOP) R = L+M 1 (N 1 M+M 1 L) e) (POS) U = r 1 +s(t+r)+s 1 t E. a) Two motors M2 and M1 are controlled by three sensors S3, S2 and S1. One motor M2 is to run any time all three sensors are on. The other motor is to run whenever sensors S2 or S1 but not both are on and S3 if off. For all sensor combinations where M1 is on, M2 is to be off except when all the three sensors are off and then both motors must remain off. Construct the truth and write the Boolean output equation. (6) (Jan.08) b) Simplify using Karnaugh map. Write the Boolean equation and realize using NAND gates. D = f(w,x,y,z) =  (0,2,4,6,8)+  d(10,11,12,13,14,15). (6) c) Simplify P = f(a,b,c) =  (0,1,4,5,7) using two variable Karnaugh map. Write the Boolean equation and realize using logic gates. (8) d) Simplify using Karnaugh map L = f(a,b,c,d) =  (2,3,4,6,7,10,11,12) (6) 17. Discuss K-map & Quine McCluskey methods for simplification of Boolean expressions. 18. Discuss K-map & Quine McCluskey methods. 19. Write advantages of K-map over Quine McCluskey method. 20. Define term Don’t care condition.  21. Explain K-map representation in detail & discuss the merits & demerits . 22. Explain the tabulation procedure in detail & discuss merits & demerits. 23. Compare K-map & Quine-Mcclusky methods for simplification of Boolean Expression.  24. Obtain the simplified expression in sum of products for the following: F(A,B,C,D,E) =  (0,1,4,5,16,17,21,25,29) 25. Obtain simplified expression in SOP & POS form i) x1z1+y1z1+yz1+xyz ii) w1yz1+vw1z1+vw1x+v1wz+v1w1y1z1 and draw gate implementation using AND & OR gates 26. Given the function T(w,x,y,z)=Σ(1,3,4,5,7,8,9,11,14,15).Use K map to determine the set of all prime implicants. Indicate essential prime implicants, find three distinct mininmal expressions for T 27. Using tabulation method, determine the set of all prime implicants for the function f(w,x,y,z) = Σ(0,1,2,5,7,8,9,10,13,15) and hence obtain the minimal form of given function, employing decimal notation. 28. Compare K-map & Quine-Mcclusky methods for simplification of Boolean Expression. Give their merits and demerits 29. Using K-map simplify following Boolean expression & give implementation of same using i) NAND gates only ii) AND,OR & Invert gates for F(A,B,C,D) =  (2,4,8,16,31)+  D (0,3,9,12,15,18) 30. Using K-map obtain Simplified expression in SOP & POS form of function F(A,B,C,D)=(A 1 +B 1 +C 1 +D 1 )(A 1 +B 1 +C+D 1 )(A+B 1 +C+D 1 )(A+B+C+D 1 )(A+B+C+D) 31. Simplify Boolean function using don’t care condition for SOP & POS  F=w1(x1y+x1y1+xyz)+x1z1(Y+w), d=w1x(y1z+yz1)+wyz F=ACE+A 1 CD 1 E 1 +A 1 C 1 DE, d= DE 1 +A 1 D 1 E+AD 1 E 1 32. Simplify the following Boolean function using K-map method i) xy+x 1 y 1 z 1 +x 1 yz 1  ii) x 1 yz+xy 1 z+xyz+xyz 1  iii)F=A 1 C+A 1 B+AB 1 C+BC iv)f (w,x,y,z)=  (0,1,2,4,5,6,8,9,12,13,14) 33. Determine set of Prime implicants for function F(w,x,y,z)=  (0,1,2,5,7,8,9,10,13,15) 34. Minimize the following function with don’t care terms using Q.M. method  i) f(A,B,C,D)=  m(5,7,11,12,27,29)+d(14,20,21,22,23) ii) f(A,B,C,D)=  m(1,4,6,9,14,17,22,27,28,)+d(12,15,20,30,31) 35. Determine the set of Prime implicants for function F(w,x,y,z)=  (0,1,2,5,7,8,9,10,13,15) 36. Using Quine-McCluskey obtain the set of Prime implicants for function   F(a,b,c,d,e)=  (4,12,13,14,16,19,22,24,25,26,29,30)+  d (1,3,5,20,27) 37. Identify the prime and essential prime implicants for the following expressions a) S = f(a,b,c,d) = ∑(1,5,7,8,9,10,11,13,15)   b) T = f(a,b,c,d,e) = ∑(0,4,8,9,10,11,12,13,14,15,16,20,24,28)  38. Simplify the SOP equations given below. Let the MEV term be the least significant variable in each expression. a) Construct the MEV truth table b) Create the MEV K-map c) Write the simplified equations d) Is the trial expression optimal (compare it to a regular K-map simplified expression) (i) V = f(a,b,c,d) = ∑(2,3,4,5,13,15) + ∑d(8,9,10,11)   (ii) Y = f(u,v,w,x) = ∑(1,5,7,9,13,15) + ∑d(8,10,11,14)  (iii) P = f(r,s,t,u) = ∑(0,2,4,8,10,14) + ∑d(5,6,7,12)   (iv) F = f(u,v,w,x,y) = ∑(0,2,8,10,16,18,24,26)  E. a) Simplify using Quine Mc Clusky tabulation algorithm- (14) V = f(a,b,c,d) =  (2,3,4,5,13,15)+  d(8,9,10,11) 39. Define combinational circuit with block diagram, Explain the elements of combinational circuit. 40. Discuss the full adder with an example. 41. Discuss the Half adder with an example. 42. Given 3x8 decoder , show the construction of 4x16 decoder. 43. Explain grouping and simplification process in K maps using the 3 variable and 4 variable maps. 44. Give the main steps for designing combinational circuits. 45. What is decoder? what are its advantages? Design a decimal decoder which converts information from BCD to DECIMAL. 46. Mention the difference between full and half adder. 47. Design BCD to 7 segment decoder using NAND gates only. 48. Mention the application of decoder. 49. Using decoder implement the following Logic functions. a) Active High decoder with OR gate. b) Active Low decoder with NAND gate. c) Active High decoder with NOR gate.
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