1. EEL-3705 TPS QUIZZES

2. Quiz 2-1

3. Use a Venn Diagram to show

5. Quiz 2-2

6. Prove the following using a Venn Diagram

7. OR

8. Quiz 2-3

9. Use a Venn Diagram to find

10. Use a Venn Diagram to show

11. Quiz 2-4

12. Problem Use a Venn Diagram to show Given Hint: Draw

13. Solution

15. Quiz 2-5

16. Prove the following using Switching Algebra

18. Quiz 2-6

19. Problem Given Use Demorgan’s Thm to find

20. Solution Find Use DeMorgan’s Theorem

21. Quiz 2-7

22. Problem Given Use Demorgan’s Thm to find:

23. Solution Given Find

24. Quiz 2-8

25. Use a Venn Diagram to show

27. Quiz 2-9

28. Problem Use a Truth Table to evaluate

29. Solution ABCF 0001 0010 0101 0110 1001 1010 1101 1111

30. Quiz 2-10

31. Problem Use a Truth Table to evaluate

32. Solution ABCF 0000 0010 0101 0110 1001 1011 1101 1111

33. Quiz 2-11

34. Problem Expand the following function represent F in truth table form

35. Solution

36. ABCF 0001 0011 0100 0110 1000 1010 1100 1111

37. Quiz 2-12

38. Problem Expand the following function represent F in truth table form

39. Solution

40. ABCF 0000 0010 0101 0111 1001 1011 1101 1110

41. Quiz 2-13

42. Problem Expand F into SOP canonical form Re-write F using the minterms notation and in a truth table.

43. Solution Expand F into SOP canonical form

44. Solution Rewrite using minterms ABCF 0001 0010 0101 0110 1001 1010 1101 1111

45. Quiz 2-14

46. Problem Expand F into POS canonical form Re-write F using only Maxterms notation and in a truth table

47. Solution Expand F into POS canonical form

48. Solution Re-write F using Maxterms and TT ABCF 0000 0010 0101 0110 1001 1011 1101 1111

49. Quiz 2-15

50. Problem Simplify F and express using SOP minterms and in a truth table

51. Solution Simplify F and express using SOP minterms and in a truth table

52. Solution Simplify F and express using SOP minterms

53. Solution Simplify F and express using SOP minterms

54. Solution ABCF 0000 0010 0101 0110 1001 1011 1101 1111

55. Quiz 2-16

56. Problem Complete the 2-input Truth Table for the following Basic Logic Gates

57. Solution Complete the 2-input Truth Table for the following Basic Logic Gates ABY 001 010 100 110 Truth Table ABY 000 010 100 111

58. Quiz 2-17

59. Problem Given Use Demorgan’s Thm to show:

60. Solution 0 0

61. Quiz 2-18

62. Problem Given inputs a,b, and c, and using AND, OR, and NOT gates, Design a digital logic circuit that implements How many gates are needed for your design?

63. Solution

64. Quiz 2-19

65. Problem Given inputs a,b, and c, and using only NAND gates, Design a digital logic circuit that implements How many gates are needed for your design?

66. Solution OR AND NOT

67. Solution

68. Quiz 2-20

69. Problem Show that this circuit implements the expression

70. Solution P1

71. Solution ABCF*=(ab)’F=(F*c)’ab+c’ 000111 001100 010111 011100 100111 101100 110011 111011

72. Quiz 2-21

73. Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results

74. Solution P2 P3 P1

75. Solution

76. Verification ABCP2P3FoFs 0000000 0010100 0101111 0111111 1000000 1010100 1100100 1110100

77. Quiz 2-22

78. Problem Find a simplified logic expression and network for this logic circuit? Use a truth table to verify your results

79. Solution P2 P3 P1 P4

80. Solution P2 P3 P1 P4

81. Solution

82. Verification ABCP3P4FoFs 0001011 0011111 0100000 0110111 1000111 1010111 1101111 1111111

83. Solution

84. Quiz 2-22

85. Problem Design a circuit which implements the function y=2x+1. Let x be an unsigned 2- bit input vector. How many bits are needed to represent Y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.

86. Solution X1X0XY 0001 0113 1025 1137 Let’s “precompute” Y. y=2x+1

87. Solution Bits needed for Y Ylow = 1 Yhigh = 7 Since Y is positive, we can use an unsigned binary number for Y. We need n = log 2 (Yhigh+1) = log2(8) = 3 bits to represent Y

88. Solution X1X0XYY2Y1Y0 0001001 0113011 1025101 1137111 Use a three bit unsigned output vector for y. By Inspection:

89. Solution Circuit Simulation

90. Quiz 2-23

91. Problem Design a circuit which implements the function y=2x-1. Let x be an unsigned 2- bit input vector. How bits are needed to represent Y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.

92. Solution X1X0XY 000 0111 1023 1135 Let’s “precompute” Y. y=2x-1

93. Solution Bits needed for Y Ylow = -1 Yhigh = 5 Since Y is negative, we will must use a signed binary number for Y. We need n = 1+log 2 (max(abs(Yhigh),abs(Ylow))+1) = 1+log2(max(5,1)+1)=1+log2(6)=3.58 = 4 bits to represent Y Need the largest in magnitude

94. Solution X1X0YY3Y2Y1Y0 001111 0110001 1030011 1150101 Use a four bit signed output vector for y. By Inspection:

95. Solution Circuit Simulation

96. Quiz 2-24

97. Problem Design a circuit which implements the function y=2x-1. Let x be a signed 2-bit input vector. What is the range of y? Use a truth table to represent y. Design a logic circuit to implement the simplified logic expression for y.

98. Solution X1X0XY 000 0111 10-2-5 11-3 Let’s “precompute” Y. y=2x-1

99. Solution Bits needed for Y Ylow = -5 Yhigh = 1 Since Y is negative, we will must use a signed binary number for Y. We need 1+ log 2 (max(abs(Yhigh),abs(Ylow))+1) = 1+log2(6)=3.58 = 4 bits to represent Y Need the largest in magnitude

100. Solution X1X0XYY3Y2Y1Y0 0001111 01110001 10-2-51011 11-31101 Use a three bit unsigned output vector for y. By Inspection:

101. Quiz 2-25

102. Problem Design a circuit which accepts a three bit input vector x and produces a ‘1’ if the majority of the inputs bits are a ‘1’. That is, F=1, if number of ‘1’s’ in x is greater than number of ‘0’s’ in x. Simplify the function prior to its implementation

103. Solution X2X1X0F 0000 0010 0100 0111 1000 1011 1101 1111 Truth Table

104. Solution