Digital logic: gates, K-maps & flip-flops worksheet with answers

Free printable Digital logic: gates, K-maps & flip-flops worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m7 (variables A, B, C, D with A the most significant bit).

m7
  1. 1AB = 00, CD = 00
  2. 2AB = 00, CD = 01
  3. 3AB = 00, CD = 11
  4. 4AB = 00, CD = 10
  5. 5AB = 01, CD = 00
  6. 6AB = 01, CD = 01
  7. 7AB = 01, CD = 11
  8. 8AB = 01, CD = 10
  9. 9AB = 11, CD = 00
  10. 10AB = 11, CD = 01
  11. 11AB = 11, CD = 11
  12. 12AB = 11, CD = 10
  13. 13AB = 10, CD = 00
  14. 14AB = 10, CD = 01
  15. 15AB = 10, CD = 11
  16. 16AB = 10, CD = 10
2.Easy
ABCG15 nsN1: 3 nsG28 nsF

The propagation delay of every gate is written under it. Find the worst-case propagation delay tpd from the inputs to the output F.

N1: 3 nsG1: 5 nsG2: 8 ns
tpd = ns
3.Medium
ABCD000111100001111010110302140507161121131151140819011110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 1, 4, 6, 9, 10, 12, 13, 14, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(0, 1, 4, 6, 9, 10, 12, 13, 14, 15)
L =
4.Medium
ABCD000111100001111000111302041507161120131150140819111010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(1, 3, 5, 6, 9, 11, 12, 15). How many product terms N does it have?

F(A, B, C, D) = Σm(1, 3, 5, 6, 9, 11, 12, 15)
N =
5.Hard
ABCD000111100001111000011312X4150716112X13115114X809111010

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 3, 5, 6, 11, 12, 14, 15) + d(4, 8, 13), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(2, 3, 5, 6, 11, 12, 14, 15) + d(4, 8, 13)
N =
6.Hard
ABCD00011110000111101011031204X507X6012013X15014X809111010

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 1, 2, 11) + d(5, 6, 8, 15), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(0, 1, 2, 11) + d(5, 6, 8, 15)
L =

Answer key

  1. 1. AB = 01, CD = 11
  2. 2. tpd = 13 ns
  3. 3. L = 13
  4. 4. N = 5
  5. 5. N = 4
  6. 6. L = 9

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