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
ABCF000?001?010?011?100?101?110?111?

The function F = (A·C)′·(B′ + C′)′ is 1 for exactly one combination of the inputs. Click that row of the truth table.

F = (A·C)′·(B′ + C′)′
  1. 1ABC = 000
  2. 2ABC = 001
  3. 3ABC = 010
  4. 4ABC = 011
  5. 5ABC = 100
  6. 6ABC = 101
  7. 7ABC = 110
  8. 8ABC = 111
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m15 (variables A, B, C, D with A the most significant bit).

m15
  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
3.Medium
ABCD00011110000111101111111

In this Karnaugh map exactly one 1 has no neighbouring 1, so it stays a group of one cell (a full minterm of four literals) in the minimal SOP form. Neighbours across the map edges count. Click that cell.

F = Σm(1, 2, 8, 10, 11, 12, 13)
  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
4.Medium
ABCD000111100001111000010302140507060121130150140819011110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(4, 9, 10, 13). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(4, 9, 10, 13)
N =
5.Hard
ABCD000111100001111000X1031204X51716112013015X140819111010

For F(A, B, C, D) = Σm(2, 6, 7, 9, 11, 12) + d(1, 5, 14), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(2, 6, 7, 9, 11, 12) + d(1, 5, 14)
N =
6.Hard
ABCD000111100001111000011302X4150716112X130150140809011110

Find the minimal SOP form of F(A, B, C, D) = Σm(3, 5, 6, 10, 12) + d(4, 13), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(3, 5, 6, 10, 12) + d(4, 13)
N =

Answer key

  1. 1. ABC = 011
  2. 2. AB = 11, CD = 11
  3. 3. AB = 00, CD = 01
  4. 4. N = 5
  5. 5. N = 3
  6. 6. N = 4

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