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 m12 (variables A, B, C, D with A the most significant bit).

m12
  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
ABCF000?001?010?011?100?101?110?111?

The function F = ((A′ + B′)′·C′)′ is 0 for exactly one combination of the inputs. Click that row of the truth table.

F = ((A′ + 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
3.Medium
ABCD000111100001111000110312140507160121131151140819111010

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(1, 2, 4, 6, 9, 11, 13, 14, 15). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(1, 2, 4, 6, 9, 11, 13, 14, 15)
N =
4.Medium
ABC000111100101324576

Simplify F = BC + AB′C + A′B′C′ + A′B′ to its minimal sum-of-products form. How many literals L does the simplified expression contain?

F = BC + AB′C + A′B′C′ + A′B′
L =
5.Hard
CLKD1234567

A positive-edge-triggered D flip-flop starts with Q = 0 and receives the inputs shown. Click the first clock edge at which Q goes from 1 back to 0.

Q₀ = 0D
  1. 1clock edge 1
  2. 2clock edge 2
  3. 3clock edge 3
  4. 4clock edge 4
  5. 5clock edge 5
  6. 6clock edge 6
  7. 7clock edge 7
6.Hard
ABCD000111100001111010110302040517X601201311511408X9111110

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 1, 7, 10, 11, 14, 15) + d(6, 9), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(0, 1, 7, 10, 11, 14, 15) + d(6, 9)
L =

Answer key

  1. 1. AB = 11, CD = 00
  2. 2. ABC = 110
  3. 3. N = 5
  4. 4. L = 3
  5. 5. clock edge 4
  6. 6. L = 7

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