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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Name: ____________________   Date: ____________

1.Easy
ABCF000?001?010?011?100?101?110?111?

The function F = ((A·C)·(B ⊕ C′))′ is 0 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
ABCG1G2G3F

For the logic circuit shown, how many of the 8 combinations of the inputs A, B and C give the output F = 1? Find N.

A, B, C → F
N =
3.Medium
ABCD00011110000111101111

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(4, 6, 13, 14)
  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
ABC000111100101324576

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

F = AB′C′ + B′C + ABC′ + 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
ABCD000111100001111010011302X40517161120130150141809111X10

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 3, 6, 7, 8, 11, 12) + d(4, 10), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(0, 3, 6, 7, 8, 11, 12) + d(4, 10)
L =

Answer key

  1. 1. ABC = 111
  2. 2. N = 5
  3. 3. AB = 11, CD = 01
  4. 4. L = 3
  5. 5. clock edge 4
  6. 6. L = 8

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