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
A = 0B = 1C = 1N1G1G2G3F

The inputs of the logic circuit are A = 0, B = 1 and C = 1. Exactly one of its gates has the output 1. Click that gate.

A = 0B = 1C = 1
  1. 1N1
  2. 2G1
  3. 3G2
  4. 4G3
2.Easy
ABCF000?001?010?011?100?101?110?111?

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

F = ((B·C)′ + A)′
  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
ABCD000111100001111011111

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(3, 4, 5, 8, 12)
  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
ABCD000111100001111000111312141507061121131151141819111110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15)
N =
5.Hard
ABCD000111100001111000X1130204150716012113115X1418X9011110

Find the minimal SOP form of F(A, B, C, D) = Σm(3, 5, 6, 8, 10, 13, 15) + d(1, 9, 14), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(3, 5, 6, 8, 10, 13, 15) + d(1, 9, 14)
L =
6.Hard
ABCD0001111000011110000103X20405X7061120131150140819111010

For F(A, B, C, D) = Σm(9, 11, 12, 15) + d(2, 7), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(9, 11, 12, 15) + d(2, 7)
N =

Answer key

  1. 1. G3
  2. 2. ABC = 011
  3. 3. AB = 00, CD = 11
  4. 4. N = 2
  5. 5. L = 14
  6. 6. N = 2

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