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

F = (B + C′)′ + A + B
  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
BAF

NAND and NOR are universal gates: any logic function can be built from one of them alone. What is the minimum number N of 2-input NOR gates needed to build the XOR function shown?

F = A ⊕ B
N =
3.Medium
ABC000111100101324576

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

F = AB′C + AB′C′ + B′C
L =
4.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(1, 5, 11, 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
5.Hard
CLKJK1234567

A positive-edge-triggered JK flip-flop starts with Q = 0 and receives the inputs shown at 7 rising clock edges. How many times N does Q change state?

Q₀ = 0JK
N =
6.Hard
ABCD000111100001111000010302X4050716X121131151141809111010

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

F(A, B, C, D) = Σm(6, 8, 11, 13, 14, 15) + d(4, 12)
L =

Answer key

  1. 1. ABC = 000
  2. 2. N = 5
  3. 3. L = 4
  4. 4. AB = 10, CD = 11
  5. 5. N = 4
  6. 6. L = 10

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