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
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 =
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m1 (variables A, B, C, D with A the most significant bit).

m1
  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
ABC00011110011001130214051716

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 3, 4, 6, 7). How many product terms N does it have?

F(A, B, C) = Σm(0, 3, 4, 6, 7)
N =
4.Medium
ABCD000111100001111000011302040507060120130150141809111010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(3, 8, 11). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(3, 8, 11)
L =
5.Hard
CLKJK123456

A positive-edge-triggered JK 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 = 0JK
  1. 1clock edge 1
  2. 2clock edge 2
  3. 3clock edge 3
  4. 4clock edge 4
  5. 5clock edge 5
  6. 6clock edge 6
6.Hard
CLKD123456

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

Answer key

  1. 1. N = 5
  2. 2. AB = 00, CD = 01
  3. 3. N = 3
  4. 4. L = 7
  5. 5. clock edge 3
  6. 6. clock edge 5

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