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 = 1B = 0C = 1G1G2G3F

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

A = 1B = 0C = 1
  1. 1G1
  2. 2G2
  3. 3G3
2.Easy
ABCN1: 3 nsN2: 2 nsG12 nsN3: 3 nsG28 nsG35 nsF

The propagation delay of every gate is written under it. Find the worst-case propagation delay tpd from the inputs to the output F.

N1: 3 nsN2: 2 nsN3: 3 nsG1: 2 nsG2: 8 nsG3: 5 ns
tpd = ns
3.Medium
ABCD00011110000111101111111

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, 2, 3, 4, 6, 8, 11)
  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
ABC00011110010001131214151716

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(2, 3, 4, 5, 6, 7). How many product terms N does it have?

F(A, B, C) = Σm(2, 3, 4, 5, 6, 7)
N =
5.Hard
CLKJK123456

A positive-edge-triggered JK flip-flop starts with Q = 0 and receives the inputs shown at 6 rising clock edges. How many times N does Q change state?

Q₀ = 0JK
N =
6.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 =

Answer key

  1. 1. G2
  2. 2. tpd = 16 ns
  3. 3. AB = 10, CD = 00
  4. 4. N = 2
  5. 5. N = 4
  6. 6. N = 2

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