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
ABCN1: 2 nsG14 nsG25 nsG36 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: 2 nsG1: 4 nsG2: 5 nsG3: 6 ns
tpd = ns
2.Easy
A = 1B = 1C = 1G1G2G3F

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

A = 1B = 1C = 1
  1. 1G1
  2. 2G2
  3. 3G3
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(0, 1, 7, 12, 15)
  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
MUX1I0​1I1​0I2​C′I3​ABS1​S0​F

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = 1, I₁ = 1, I₂ = 0, I₃ = C′. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = 1I₁ = 1I₂ = 0I₃ = C′
N =
5.Hard
ABCD00011110000111100011031204X5X706012113015114X809X11010

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 2, 13, 14) + d(5, 7, 8, 11), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(1, 2, 13, 14) + d(5, 7, 8, 11)
L =
6.Hard
CLKJK1234567

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
  7. 7clock edge 7

Answer key

  1. 1. tpd = 12 ns
  2. 2. G2
  3. 3. AB = 11, CD = 00
  4. 4. N = 5
  5. 5. L = 14
  6. 6. clock edge 6

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