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 = 0N1G1G2F

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

A = 0B = 1C = 0
  1. 1N1
  2. 2G1
  3. 3G2
2.Easy
ABCG14 nsN1: 2 nsG28 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: 8 nsG3: 6 ns
tpd = ns
3.Medium
ABCD000111100001111010111302041507160120130151140809011010

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 1, 3, 5, 6, 14). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(0, 1, 3, 5, 6, 14)
N =
4.Medium
ABCD0001111000011110111111

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(2, 5, 6, 9, 11, 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
5.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
6.Hard
ABCD0001111000011110001103X2040507161120131150140819X11X10

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 6, 9, 12, 15) + d(2, 10, 11), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(1, 6, 9, 12, 15) + d(2, 10, 11)
N =

Answer key

  1. 1. G2
  2. 2. tpd = 16 ns
  3. 3. N = 5
  4. 4. AB = 01, CD = 01
  5. 5. clock edge 5
  6. 6. N = 4

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