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 nsG26 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: 6 ns
tpd = ns
2.Easy
ABCF000?001?010?011?100?101?110?111?

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

F = ((B′·C)·(A·C)′)′
  1. 1ABC = 000
  2. 2ABC = 001
  3. 3ABC = 010
  4. 4ABC = 011
  5. 5ABC = 100
  6. 6ABC = 101
  7. 7ABC = 110
  8. 8ABC = 111
3.Medium
ABCD000111100001111000011302140517060121131151141819111110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(3, 4, 7, 8, 9, 10, 11, 13, 14, 15). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(3, 4, 7, 8, 9, 10, 11, 13, 14, 15)
N =
4.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(2, 4, 5, 6, 8, 9, 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
CLKJK12345678

A positive-edge-triggered JK flip-flop starts with Q = 0 and receives the inputs shown at 8 rising clock edges. How many times N does Q change state?

Q₀ = 0JK
N =
6.Hard
TQ0​Q0​TQ1​Q1​TQ2​Q2​TQ3​Q3​CLKMOD-12

A synchronous mod-12 counter counts 0, 1, …, 11 and then returns to 0. It starts at 11. Which count Q (in decimal) does it show after 27 clock pulses?

Q0 = 1127N = 12
Q =

Answer key

  1. 1. tpd = 12 ns
  2. 2. ABC = 001
  3. 3. N = 4
  4. 4. AB = 11, CD = 11
  5. 5. N = 5
  6. 6. Q = 2

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