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
ABCN1G1N2N3G2G3F

For the logic circuit shown, how many of the 8 combinations of the inputs A, B and C give the output F = 1? Find N.

A, B, C → F
N =
2.Easy
ABCN1: 2 nsN2: 1 nsG15 nsN3: 1 nsG26 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 nsN2: 1 nsN3: 1 nsG1: 5 nsG2: 6 nsG3: 6 ns
tpd = ns
3.Medium
ABC000111100101324576

Simplify F = AB′C + A′B′C + A′B′C′ to its minimal sum-of-products form. How many literals L does the simplified expression contain?

F = AB′C + A′B′C + A′B′C′
L =
4.Medium
ABCD00011110000111101111111111

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, 5, 6, 8, 9, 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
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
DQ0​Q0​DQ1​Q1​DQ2​Q2​CLKRING

A ring counter is made of 3 D flip-flops with the last output fed back to the first input, and starts with a single 1. How many different states N does it go through?

n = 3
N =

Answer key

  1. 1. N = 6
  2. 2. tpd = 13 ns
  3. 3. L = 4
  4. 4. AB = 11, CD = 11
  5. 5. N = 5
  6. 6. N = 3

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