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 = 0C = 1N1G1G2G3F

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

A = 0B = 0C = 1
  1. 1N1
  2. 2G1
  3. 3G2
  4. 4G3
2.Easy
BAF

NAND and NOR are universal gates: any logic function can be built from one of them alone. What is the minimum number N of 2-input NAND gates needed to build the OR function shown?

F = A + B
N =
3.Medium
ABC00011110010011031204151716

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(1, 2, 5, 6, 7). How many product terms N does it have?

F(A, B, C) = Σm(1, 2, 5, 6, 7)
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(1, 2, 6, 7, 8, 12)
  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
ABCD00011110000111100001130214051706X1211301511418X9011010

For F(A, B, C, D) = Σm(3, 4, 7, 8, 13, 14) + d(9, 12), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(3, 4, 7, 8, 13, 14) + d(9, 12)
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. N = 3
  3. 3. N = 3
  4. 4. AB = 00, CD = 01
  5. 5. N = 4
  6. 6. N = 4

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