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 = 0G1N1G2G3F

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

A = 0B = 1C = 0
  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 NOR gates needed to build the NAND function shown?

F = (A·B)′
N =
3.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, 5, 6, 8, 9, 11, 14)
  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
ABC00011110010011131214050706

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C) = Σm(1, 2, 3, 4). How many sum terms (factors) N does it have?

F(A, B, C) = Σm(1, 2, 3, 4)
N =
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
ABCD0001111000011110X01113121405X7161120131150140809111X10

For F(A, B, C, D) = Σm(1, 2, 3, 4, 6, 11, 12, 15) + d(0, 7, 10), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(1, 2, 3, 4, 6, 11, 12, 15) + d(0, 7, 10)
N =

Answer key

  1. 1. N1
  2. 2. N = 4
  3. 3. AB = 01, CD = 01
  4. 4. N = 3
  5. 5. N = 2
  6. 6. N = 3

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