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 = 1B = 0C = 0N1G1N2G2G3F

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

A = 1B = 0C = 0
  1. 1N1
  2. 2N2
  3. 3G1
  4. 4G2
  5. 5G3
2.Easy
ABCG1G2G3F

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 =
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, 4, 8, 9, 11, 12, 13)
  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
ABCD000111100001111010010302141517060121130150140819011110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 4, 5, 7, 9, 10, 13). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(0, 4, 5, 7, 9, 10, 13)
N =
5.Hard
ABCD00011110000111101001131204151716X12113115X140809111X10

For F(A, B, C, D) = Σm(0, 2, 3, 5, 6, 7, 11, 13, 15) + d(10, 12, 14), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 2, 3, 5, 6, 7, 11, 13, 15) + d(10, 12, 14)
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 8. Which count Q (in decimal) does it show after 38 clock pulses?

Q0 = 838N = 12
Q =

Answer key

  1. 1. N1
  2. 2. N = 2
  3. 3. AB = 00, CD = 10
  4. 4. N = 5
  5. 5. N = 3
  6. 6. Q = 10

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