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
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 =
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m13 (variables A, B, C, D with A the most significant bit).

m13
  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
3.Medium
ABC00011110010011031214051716

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C) = Σm(1, 2, 4, 6, 7). How many sum terms (factors) N does it have?

F(A, B, C) = Σm(1, 2, 4, 6, 7)
N =
4.Medium
ABCD000111100001111000010312040507161121130151141819011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(2, 6, 8, 9, 12, 13, 14). How many product terms N does it have?

F(A, B, C, D) = Σm(2, 6, 8, 9, 12, 13, 14)
N =
5.Hard
ABCD0001111000011110X0010302X4151706112113015014X819111110

Find the minimal SOP form of F(A, B, C, D) = Σm(5, 7, 9, 10, 11, 12, 13) + d(0, 4, 8), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(5, 7, 9, 10, 11, 12, 13) + d(0, 4, 8)
N =
6.Hard
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​FFQ3​Q3​FFQ4​Q4​CLKMOD-20

A mod-20 counter has to count through 20 different states. What is the minimum number of flip-flops n it needs?

N = 20
n =

Answer key

  1. 1. N = 3
  2. 2. AB = 11, CD = 01
  3. 3. N = 3
  4. 4. N = 3
  5. 5. N = 3
  6. 6. n = 5

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