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
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m10 (variables A, B, C, D with A the most significant bit).

m10
  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
2.Easy
AF

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 NOT function shown?

F = A′
N =
3.Medium
ABCD000111100001111000111312040517061121130150140809011110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(1, 2, 3, 7, 10, 12, 13). How many product terms N does it have?

F(A, B, C, D) = Σm(1, 2, 3, 7, 10, 12, 13)
N =
4.Medium
ABCD000111100001111000010312041507060120131151140819111010

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(2, 5, 9, 11, 14, 15). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(2, 5, 9, 11, 14, 15)
N =
5.Hard
ABCD0001111000011110100103120415X716X12X131150141809111110

For F(A, B, C, D) = Σm(0, 2, 5, 6, 8, 10, 11, 15) + d(7, 12, 13), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 2, 5, 6, 8, 10, 11, 15) + d(7, 12, 13)
N =
6.Hard
ABCD00011110000111100001031214X5X7X61121130150140819011X10

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 4, 9, 12, 13) + d(5, 6, 7, 10), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(2, 4, 9, 12, 13) + d(5, 6, 7, 10)
N =

Answer key

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

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