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
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
ABC000111100101324576

Simplify F = ABC′ + AB′ + AB′C to its minimal sum-of-products form. How many literals L does the simplified expression contain?

F = ABC′ + AB′ + AB′C
L =
4.Medium
ABCD000111100001111011111

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, 4, 6, 7, 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
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​FFQ3​Q3​FFQ4​Q4​FFQ5​Q5​CLKMOD-60

A mod-60 counter is built from the minimum number of flip-flops. How many of the possible states U are never used?

N = 60
U =
6.Hard
ABCD000111100001111000111312X40507X6012X13015X1408X9011110

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 2, 3, 10) + d(4, 6, 9, 13, 14), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(1, 2, 3, 10) + d(4, 6, 9, 13, 14)
N =

Answer key

  1. 1. N = 3
  2. 2. N = 4
  3. 3. L = 4
  4. 4. AB = 00, CD = 01
  5. 5. U = 4
  6. 6. N = 2

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