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
ABCF000?001?010?011?100?101?110?111?

The function F = (B ⊕ C)·(A′ + C′)′ is 1 for exactly one combination of the inputs. Click that row of the truth table.

F = (B ⊕ C)·(A′ + C′)′
  1. 1ABC = 000
  2. 2ABC = 001
  3. 3ABC = 010
  4. 4ABC = 011
  5. 5ABC = 100
  6. 6ABC = 101
  7. 7ABC = 110
  8. 8ABC = 111
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
ABC00011110011011031214051706

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 1, 2, 4, 7). How many product terms N does it have?

F(A, B, C) = Σm(0, 1, 2, 4, 7)
N =
4.Medium
ABCD00011110000111101111

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, 3, 7, 8)
  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
ABCD00011110000111101011031204151706012X13X150140819X11010

For F(A, B, C, D) = Σm(0, 1, 2, 5, 7, 9) + d(11, 13, 15), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 1, 2, 5, 7, 9) + d(11, 13, 15)
N =
6.Hard
CLKD1234567

A positive-edge-triggered D flip-flop starts with Q = 0 and receives the inputs shown at 7 rising clock edges. How many times N does Q change state?

Q₀ = 0D
N =

Answer key

  1. 1. ABC = 101
  2. 2. N = 4
  3. 3. N = 4
  4. 4. AB = 10, CD = 00
  5. 5. N = 2
  6. 6. N = 4

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