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
ABCN1: 1 nsG18 nsN2: 2 nsG23 nsG34 nsF

The propagation delay of every gate is written under it. Find the worst-case propagation delay tpd from the inputs to the output F.

N1: 1 nsN2: 2 nsG1: 8 nsG2: 3 nsG3: 4 ns
tpd = ns
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m15 (variables A, B, C, D with A the most significant bit).

m15
  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
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, 6, 7, 9, 10)
  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
ABC000111100101324576

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

F = B′C + A′C′ + A′BC′ + A′B′
L =
5.Hard
DQ0​Q0​DQ1​Q1​DQ2​Q2​CLKJOHNSON

A Johnson (twisted-ring) counter is made of 3 D flip-flops, with the inverted last output fed back to the first input, and starts at all zeros. How many different states N does it go through?

n = 3
N =
6.Hard
ABCD00011110000111100001131214050706112013X151140809X11110

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 3, 4, 10, 12, 14) + d(11, 15), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(2, 3, 4, 10, 12, 14) + d(11, 15)
N =

Answer key

  1. 1. tpd = 13 ns
  2. 2. AB = 11, CD = 11
  3. 3. AB = 10, CD = 10
  4. 4. L = 4
  5. 5. N = 6
  6. 6. N = 3

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