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
A = 1B = 1C = 0N1G1G2G3F

The inputs of the logic circuit are A = 1, B = 1 and C = 0. Exactly one of its gates has the output 0. Click that gate.

A = 1B = 1C = 0
  1. 1N1
  2. 2G1
  3. 3G2
  4. 4G3
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m0 (variables A, B, C, D with A the most significant bit).

m0
  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
MUXC′I0​0I1​0I2​C′I3​ABS1​S0​F

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = C′, I₁ = 0, I₂ = 0, I₃ = C′. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = C′I₁ = 0I₂ = 0I₃ = C′
N =
4.Medium
ABCD000111100001111000110302140507061120130150140809011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(1, 4, 12). How many product terms N does it have?

F(A, B, C, D) = Σm(1, 4, 12)
N =
5.Hard
ABCD000111100001111010111302X4X50706112113115114X819111110

For F(A, B, C, D) = Σm(0, 1, 3, 9, 10, 11, 12, 13, 14, 15) + d(4, 5, 8), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 1, 3, 9, 10, 11, 12, 13, 14, 15) + d(4, 5, 8)
N =
6.Hard
ABCD00011110000111100001131214150716112113115014X819X11110

For F(A, B, C, D) = Σm(2, 3, 4, 5, 6, 9, 10, 12, 13, 15) + d(8, 11), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(2, 3, 4, 5, 6, 9, 10, 12, 13, 15) + d(8, 11)
N =

Answer key

  1. 1. G1
  2. 2. AB = 00, CD = 00
  3. 3. N = 2
  4. 4. N = 2
  5. 5. N = 3
  6. 6. N = 3

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