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 m11 (variables A, B, C, D with A the most significant bit).

m11
  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
ABCF000?001?010?011?100?101?110?111?

The function F = (A′·B)′ + (A′·C′) is 0 for exactly one combination of the inputs. Click that row of the truth table.

F = (A′·B)′ + (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
3.Medium
MUX1I0​0I1​0I2​1I3​ABS1​S0​F

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

I₀ = 1I₁ = 0I₂ = 0I₃ = 1
N =
4.Medium
ABCD000111100001111000011312141507061120131151141819011110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(2, 3, 4, 5, 8, 9, 10, 12, 14, 15). How many product terms N does it have?

F(A, B, C, D) = Σm(2, 3, 4, 5, 8, 9, 10, 12, 14, 15)
N =
5.Hard
ABCD0001111000011110X001031204051716012X1311511418X9111X10

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 6, 7, 8, 11, 14, 15) + d(0, 9, 10, 13), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(2, 6, 7, 8, 11, 14, 15) + d(0, 9, 10, 13)
L =
6.Hard
ABCD0001111000011110X011X312041517X6X12113115X140809011010

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 2, 5, 7, 13, 15) + d(0, 3, 6, 12, 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, 5, 7, 13, 15) + d(0, 3, 6, 12, 14)
N =

Answer key

  1. 1. AB = 10, CD = 11
  2. 2. ABC = 011
  3. 3. N = 4
  4. 4. N = 5
  5. 5. L = 6
  6. 6. N = 2

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