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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Name: ____________________   Date: ____________

1.Easy
ABCF000?001?010?011?100?101?110?111?

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

F = (A′ + C)′·(A·B)
  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
A = 0B = 0C = 0G1G2G3F

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

A = 0B = 0C = 0
  1. 1G1
  2. 2G2
  3. 3G3
3.Medium
MUXC′I0​1I1​CI2​CI3​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 = 1, I₂ = C, I₃ = C. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = C′I₁ = 1I₂ = CI₃ = C
N =
4.Medium
MUXC′I0​0I1​C′I2​0I3​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 = C′, I₃ = 0. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = C′I₁ = 0I₂ = C′I₃ = 0
N =
5.Hard
ABCD000111100001111010110302041517X6012013X151140809111X10

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 1, 5, 7, 11, 14) + d(6, 10, 15), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(0, 1, 5, 7, 11, 14) + d(6, 10, 15)
N =
6.Hard
ABCD0001111000011110X011X302040507X61120131150141809011X10

For F(A, B, C, D) = Σm(1, 8, 12, 15) + d(0, 3, 6, 10), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(1, 8, 12, 15) + d(0, 3, 6, 10)
N =

Answer key

  1. 1. ABC = 110
  2. 2. G1
  3. 3. N = 5
  4. 4. N = 2
  5. 5. N = 3
  6. 6. N = 2

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