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

F = (A′ + B′ + (B ⊕ 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
ABCN1G1G2G3F

For the logic circuit shown, how many of the 8 combinations of the inputs A, B and C give the output F = 1? Find N.

A, B, C → F
N =
3.Medium
ABCD000111100001111010011302041517161120130151141809111110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 3, 5, 6, 7, 8, 10, 11, 12, 14). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(0, 3, 5, 6, 7, 8, 10, 11, 12, 14)
L =
4.Medium
MUXC′I0​1I1​1I2​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 = 1, 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 = 1I₃ = C
N =
5.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 =
6.Hard
ABCD00011110000111101001130214X507161121131150141819X11110

For F(A, B, C, D) = Σm(0, 3, 4, 6, 8, 9, 10, 12, 13, 15) + d(5, 11), where d marks the don't-care conditions, find the number N of essential prime implicants.

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

Answer key

  1. 1. ABC = 110
  2. 2. N = 6
  3. 3. L = 14
  4. 4. N = 6
  5. 5. N = 3
  6. 6. N = 5

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