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 = 1N1G1G2F

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

A = 1B = 1C = 1
  1. 1N1
  2. 2G1
  3. 3G2
2.Easy
A = 0B = 0C = 1G1G2G3F

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

A = 0B = 0C = 1
  1. 1G1
  2. 2G2
  3. 3G3
3.Medium
ABC000111100101324576

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

F = A′BC′ + A′B′C + A′B′
L =
4.Medium
ABCD000111100001111010110302041507060120130151140819111110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 1, 5, 9, 10, 11, 14). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(0, 1, 5, 9, 10, 11, 14)
L =
5.Hard
ABCD000111100001111010X1131204X50706X121130151140809111X10

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 2, 3, 11, 13, 14) + d(1, 5, 10, 12), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(0, 2, 3, 11, 13, 14) + d(1, 5, 10, 12)
N =
6.Hard
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​FFQ3​Q3​FFQ4​Q4​CLKMOD-25

A mod-25 counter is built from the minimum number of flip-flops. How many of the possible states U are never used?

N = 25
U =

Answer key

  1. 1. G2
  2. 2. G1
  3. 3. L = 4
  4. 4. L = 12
  5. 5. N = 4
  6. 6. U = 7

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