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
ABCN1G1N2G2G3F

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 =
2.Easy
ABCF000?001?010?011?100?101?110?111?

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

F = ((B + C)′·(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
ABCD000111100001111010010302040517160121131150140819011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 6, 7, 9, 13, 15). How many product terms N does it have?

F(A, B, C, D) = Σm(0, 6, 7, 9, 13, 15)
N =
4.Medium
ABC000111100101324576

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

F = A′BC + AB′C′ + A′B′C + BC
L =
5.Hard
DQ3​Q3​DQ2​Q2​DQ1​Q1​DQ0​Q0​CLKRING

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1100. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 11 clock edges.

Q₃Q₂Q₁Q₀ = 110011
Q =
6.Hard
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​CLKMOD-7

A mod-7 counter is built from the minimum number of flip-flops. How many of the possible states U are never used?

N = 7
U =

Answer key

  1. 1. N = 1
  2. 2. ABC = 000
  3. 3. N = 4
  4. 4. L = 7
  5. 5. Q = 9
  6. 6. U = 1

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