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 = 0N1G1G2F

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

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

NAND and NOR are universal gates: any logic function can be built from one of them alone. What is the minimum number N of 2-input NOR gates needed to build the XNOR function shown?

F = (A ⊕ B)′
N =
3.Medium
ABCD000111100001111010010302140517061121131150141809011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 4, 7, 8, 12, 13, 15). How many product terms N does it have?

F(A, B, C, D) = Σm(0, 4, 7, 8, 12, 13, 15)
N =
4.Medium
MUXCI0​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 = CI₁ = 0I₂ = C′I₃ = 0
N =
5.Hard
CLKT12345678

A positive-edge-triggered T flip-flop starts with Q = 0 and receives the inputs shown. Click the first clock edge at which Q goes from 1 back to 0.

Q₀ = 0T
  1. 1clock edge 1
  2. 2clock edge 2
  3. 3clock edge 3
  4. 4clock edge 4
  5. 5clock edge 5
  6. 6clock edge 6
  7. 7clock edge 7
  8. 8clock edge 8
6.Hard
ABCD00011110000111100011030214151706X1211311511408X9X11010

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 4, 5, 7, 13, 14, 15) + d(9, 11, 12), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(1, 4, 5, 7, 13, 14, 15) + d(9, 11, 12)
L =

Answer key

  1. 1. G2
  2. 2. N = 4
  3. 3. N = 3
  4. 4. N = 2
  5. 5. clock edge 5
  6. 6. L = 8

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