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
ABCN1: 2 nsG16 nsN2: 1 nsN3: 2 nsG26 nsG34 nsF

The propagation delay of every gate is written under it. Find the worst-case propagation delay tpd from the inputs to the output F.

N1: 2 nsN2: 1 nsN3: 2 nsG1: 6 nsG2: 6 nsG3: 4 ns
tpd = ns
2.Easy
ABC0001111001

Click the cell of the 3-variable Karnaugh map that belongs to minterm m2 (variables A, B, C with A the most significant bit).

m2
  1. 1A = 0, BC = 00
  2. 2A = 0, BC = 01
  3. 3A = 0, BC = 11
  4. 4A = 0, BC = 10
  5. 5A = 1, BC = 00
  6. 6A = 1, BC = 01
  7. 7A = 1, BC = 11
  8. 8A = 1, BC = 10
3.Medium
ABC00011110011001130214051706

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 3, 4, 7). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C) = Σm(0, 3, 4, 7)
L =
4.Medium
ABCD000111100001111010110302040517161120131150141809011010

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 1, 6, 7, 8, 12, 15). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(0, 1, 6, 7, 8, 12, 15)
N =
5.Hard
ABCD00011110000111101011130214150716112013015X14X8X9111010

For F(A, B, C, D) = Σm(0, 1, 3, 4, 5, 6, 11, 12) + d(8, 9, 14), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 1, 3, 4, 5, 6, 11, 12) + d(8, 9, 14)
N =
6.Hard
CLKJK12345678

A positive-edge-triggered JK flip-flop starts with Q = 0 and receives the inputs shown at 8 rising clock edges. How many times N does Q change state?

Q₀ = 0JK
N =

Answer key

  1. 1. tpd = 12 ns
  2. 2. A = 0, BC = 10
  3. 3. L = 4
  4. 4. N = 4
  5. 5. N = 3
  6. 6. N = 2

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