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
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 =
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
ABCD000111100001111000011302040517160120131150141819011110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(3, 6, 7, 8, 9, 10, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(3, 6, 7, 8, 9, 10, 15)
L =
4.Medium
ABC00011110011011031204051716

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 1, 2, 6, 7). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C) = Σm(0, 1, 2, 6, 7)
L =
5.Hard
CLKJK123456

A positive-edge-triggered JK flip-flop starts with Q = 0 and receives the inputs shown at 6 rising clock edges. How many times N does Q change state?

Q₀ = 0JK
N =
6.Hard
ABCD0001111000011110000113X2X4051706112013115114X809111010

For F(A, B, C, D) = Σm(3, 7, 11, 12, 14, 15) + d(2, 4, 8), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(3, 7, 11, 12, 14, 15) + d(2, 4, 8)
N =

Answer key

  1. 1. N = 6
  2. 2. N = 4
  3. 3. L = 15
  4. 4. L = 6
  5. 5. N = 3
  6. 6. N = 1

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