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
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 NAND gates needed to build the NOR function shown?

F = (A + B)′
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 NAND gates needed to build the XNOR function shown?

F = (A ⊕ B)′
N =
3.Medium
ABCD000111100001111000110312040507160121130150140819111110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(1, 2, 6, 9, 10, 11, 13). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(1, 2, 6, 9, 10, 11, 13)
N =
4.Medium
ABCD000111100001111000110312141517160120131150141809011110

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(1, 2, 4, 5, 6, 7, 8, 10, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(1, 2, 4, 5, 6, 7, 8, 10, 15)
L =
5.Hard
ABCD0001111000011110X0X11312140507X61120131150140809111010

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 3, 4, 11, 12, 15) + d(0, 1, 6), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(2, 3, 4, 11, 12, 15) + d(0, 1, 6)
N =
6.Hard
CLKJK1234567

A positive-edge-triggered JK 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 = 0JK
  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

Answer key

  1. 1. N = 4
  2. 2. N = 5
  3. 3. N = 4
  4. 4. L = 14
  5. 5. N = 3
  6. 6. clock edge 4

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