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 = 0B = 0C = 0G1N1G2G3F

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

A = 0B = 0C = 0
  1. 1N1
  2. 2G1
  3. 3G2
  4. 4G3
2.Easy
ABCN1: 2 nsN2: 3 nsG18 nsN3: 2 nsG22 nsG38 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: 3 nsN3: 2 nsG1: 8 nsG2: 2 nsG3: 8 ns
tpd = ns
3.Medium
ABC000111100101324576

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

F = A′C′ + A′B′C′ + B′C + AB′
L =
4.Medium
ABCD000111100001111000010312140507160120131151141819011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(2, 4, 6, 8, 9, 14, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(2, 4, 6, 8, 9, 14, 15)
L =
5.Hard
ABCD000111100001111010X10302041517060121131150140809X11010

For F(A, B, C, D) = Σm(0, 5, 7, 13, 15) + d(1, 11), where d marks the don't-care conditions, find the number N of essential prime implicants.

F(A, B, C, D) = Σm(0, 5, 7, 13, 15) + d(1, 11)
N =
6.Hard
ABCD00011110000111101001131214X51706112113015114X809111110

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 2, 3, 4, 7, 10, 11, 12, 13, 14) + d(5, 8), where d marks the don't-care conditions. How many product terms N does it have?

F(A, B, C, D) = Σm(0, 2, 3, 4, 7, 10, 11, 12, 13, 14) + d(5, 8)
N =

Answer key

  1. 1. G2
  2. 2. tpd = 19 ns
  3. 3. L = 3
  4. 4. L = 12
  5. 5. N = 2
  6. 6. N = 5

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