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 OR function shown?

F = A + B
N =
2.Easy
ABCD0001111000011110

Click the cell of the 4-variable Karnaugh map that belongs to minterm m14 (variables A, B, C, D with A the most significant bit).

m14
  1. 1AB = 00, CD = 00
  2. 2AB = 00, CD = 01
  3. 3AB = 00, CD = 11
  4. 4AB = 00, CD = 10
  5. 5AB = 01, CD = 00
  6. 6AB = 01, CD = 01
  7. 7AB = 01, CD = 11
  8. 8AB = 01, CD = 10
  9. 9AB = 11, CD = 00
  10. 10AB = 11, CD = 01
  11. 11AB = 11, CD = 11
  12. 12AB = 11, CD = 10
  13. 13AB = 10, CD = 00
  14. 14AB = 10, CD = 01
  15. 15AB = 10, CD = 11
  16. 16AB = 10, CD = 10
3.Medium
MUX0I0​1I1​CI2​1I3​ABS1​S0​F

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = 0, I₁ = 1, I₂ = C, I₃ = 1. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = 0I₁ = 1I₂ = CI₃ = 1
N =
4.Medium
ABC00011110010011131214051706

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(1, 2, 3, 4, 7). How many product terms N does it have?

F(A, B, C) = Σm(1, 2, 3, 4, 7)
N =
5.Hard
ABCD0001111000011110X01103X2X41507160121131151141819011110

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 5, 6, 8, 9, 10, 13, 14, 15) + d(0, 2, 4), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(1, 5, 6, 8, 9, 10, 13, 14, 15) + d(0, 2, 4)
L =
6.Hard
TQ0​Q0​TQ1​Q1​TQ2​Q2​TQ3​Q3​CLKMOD-12

A synchronous mod-12 counter counts 0, 1, …, 11 and then returns to 0. It starts at 1. Which count Q (in decimal) does it show after 34 clock pulses?

Q0 = 134N = 12
Q =

Answer key

  1. 1. N = 3
  2. 2. AB = 11, CD = 10
  3. 3. N = 5
  4. 4. N = 4
  5. 5. L = 9
  6. 6. Q = 11

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