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 = 1C = 1N1G1N2G2F

The inputs of the logic circuit are A = 0, B = 1 and C = 1. Exactly one of its gates has the output 0. Click that gate.

A = 0B = 1C = 1
  1. 1N1
  2. 2N2
  3. 3G1
  4. 4G2
2.Easy
ABCN1: 3 nsG16 nsN2: 3 nsG22 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: 3 nsN2: 3 nsG1: 6 nsG2: 2 ns
tpd = ns
3.Medium
MUX1I0​C′I1​1I2​C′I3​ABS1​S0​F

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

I₀ = 1I₁ = C′I₂ = 1I₃ = C′
N =
4.Medium
ABCD0001111000011110111111

In this Karnaugh map exactly one 1 has no neighbouring 1, so it stays a group of one cell (a full minterm of four literals) in the minimal SOP form. Neighbours across the map edges count. Click that cell.

F = Σm(0, 3, 4, 13, 14, 15)
  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
5.Hard
TQ0​Q0​TQ1​Q1​TQ2​Q2​TQ3​Q3​CLKDOWN

A 4-bit binary down counter starts at 5 (decimal, Q = 0101). Which count Q (in decimal) does it show after 39 clock pulses?

Q0 = 539n = 4
Q =
6.Hard
ABCD000111100001111010010312X4X51706012113015014X809111010

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 2, 7, 11, 13) + d(4, 5, 8), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(0, 2, 7, 11, 13) + d(4, 5, 8)
L =

Answer key

  1. 1. N2
  2. 2. tpd = 11 ns
  3. 3. N = 6
  4. 4. AB = 00, CD = 11
  5. 5. Q = 14
  6. 6. L = 13

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