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
ABCG12 nsN1: 1 nsG25 nsG33 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: 1 nsG1: 2 nsG2: 5 nsG3: 3 ns
tpd = ns
3.Medium
ABCD000111100001111010010302140517160121130151140809011010

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 4, 6, 7, 13, 14). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C, D) = Σm(0, 4, 6, 7, 13, 14)
L =
4.Medium
ABCD000111100001111000010312141517061120130151140809111110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(2, 4, 5, 7, 10, 11, 12, 14). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(2, 4, 5, 7, 10, 11, 12, 14)
N =
5.Hard
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​FFQ3​Q3​FFQ4​Q4​CLKMOD-25

A mod-25 counter is built from the minimum number of flip-flops. How many of the possible states U are never used?

N = 25
U =
6.Hard
CLKD12345678

A positive-edge-triggered D 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 = 0D
  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
  8. 8clock edge 8

Answer key

  1. 1. N = 3
  2. 2. tpd = 9 ns
  3. 3. L = 13
  4. 4. N = 4
  5. 5. U = 7
  6. 6. clock edge 4

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