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
ABCN1: 1 nsN2: 3 nsG12 nsN3: 1 nsN4: 2 nsG25 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: 1 nsN2: 3 nsN3: 1 nsN4: 2 nsG1: 2 nsG2: 5 nsG3: 8 ns
tpd = ns
2.Easy
A = 0B = 0C = 1N1G1N2G2F

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

A = 0B = 0C = 1
  1. 1N1
  2. 2N2
  3. 3G1
  4. 4G2
3.Medium
ABC00011110011001031204050716

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 2, 6). How many literals L does it contain in total (a primed variable counts as one literal)?

F(A, B, C) = Σm(0, 2, 6)
L =
4.Medium
ABCD000111100001111000010302141507060120130150141819011110

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(4, 5, 8, 9, 10). How many sum terms (factors) N does it have?

F(A, B, C, D) = Σm(4, 5, 8, 9, 10)
N =
5.Hard
ABCD000111100001111010X1X302041507160120130150141819011010

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 5, 6, 8, 9) + d(1, 3), where d marks the don't-care conditions. How many literals L does it contain?

F(A, B, C, D) = Σm(0, 5, 6, 8, 9) + d(1, 3)
L =
6.Hard
TQ0​Q0​TQ1​Q1​TQ2​Q2​TQ3​Q3​CLKMOD-10

A synchronous decade (mod-10) counter counts 0, 1, …, 9 and then returns to 0. It starts at 0. Which count Q (in decimal) does it show after 14 clock pulses?

Q0 = 014N = 10
Q =

Answer key

  1. 1. tpd = 15 ns
  2. 2. G1
  3. 3. L = 4
  4. 4. N = 4
  5. 5. L = 9
  6. 6. Q = 4

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