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 = 0N1G1G2G3F

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
ABCG1G2F

For the logic circuit shown, how many of the 8 combinations of the inputs A, B and C give the output F = 1? Find N.

A, B, C → F
N =
3.Medium
ABC000111100101324576

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

F = A′B + B′C′ + A′B′C
L =
4.Medium
MUX0I0​C′I1​C′I2​CI3​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 = C′, I₂ = C′, I₃ = C. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

I₀ = 0I₁ = C′I₂ = C′I₃ = C
N =
5.Hard
FFQ0​Q0​FFQ1​Q1​FFQ2​Q2​FFQ3​Q3​FFQ4​Q4​FFQ5​Q5​CLKMOD-50

A mod-50 counter is built from the minimum number of flip-flops. How many of the possible states U are never used?

N = 50
U =
6.Hard
DQ0​Q0​DQ1​Q1​DQ2​Q2​DQ3​Q3​CLKJOHNSON

A Johnson (twisted-ring) counter is made of 4 D flip-flops, with the inverted last output fed back to the first input, and starts at all zeros. How many different states N does it go through?

n = 4
N =

Answer key

  1. 1. G3
  2. 2. N = 2
  3. 3. L = 3
  4. 4. N = 3
  5. 5. U = 14
  6. 6. N = 8

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