Digital logic: gates, K-maps & flip-flops worksheet with answers

The function F = A′ + C′ + B′ is 0 for exactly one combination of the inputs. Click that row of the truth table.

1. 1ABC = 000
2. 2ABC = 001
3. 3ABC = 010
4. 4ABC = 011
5. 5ABC = 100
6. 6ABC = 101
7. 7ABC = 110
8. 8ABC = 111

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

1. 1N1
2. 2G1
3. 3G2

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

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

Find the minimal SOP form of F(A, B, C, D) = Σm(0, 4, 10, 12, 14) + d(6, 13), where d marks the don't-care conditions. How many literals L does it contain?

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 3 clock edges.