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

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.

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.

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

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(3, 5, 6). How many product terms N does it have?

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

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 6, 7, 8, 10) + d(4, 13, 14), where d marks the don't-care conditions. How many product terms N does it have?

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1100. 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 9 clock edges.