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

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

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

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.

1. 1G1
2. 2G2
3. 3G3

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

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(3, 4, 6, 7, 8, 11, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 0111. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀, Q₀ is lost) and the serial input enters Q₃. The serial input is 1, 1, 1, 0, 1 at the 5 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.

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 5 clock edges.