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 = 1, B = 1 and C = 0. Exactly one of its gates has the output 0. Click that gate.

1. 1N1
2. 2G1
3. 3G2
4. 4G3

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C, D) = Σm(0, 2, 4, 5, 6, 9, 11, 13, 14, 15). How many sum terms (factors) N does it have?

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(6, 7, 9, 11, 13, 15). How many literals L does it contain in total (a primed variable counts as one literal)?

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1001. 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 10 clock edges.

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 1010. 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 0, 1, 1, 1, 0 at the 5 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.