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

The function F = (A ⊕ B)·(A + C′)′ is 1 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 propagation delay of every gate is written under it. Find the worst-case propagation delay t_pd from the inputs to the output F.

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(1, 2, 3). How many product terms N does it have?

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

For F(A, B, C, D) = Σm(0, 2, 9, 10) + d(4, 5, 12), where d marks the don't-care conditions, find the number N of essential prime implicants.

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 6 clock edges.