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

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.

Click the cell of the 4-variable Karnaugh map that belongs to minterm m7 (variables A, B, C, D with A the most significant bit).

1. 1AB = 00, CD = 00
2. 2AB = 00, CD = 01
3. 3AB = 00, CD = 11
4. 4AB = 00, CD = 10
5. 5AB = 01, CD = 00
6. 6AB = 01, CD = 01
7. 7AB = 01, CD = 11
8. 8AB = 01, CD = 10
9. 9AB = 11, CD = 00
10. 10AB = 11, CD = 01
11. 11AB = 11, CD = 11
12. 12AB = 11, CD = 10
13. 13AB = 10, CD = 00
14. 14AB = 10, CD = 01
15. 15AB = 10, CD = 11
16. 16AB = 10, CD = 10

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

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C) = Σm(1, 2, 5, 6, 7). How many sum terms (factors) N does it have?

For F(A, B, C, D) = Σm(1, 2, 3, 7, 10, 13) + d(4, 8, 11, 15), where d marks the don't-care conditions, find the number N of essential prime implicants.

A 4-bit Johnson counter Q₃Q₂Q₁Q₀ starts at 0000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives the inverse of Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 4 clock edges.