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

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. 1G1
2. 2G2
3. 3G3

Click the cell of the 4-variable Karnaugh map that belongs to minterm m12 (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 = AB′C′ + A′BC′ + AB 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) = Σm(0, 1, 3, 4, 6). How many literals L does it contain in total (a primed variable counts as one literal)?

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 7, 8, 9, 10) + d(3, 14), where d marks the don't-care conditions. How many literals L does it contain?

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1010. 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.