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

Click the cell of the 4-variable Karnaugh map that belongs to minterm m13 (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

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.

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 1, 4, 5, 9, 10, 13, 14). How many product terms N does it have?

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = 1, I₁ = 0, I₂ = 0, I₃ = 0. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

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.

Find the minimal SOP form of F(A, B, C, D) = Σm(2, 5, 6, 7, 8, 10, 13) + d(4, 11, 12, 15), where d marks the don't-care conditions. How many product terms N does it have?