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

Click the cell of the 4-variable Karnaugh map that belongs to minterm m14 (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 product-of-sums (POS) form of F(A, B, C, D) = Σm(3, 4, 5, 7, 10, 11, 12, 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) = Σm(2, 5, 7). How many literals L does it contain in total (a primed variable counts as one literal)?

A 4-bit binary up counter starts at 12 (decimal, Q = 1100). Which count Q (in decimal) does it show after 39 clock pulses?

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 1100. 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, 0, 1, 1, 1, 0, 1 at the 7 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.