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

Click the cell of the 4-variable Karnaugh map that belongs to minterm m1 (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

NAND and NOR are universal gates: any logic function can be built from one of them alone. What is the minimum number N of 2-input NOR gates needed to build the AND function shown?

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

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 1, 2, 3, 5). How many product terms N does it have?

A positive-edge-triggered D flip-flop starts with Q = 0 and receives the inputs shown. Click the first clock edge at which Q goes from 1 back to 0.

1. 1clock edge 1
2. 2clock edge 2
3. 3clock edge 3
4. 4clock edge 4
5. 5clock edge 5
6. 6clock edge 6
7. 7clock edge 7
8. 8clock edge 8

A 3-bit binary up counter starts at 7 (decimal, Q = 111). Which count Q (in decimal) does it show after 22 clock pulses?