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

The inputs of the logic circuit are A = 1, B = 1 and C = 1. Exactly one of its gates has the output 0. Click that gate.

1. 1N1
2. 2G1
3. 3G2
4. 4G3

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 NAND gates needed to build the NOT function shown?

In this Karnaugh map exactly one 1 has no neighbouring 1, so it stays a group of one cell (a full minterm of four literals) in the minimal SOP form. Neighbours across the map edges count. Click that cell.

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

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 = 1, I₃ = C′. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

A synchronous mod-5 counter counts 0, 1, …, 4 and then returns to 0. It starts at 2. Which count Q (in decimal) does it show after 10 clock pulses?

A 2 kHz clock drives a mod-60 counter. Find the frequency f_out of its most significant output, which completes one cycle per counting cycle.