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

Click the cell of the 4-variable Karnaugh map that belongs to minterm m6 (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 NAND gates needed to build the NOR function shown?

Simplify F = A′BC′ + AB′C + ABC′ to its minimal sum-of-products form. How many literals L does the simplified expression contain?

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

An 8-bit ripple (asynchronous) counter is built from flip-flops with a propagation delay of 5 ns each. All outputs must have settled before the next clock edge. Find the maximum clock frequency f_max.

A positive-edge-triggered T flip-flop starts with Q = 0 and receives the inputs shown at 7 rising clock edges. How many times N does Q change state?