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

The function F = ((A·B)·(A·C)′)′ is 0 for exactly one combination of the inputs. Click that row of the truth table.

1. 1ABC = 000
2. 2ABC = 001
3. 3ABC = 010
4. 4ABC = 011
5. 5ABC = 100
6. 6ABC = 101
7. 7ABC = 110
8. 8ABC = 111

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 AND function shown?

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(0, 2, 5, 8, 11, 12). How many product terms N does it have?

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

A positive-edge-triggered JK 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

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 3 clock edges.