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

The inputs of the logic circuit are A = 1, B = 1 and C = 0. 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 XOR function shown?

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C) = Σm(0, 2, 3, 5, 6, 7). How many literals L does it contain in total (a primed variable counts as one literal)?

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 = 0, I₃ = C. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

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

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 9 clock edges.