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

The function F = (B′·C′)·A′ is 1 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

Click the cell of the 3-variable Karnaugh map that belongs to minterm m6 (variables A, B, C with A the most significant bit).

1. 1A = 0, BC = 00
2. 2A = 0, BC = 01
3. 3A = 0, BC = 11
4. 4A = 0, BC = 10
5. 5A = 1, BC = 00
6. 6A = 1, BC = 01
7. 7A = 1, BC = 11
8. 8A = 1, BC = 10

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

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = 0, I₁ = C′, I₂ = C′, 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 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?

A 4-bit Johnson counter Q₃Q₂Q₁Q₀ starts at 0000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives the inverse of Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 10 clock edges.