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

The function F = B′ + C′ + (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

The propagation delay of every gate is written under it. Find the worst-case propagation delay t_pd from the inputs to the output F.

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

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

A 4-bit shift register Q₃Q₂Q₁Q₀ holds 0000. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀, Q₀ is lost) and the serial input enters Q₃. The serial input is 1, 1, 0, 1, 1, 1, 1 at the 7 edges. Give the final state Q = Q₃Q₂Q₁Q₀ as a decimal number.

A 12 kHz clock drives a mod-100 counter. Find the frequency f_out of its most significant output, which completes one cycle per counting cycle.