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

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.

For the logic circuit shown, how many of the 8 combinations of the inputs A, B and C give 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 = C′, I₁ = 0, I₂ = C, I₃ = 1. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(1, 3, 5, 6, 8, 10, 12). How many literals L does it contain in total (a primed variable counts as one literal)?

Find the minimal SOP form of F(A, B, C, D) = Σm(4, 5, 8, 9, 14) + d(10, 11, 12), where d marks the don't-care conditions. How many literals L does it contain?

A synchronous decade (mod-10) counter counts 0, 1, …, 9 and then returns to 0. It starts at 7. Which count Q (in decimal) does it show after 19 clock pulses?