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

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 NOR gates needed to build the NAND function shown?

The inputs of the logic circuit are A = 0, B = 1 and C = 1. Exactly one of its gates has the output 0. Click that gate.

1. 1N1
2. 2G1
3. 3G2

Use the Karnaugh map to find the minimal product-of-sums (POS) form of F(A, B, C) = Σm(0, 2, 4, 5, 7). How many sum terms (factors) N does it have?

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

A 5-bit ripple (asynchronous) counter is built from flip-flops with a propagation delay of 25 ns each. All outputs must have settled before the next clock edge. Find the maximum clock frequency f_max.

A 3-bit ripple (asynchronous) counter is built from flip-flops with a propagation delay of 25 ns each. All outputs must have settled before the next clock edge. Find the maximum clock frequency f_max.