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 NAND gates needed to build the NOR function shown?

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 = C, I₂ = 1, I₃ = 1. For how many of the 8 combinations of A, B and C is the output F = 1? Find N.

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

Find the minimal SOP form of F(A, B, C, D) = Σm(1, 3, 4, 9) + d(2, 6, 7, 14), where d marks the don't-care conditions. How many product terms N does it have?

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 11 clock edges.