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 XOR function shown?

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 XNOR function shown?

A 4-to-1 multiplexer has its select inputs S₁ = A and S₀ = B, and its data inputs tied to I₀ = 1, I₁ = C, I₂ = 1, I₃ = C′. 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(3, 11, 12, 13, 14, 15). 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(1, 2, 3, 4, 7, 8, 9) + d(5, 15), where d marks the don't-care conditions. How many literals L does it contain?

A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1001. At every clock edge the bits shift one place to the right (Q₃ → Q₂ → Q₁ → Q₀) and Q₃ receives Q₀. Give the state Q = Q₃Q₂Q₁Q₀ as a decimal number after 6 clock edges.