Click the cell of the 4-variable Karnaugh map that belongs to minterm m9 (variables A, B, C, D with A the most significant bit).
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 XNOR function shown?
In this Karnaugh map exactly one 1 has no neighbouring 1, so it stays a group of one cell (a full minterm of four literals) in the minimal SOP form. Neighbours across the map edges count. Click that cell.
Use the Karnaugh map to find the minimal sum-of-products (SOP) form of F(A, B, C, D) = Σm(2, 3, 4, 5, 7, 14). How many product terms N does it have?
Find the minimal SOP form of F(A, B, C, D) = Σm(4, 10, 13, 14) + d(9, 11), where d marks the don't-care conditions. How many literals L does it contain?
A 4-bit ring counter Q₃Q₂Q₁Q₀ starts at 1100. 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 10 clock edges.
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